Oriented Polymer Materials

Oriented Polymer Materials

Edited by Stoyko Fakirov

WILEYVCH

WILEY-VCH Verlag GmbH & Co. KGaA

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Oriented Polymer Materials Edited by

Stoyko Fakirov

Oriented Polymer Materials

Edited by Stoyko Fakirov

WILEYVCH

WILEY-VCH Verlag GmbH & Co. KGaA

This Page Intentionally Left Blank

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Printed in the Federal Republic of Germany Printed on acid-free paper ISBN: 978-3-527-29693-4

Contributors

Argon, A. S. Massachusetts Institute of Technology, Cambridge, MA 02139, USA Bahar, I. Bogazici University, Polymer Research Center, School of Engineering, and TUBITAK Advanced Polymeric Materials Research Center, Bebek 80815, Istanbul, Turkey Bartczak, Z. Massachusetts Institute of Technology, Cambridge, MA 02139, USA Present address: Center of Molecular and Macromolecular Studies, Polish Academy of Sciences, 99-368 Lodz, Poland Bonart, R. Universitat Regensburg, Institut fur Angewandte Physik, Postfach 10 10 42, 8401 Regensburg, Germany Cohen, R. E. Massachusetts Institute of Technology, Cambridge, MA 02139, USA Erman, B. Bogazici University, Polymer Research Center, School of Engineering and TUBITAK Advanced Polymeric Materials Research Center, Bebek 80815, Istanbul, Turkey

V

Fakirov, S. Bogazici University, Polymer Research Center, School of Engineering, and TUBITAK Advanced Polymeric Materials Research Center, Bebek 80815, Istanbul, Turkey Permanent address: Sofia University, Laboratory on Structure and Properties of Polymers, 1126 Sofia, Bulgaria

F'renkel, S. Institute of Macromolecular Compounds, Russian Academy of Sciences, 199004 St. Petersburg, Russia F'riedrich, K . Institut fur Verbundwerkstoffe GmbH, University of Kaiserslautern, D-67663 Kaiserslautern, Germany Galeski, A. Massachusetts Institute of Technology, Cambridge, MA 02139, USA Present address: Center of Molecular and Macromolecular Studies, Polish Academy of Sciences, 99-368 Lodz, Poland

Godovsky, Y. K. Karpov Institute of Physical Chemistry, 103064 Moscow K-64. Russia Gupta, V. B. Indian Institute of Technology, Textile Technology Department, New Delhi 110016, India Kunugi, T. Yamanashi University, Faculty of Engineering, Takeda-4, Kofu, 400 Japan

vi

Lee, B. J . Massachusetts Institute of Technology, Cambridge, MA 02139, USA Present address: University of California, Department of Applied Mechanics and Engineering Sciences, San Diego, LaJolla, CA 92093, USA

Marikhin, V. A. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia Matsuo, M. Department of Clothing Science, Nara Women’s University, Nara 630, Japan Miiller, M. Faculteit der Chemische Technologie, Universiteit Twente, P.0.Box 2 17, 7500 AE Enschede, The Netherlands Present address: Universitat Ulm, Abteilung Organische Chemie I11 89069 Ulm, Germany

Moneva, I. T. Institute of Polymers, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria Myasnikova, L. P. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia Parks, D. M. Massachusetts Insti t Ute of Technology, Cambridge, MA 02139, USA Petermann, J . Universitat Dortmund, Fachbereich Chemietechnik, 44227 Dortmund 50, Germany

vii

Prevorsek, D. C. Allied-Signal Inc., Research & Technology P.O.Box 1021, Morristown, NJ 07962, USA Schledjewski, R. Institut fur Verbundwerkstoffe GmbH, University of Kaiserslautern, D-67663 Kaiserslautern, Germany Schultz, J . M. University of Delaware, Materials Science Program, Newark, DE 19716, USA Sheiko, S. S. Faculteit der Chemische Technologie, Universiteit Twente, P.O.Box 217, 7500 AE Enschede, The Netherlands Present address: Universitat Ulm, Abteilung Organische Chemie 111, 89069 Ulm, Germany

Siesler, H. W. Universitat GH Essen, Abteilung Physikalishe Chemie, 45117 Essen, Germany

...

Vlll

CONTENTS

Chapter 1

Problems of the physics of the oriented state of polymers S . Frenkel

1 . Introductory considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.1. Interplay of fundamental and applied problems . Molecular cybernetics ..................................... 1.2. Principal routes to the formation of uniaxially oriented structures in olymers ..................................... 2 . Configurational in ormation and orientation phenomena in synthetic polymers ...........................................

P

3. 4. 5. 6.

2.1. Direct generation of orientational order from solutions and melts . Orientational hardening, orientational crystallization. and orientational catastrophes . . . . . . . . . . . . . . 2 . 2 . Assemblage; liquid crystalline polymers .................... 2 . 3 . Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Failure under load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Some specific properties of superoriented polymers . . . . . . . . . . . . . . Technological implications ...................................... General conclusions and summary .............................. 6.1. What 6.2. What 6 . 3 . What References

Chapter 2

is clear? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . is incomprehensible? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . needs better understanding? .........................

.....................................................

1

1

8 10

10 22 25 26 30 31 32 32 33 34 36

Structural basis of high-strength high-modulus polymers V . A . Marikhin. L . P. Myasnikova

ix

1 . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . Structural transformation in semicrystalline polymers on stretching ...................................................

38

2.1. Deformation mechanisms at small strain . . . . . . . . . . . . . . . . . . . 2.2. Folded-extended chain solid phase transition in the neck region ............................................ 2.3. Micro- and macrofibrillar structure in oriented polymers and its plastic deformation ....................... 2.4. Drawing arrest and fracture of oriented polymers .......... 2.5. Alternative mechanisms of drawing ........................ 3 . Deformation-induced strengthening of semicrystalline polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

3.1. Structural kinetic approach to the enhancement of polymer characteristics by deformation . . . . . . . . . . . . . . . . . . 3.2. Physical criteria for the optimization of the drawing process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Optimal molecular weight and molecular weight distribution ............................................... 4 . Mechanical properties of highly oriented polymers . . . . . . . . . . . . . . 5 . Thermal properties of superstrong high-modulus polymers ....................................................... 6 . Structural peculiarities of highly oriented polymers . . . . . . . . . . . . . References .....................................................

Chapter 3

39

42 47 57 59 62

62 67 72 76 80 85 92

X-ray diffraction by quasiperiodic polymer structures R . Bonart

1 . Introduction ................................................... 2 . Qualitative phenomenological aspects ...........................

2.1. Fibre diagrams ............................................ 2.2. Crystal density, chain cross section and chain conformation 2.3. Anisotropy perpendicular to the chain direction, planes of plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Position sphere ............................................ 2.5. Lattice distortions of the first and second kind . Distortion parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X

99 102 102 107 108 109 111

2.6. Special lattice types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 2.7. Small-angle scattering, fibrils, layer lattices . . . . . . . . . . . . . . . . 117 120 3 . Basics of experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. X-ray spectrum and absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . Theoretical relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

120 122

4.1. Structure factor ........................................... 4.2. The Ewald sphere ......................................... 4.3. Pair distribution .......................................... 4.4. A special application example ............................. 5 . Simple lattice models ...........................................

122 125 126 128 129

5.1. Ideal periodic lattices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Distortions of the first kind ................................ 5.3. Distortions of the second kind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. Inhomogeneous coordination statistics . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

129 130 132 133 136

Chapter 4

Characterization of polymer deformation by vibrational spectroscopy H . W . Siesler

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 Experimental and instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Orientational measurements by infrared dichroism . . . . . . . . . . . . . . 143 Segmental mobility in liquid crystalline side-chain polymers ....................................................... 145 5 . Rheo-optical FT-IR studies of the poly(ethy1ene terephthalate) film forming process ............................. 148

1. 2. 3. 4.

5.1. Drawing of P E T in the machine direction . . . . . . . . . . . . . . . . . . 153 5.2. Drawing of P E T in the transverse direction . . . . . . . . . . . . . . . . 154 5.3. Rheo-optical FT-NIR spectroscopic light-fiber investigations of the P E T film process ..................... 157 6 . Rheo-optical FT-Raman spectroscopy of the stress-induced conformational changes in poly(viny1idene fluoride) . . . . . . . . . . . . . 160 7 . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

xi

Chapter 5

Morphology in oriented semicrystalline polymers J . Petermann

1. General considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 168 2 . Morphologies in oriented polymers .............................. 3 . Formation of morphologies in oriented polymers ................ 171

3.1. Morphologies obtained by crystallization of oriented melts .......................................... 171 3.2. Orientation at interfaces ................................... 172 174 3.3. Orientation in thermal gradients ........................... 3.4. Orientation by plastic deformation ......................... 174 3.5. Polymerization induced orientations ....................... 175 4 . Morphological changes during thermal treatments . . . . . . . . . . . . . . .177 5 . Outlook to morphology-property relationships . . . . . . . . . . . . . . . . . . 181 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

Chapter 6

Deformation calorimetry of oriented polymers Y . K . Godovsky

1 . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . Deformation calorimetry ........................................

184 185

185 2.1. Gas calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Heat-conducted deformation calorimeters .................. 187 3 . Thermodynamics of the stretching of oriented polymers ......... 189 4 . Thermophysical behaviour of oriented polymers during deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 4.1. Oriented amorphous polymers ............................. 4.2. Oriented crystalline polymers .............................. 4.3. Superoriented crystalline polymers ......................... 5. Anisotropy of thermophysical behaviour of oriented polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 . Mechanisms of deformation of oriented polymers as revealed by deformation calorimetry and their relation t o morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii

193 194 199 200

202

7 . Thermophysical behaviour of oriented polymers under fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References .....................................................

Chapter 7

204 208

on the orienultrahigh molecS . S. Sheiko. M . Moller

1 . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 2 . On the structure of dried and solvent containing gels . . . . . . . . . . . . 211 3 . Gel necking .................................................... 215 4 . Fibrillar structure .............................................. 223 5 . Gel blending ................................................... 232 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

Chapter 8

Polarized light scattering from polymer textures I . T . Moneva

1 . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 2 . Polarized light scattering: theory and instrumentation . . . . . . . . . . .243

2.1. Fluctuations in density and fluctuations in optical anisotropy and orientation ................................. 2.2. Scattering considerations .................................. 2.3. Polarized light scattering technique ........................ 3 . Applications of the scattering analysis ..........................

243 244 250 251

3.1. Formation of shear bands during zone drawing . . . . . . . . . . . . . 252 3.2. Formation of macrofibrils in shear crystallization . . . . . . . . . . . 253 3.3. Determination of Poisson’s ratio by double exposure speckle photography ....................................... 255 4 . Polarized light scattering from textures of liquid crystalline polymers ....................................................... 257 4.1. Polarized light scattering from schlieren textures . . . . . . . . . . . 257 xiii

4.2. Polarized light scattering from banded and other nematic textures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 . Concluding remarks ............................................ References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 9

259 260 261

Deformation induced texture development in polyethylene: computer simulation and experiments A . S . Argon. Z . Bartczak. R . E . Cohen. A . Galeski. B . J . Lee. D . M . Parks

1. Introduction ................................................... 2 . Model description ..............................................

265 269

2.1. Basic assumptions ......................................... 269 2.2. Constitutive relations ...................................... 270 275 2.3. Composite inclusion ....................................... 2.4. Interaction law and solution procedure ..................... 276 2.5. Parameter selection ....................................... 278 3 . Predicted results and comparison with experiments . . . . . . . . . . . . . 279

. . . . . . . . . . . . . . .279 3.1. Modes of straining ....................... 3.2. Uniaxial compression ..................... . . . . . . . . . . . . . . . . . 280 3.3. Plane strain compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 4 . Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .298 . . . . . . . . . . . . . . . 299 5 . Conclusions ................................... References .................................... ............... 300 Chapter 10

Intrinsic anisotropy of highly oriented polymeric systems in relation to molecular orientation and crystallinity M . Matsuo

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 2 . Crystal lattice moduli of crystalline polymers . . . . . . . . . . . . . . . . . . . 303 3 . Theoretical approach t o the estimation of the crystal lattice modulus as measured by X-ray diffraction ............................................... 307 xi v

4 . Effect of crystallinity and molecular orientation on Young’s modulus in UHMWPE and LMWPE blend films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Temperature dependence of the crystal lattice modulus and Young’s modulus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 . Viscoelastic properties of ultradrawn polyethylene . . . . . . . . . . . . . . 7 . Morphological and mechanical properties of UHMWPE-UHMWPP blend gel films .......................... 8. Conclusion ..................................................... References .....................................................

Chapter 11

310 311 318 324 327 329

Nature of the crystalline and amorphous phases in oriented polymers and their influence on physical properties V . B . Gupta

1 . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . Nature and role of molecular architecture . . . . . . . . . . . . . . . . . . . . . . .

331 334

2.1. Axial modulus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Axial strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Thermal expansion . . . . . . . . . . . . . . .......................... 2.4. Melting point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . Nature and role of defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

334 338 339 339 341

3.1. Nature of defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Effect on thermal properties ............................... 3.3. Effect on optical properties ................................ 3.4. Effect on crystallization ................................... 4 . Coupling effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

341 342 342 344 344

5. 6. 7. 8.

4.1. Nature of coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344 4.2. Effect on mechanical properties of fib . . . . . . . . . . . . . 346 4.3. Effect on deformation mechanisms . . . . . . . . . . . . . . . . . . 4.4. Effect on thermal behaviour . . . . . . . . . . . . . . . . . . Content and size of the phase . . . . . . . . . . . . . . . . . . . . . . Crystal and amorphous orientation Structure formation Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 xv

Chapter 12

Structure development in highly oriented

PET J . M . Schultz 1 . Background ....................................................

361

1.1. Post mortem studies ....................................... 1.2. In situ studies: spinline observations ....................... 1.3. Models of structure development ........................... 2 . Interrupted transformation experiments ......................... 3 . Transmission electron microscopy ............................... 4 . Property isotherms .............................................

363 366 367 369 371 374

4.1. Structure ............................. . . . . . . . . . . . . . . . 374 . . . . . . . . . . . . . . . . 378 4.2. Kinetics .......................... 5 . Low temperature transformation: radial ....................... 379 distribution function studies . . . . . . 6 . Thermal dendrite model ............................ . . 383 . . . . . . . . . . . . . . . . . . 390 7 . Concluding remarks . . . . . . . . . . . . . . . ............................ . 391 References . . . . . .

Chapter 13

Preparation of highly oriented fibres or films with excellent mechanical properties by the zone-drawing/zone-annealing met hod T . Kunugi

1 . Basics of the zone-drawinglzone-annealing

method . . . . . . . . . . . . . 394

1.1. Original zone-drawingfzone-annealing method ............. 394 1.2. Multistep zone-drawinglzone-annealing method . . . . . . . . . . . 395 1.3. High-temperature zone-drawing method . . . . . . . . . . . . . . . . . . .396 1.4. Vertical two-step zone-drawing method .................... 396 2 . Application to polymer fibres or films . . . . . . . . . . . . . . . . . . . . . . . . . . . 398

2.1. 2.2. 2.3. 2.4. xvi

Polyethylene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polypropylene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polyvinyl alcohol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Poly(ethy1ene terephthalate) ...............................

398 401 404 406

2 . 5 . Nylon 6 and 66 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6. Pol y (et her-et her- ketone) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7. Polyimide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. A recent development of the zone-drawing/zone method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Conclusion ....................... References ....................

Chapter 14

410 4 13 417 419

Alternative approaches t o highly oriented polyesters and polyamides with improved mechanical properties S. Fakirov

1. General considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422 2. Improvement of the mechanical properties of polycondensates by ultraquenching of their melts . . . . . . . . . . . . . . .425

2.1. Creation of optimal initial structure for preparing highly oriented polycondensates . . . . . . . . . . . . . . . . .425 2.2. Ultraquenching with previous melt annealing . . . . . . . . . . . . . . 428 429 2.3. Ultraquenching of polymer blends ......................... 3. Improvement of the mechanical properties of oriented polycondensates by drawing and thermal treatment . . . . . . . . . . . . .430 3.1. Contribution of solid state reactions to the improvement of the mechanical properties of polyesthers and polyamides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Improvement of mechanical properties of polyesters and polyamides by zone annealing under stress ............................................... 4. Attempts to overcome the mechanical anisotropy of highly drawn polymer films . . . . . . . . . . . . . . . . . . .

430 435 437

4.1. Cross-plied laminates bonded through physical healing of highly drawn polyolefin films . . . . . . . . . . . . . . . . . . . . 437 4.2. Laminates bonded through chemical healing of highly drawn polycondensate films .................... 438 4.3. Laminates bonded through chemical healing with coupling agent of highly drawn polycondensate films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439 5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440 xvii

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 15

44 1

Structural aspects of the damage tolerance of Spectra fibres and composites D . C . Prevorsek

1. Introduction ...................................................

444

1.1. Theoretical limits in modulus and strength ................ 445 1.2. The ultrastrong polyethylene fibres ........................ 446 448 2 . Creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Structural parameters affecting creep ...................... 2.2. Deformation in creep versus plastic deformation in drawing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . Strain rate effects in ultrastrong polyethylene fibres and composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

448

3.1. Ballistic impact on fibres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Ballistic impact on Spectra composites ..................... 4 . Damage tolerance in penetration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

452 453 455

4.1. Mechanisms of penetration and analysis of penetration resistance ................................... 4.2. Repeated impact and additional energy absorption mechanism of P E fibre ......................... 5 . Morphology of ultrastrong P E fibres ............................ References .....................................................

Chapter 16

451 451

456 459 462 465

Segmental orientation in deformed rubbery networks I . Bahar. B . Erman

1 . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467 2 . Relationships between macroscopic and molecular deformation and network structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469 3 . Segmental orientation in network chains ........................ 470 4 . Higher order approximation for segmental orientation . . . . . . . . . . . 473 xviii

5. Experimental determination of segmental orientation in rubbery networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474 6. Theoretical interpretation of infrared dichroism measurements of segmental orientation in rubbery networks . . . . . 476 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480

Chapter 17

Orientation effects on the thermal mechanical and tribological performance of neat, reinforced and blended liquid crystalline polymers R. Schledjewski, K. Friedrich

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Liquid crystalline polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

483 484

2.1. Liquid crystals and their history ........................... 484 485 2.2. Structure of LCPs ......................................... 3. Thermotropic liquid crystalline polymers and their properties ... 486 3.1. Neat, filled or reinforced LCP ...................... 487 .............................. 500 3.2. LCP blends . . . . . . . . . . . . . . . . . . . . . . . . 503 References . . . . . . . . . . . . . . . . . 505 ................... 507 Author Index ........................ Subject Index .................. . . . . . . . . . . . . . . 510

xix

Preface

The orientation phenomenon is a basic inherent peculiarity of polymers, arising from the chain character of macromolecules and their ability t o adopt different conformations - from a coil t o an extended chain. The realization of these two extreme conformations or some intermediate ones determines t o the greatest extent the mechanical properties of polymers as materials. In addition to the synthesis of new polymers, orientation is a basic approach to the obtaining of polymeric materials with superior properties. Incidentally, the outstanding mechanical properties of liquid crystalline polymers do not stem directly from their chemical composition, but are related to their unique ability of perfect orientation due t o the peculiarities of their chemical composition. The driving forces for the preparation of this book were the clear understanding of the importance of orientation itself and of the oriented polymeric materials, I met everywhere, as well as the fact that the last book related t o this important topic appeared more then ten years ago. This situation was recognized somewhat earlier by other polymer scientists, too, and I a m pleased t o note here that this project was started, although in another form, by Dr. I. Moneva and some colleagues of ours from St. Petersburg, but the turbulent changes in the former Soviet Union and in the contries of Central and Eastern Europe affected it badly. Owing t o the generous encouragement and support of Dr. R. E. Bareiss from Die Makromolekulare Chemie, the project was modified and could be materialized. Although the chapters are not formally organized in larger units, an attempt is made to start the book with an overview of the orientation phenomenon, followed by chapters dealing with basic techniques for the study and characterization of orientation and oriented polymers. Another goal was to include as much as possible different representatives of oriented polymer materials, as well as approaches to the improvement of their mechanical properties. These two fields are by far not completely covered and many more contributions are required for doing so. Like many books of this type, the present one suffers from the diversity of styles and ways of presentation of the chapters, but we hope that this disadvantage is compensated by the high professionalism of the co-authors and by the updated results they have offered. Here it should be mentioned that the chapters differ also in their volume, the contributions from the

Russian co-authors being the longest. The reason is that for many decades there were no equal opportunities for worldwide exchange of information, therefore research in the former Soviet Union did not have access to Western scientists. The review character of the two introductory chapters is an attempt to overcome partially this situation. As editor, I wish t o express my sincere gratitude to the individual contributors, because this type of publication requires perseverance and a great deal of patience. I a m greatly indebted to my co-worker Mrs. S. Petrovich - without her everyday help this project could not have been undertaken. A special note of thanks to Dr. Z. Denchev for preparing the Author and Subject Indices as well as appreciation t o the Bosphorus University in Istanbul for the hospitality offered to me during my sabbatical year when the book was finalized. Sofia 1991 - Istanbul 1994

S. Fakirov Editor

xxi

The book is dedicated to Professor Anton Peterlin in recognition of his essential contribution to the understanding of orientation phenomena and oriented polymers. Professor Peterlin was one of the most enthusiastic coauthors at the beginning of this project but, to our deep sorrow, he passed away before completing the chapter he had started on the influence of amorphous layers.

Oriented Polymer Material> Stoyko Fakirov Copyright 0 2002 Wiley-VCH Verlag GmbH & Co. KGaP

Chapter 1

Problems of the physics of the oriented state of polymers

S. F’renkel

1. Introductory considerations

I preferred this subtitle t o “Introductory notes” for the following reasons. Quite a lot is already written on orientation phenomena and physical properties of oriented polymers, and it would be difficult and even senseless t o present something substantionally new on this subject using common terms and formalism. An additional difficulty arises from the fact that a similar contribution [l] is supposed t o appear. Therefore, to avoid autoplagiary, I have to discuss most of the problems considered in the preceding paper in a quite different manner, paying special attention to molecular cybernetics and to systemic analysis connected with a special formulation of Bohr’s complementarity principle, resulting from the recent difficulty (if not impossibility) to treat in comprehensible and/or graphic terms the multidimensional state trajectories, attractors, fractals and transitions of fractional order appearing in modern physics and particularly unavoidable when dealing with polymers. 1.1. Interplay of fundamental and applied problems. Molecular cybernetics Starting from 1973 [2], in a series of papers dealing with general or special problems of polymer science. I frequently used the term “para.doxes” in an explicit or implicit form. Most of those paradoxes are not of a real

2

S. Frenkel

physical nature, but are due to the fact that, in contrast to the normal evolution of science and practical applications in the case of polymers (including plastics, synthetic rubber, synthetic fibres, etc.), most industrial processings rapidly developed when practically nothing was known about their molecular structure, not to mention ecological implications. Chemistry and physics were needed jr,t to explain rather than to control technological results; the situation being changed only before World War 11. In certain technological circles such mistreatments (though in a new form) still exist, despite that some new trends in polymer science offer special technologies (for instance connected with plasma treatment or reactions to produce non-conventional coatings, thin films for non-linear optics, etc.) preceding full knowledge of the resulting chemical and physical structure. In these cases, the situation is quite different, and these rapidly developing technologies do not contradict or ignore fundamentals. Coming back to our main topic, we must introduce the notion of p r e destinatzon of special polymers for special uses; it is connected with such a fundamental property of macromolecules as linear memory [3] and, for better understanding, we should consider molecular biology as a main source of information for molecular cybernetics [4]. Since the latter book is, unfortunately, very difficult to obtain, some details connected with the applications of the theory of information to polymer science and technology should be given here. In the case of oriented polymers, such an approach is especially advantageous since it deals with linear coding, and uncoiling of chains on orientation has a lot in common with habitual uncoding procedures. The purely physical notion of linear memory can be enriched by treating it as configurational anformataon [2,4,5], and the latter can be best understood by the example of globular proteins. All proteins are formed by polypeptide chains consisting of 20 different aminoacid residues. In each individual protein the number and sequence of these residues R1, Ra, RS. . . R20 are coded by simple combinations of four purine and pyrimidine bases in DNA responsible for the direct storage of genetic information, and RNA, being a kind of messenger, transfers this information to the cell loci where the synthesis of protein chains proceeds. These oversimplifications of the well known subject allow us to come faster to our less common considerations. Again omitting details, the so-called primary structure of proteins, being just configurational information, or the strict sequence of Ri, predestinates local ordered @-helicalor folded p-conformations (secondary structure) and the overall globular conformation (tertiary structure) resulting as interchain repacking and bonding necessary to attain, under given conditions, the lowest possible level of free energy. These “given conditions” in aqueous solutions are pH, ionic strength, temperature, water thermodynamic activity (that can be affected by the addition of other liquids), etc. The resulting conformation is unique for the given individual protein and also allows the formation of the centres of activity (enzymatic, redox,

Problems of the physics of the oriented s t a t e of polymers

3

charge transfer, e t c . ) , rnaking the molecules of globular proteins “molecular machines” responsible for all events of energy and information exchange or production, t h a t we call “Life” [4,6,7]. These centres are usually formed - also in a predestinated way by 3 or 4 residues R; separated along t h e initial chain by sequences corresponding (as pointed by de Gennes in his Nobel lecture) to a “magic number” 13 (this number will reappear in connection with quite different considerations). Such a binding in one specifically active site of several distant (along t h e chain) residues Ri is not a statistical event, but a necessity contained in t h e configurational information. Moreover, there is no need of external forces to achieve this local configuration and the overall globular conformation; the configurational information being realized by means of “autoscanning” leading t o the mentioned repacking of a n initially extended chain into the tertiary structure . T h e type of configurational information considered and connected with selfscanning can be called the discrete configurational information since it encompasses not only the overall behaviour on molecular and higher structural levels, but in particular the details of dynamically active unique conformations. However and with synthetic polymers it becomes a necessity - one statistical type of configurational inforshould also consider a second mation, prescribing (or allowing to predict, which is particularly important in technology) the overall behaviour of a protein molecule and its overall conformation in aqueous or non-aqueous media. This type of configurational information can be given in different terms but the most obvious expression would be the fraction FH of the hydrophobic residues in the primary chain or the ratio of the number of non-polar to polar residues (m). T h e first more or less intuitive model of the molecular structure of globular proteins and their interaction with surrounding media proposed by Talmud and Bresler in pre-cybernetic times (1944; see [2],[27]) was based on the assumption t h a t - just as in micellar colloid systems the polypeptide chain forms a close-packed coil containing a lipidic “drop” in the inside, built-up by non-polar side groups enveloped by polar groups sustaining the whole molecule in aqueous solution. This model supposes inverted structures in non-aqueous media. T h e very meager information on protein structure was, in principle, sufficient enough to avoid the first orientational catastrophe in the fibre and textile industry t h a t occurred during the It,alo-Abyssinian war in the mid-thirties. It is irnportant even loday for the better understanding of orientation phenomena in polymers in general, as well as for explaining how the neglect of configurational information turns apparently sanely designed technologies into “antitechnologies” , which I shall describe in some detail. In the beginning of the thirties it was known that all proteins are almost identical in their chemical structure, the industry of synthetic fibres ~

~

~

~

4

S. Frenkel

already existed, and the composition of the natural protein fibres - silk and wool - was also known. Therefore it seemed quite logical to use some convenient ( “technologically” and “economically”) proteins for developing a spinning and textile process to obtain an artificial wool fabric. The process was patented by a certain Commodore Ferretti, and a battalion of the Italian army was equipped with a uniform made from this artificial wool. Now it is time to name the chosen protein: it was casein, the main protein constituent of cheese or curd. At present it is well known that the FH and m values for casein are unfavourable for attaining extended conformations in aqueous media or simply at high humidities. Therefore, one can easily understand what happened when the battalion got under a tropical shower. The uniform simply ravelled out. A deeper insight in this apparently anecdotic episode is however not only instructive; one should correlate information with free energy and other common physical parameters. This can be attained by considering the so-called Fisher diagram which is a plot of molecular size and/or shape vs. FH or m (Figure 1). For modern molecular biologists and biophysicists the Fisher diagram appears oversimplified and obsolete, but for polymer physics and especially for molecular cybernetics it still has an important position, giving a key for decoding the statistical configurational information and for its direct use both in fundamental research and in technology. As shown in Figure 1, the Fisher diagram is an isoenergetic curve corresponding to equilibrium, i.e. to minimal (for given conditions) Gibbs’ free energy. The upper left part of the diagram corresponding to extended con-

m or F,

Figure 1. The Fisher diagram. T h e most probable conformations for some identical “reduced molecular weight” are shown near the extremes and in the middle part of the curve

Problems of the physics of the oriented state of polymers

5

formations is occupied by fibrillar proteins (fibroin, keratin, collagen) and the right lower part, to very compact globular proteins. Casein occupies just an intermediate position. Well, fibrillar proteins are just “predestinated” t o form fibres, and t o discuss the predestination of properly said globular proteins, one should consider in more detail the discrete configurational information. Casein has a smooth conformation, and its chain can be easily attacked by proteolytic enzymes. However, it is still sufficiently compact (due to relatively high FH or m values) to resist complete uncoiling, and retains extended chain conformation in contact with water. Since after the failure with casein, new, even more ill-attempted ventures to spin fibres from several plant globulins occupying the lower right part of the Fisher diagram were made, it seems instructive to present the diagram as an isoconformational plot (the conformation being very extended) of free energy vs. FH or m in aqueous media (Figure 2). It is readily seen that not only the fibres will be unstable, the high free energy stored leading to a development of internal stresses tearing the fibres “from inside”, but spinning by itself will be very energy-consuming since globular molecules will strongly resist uncoiling for the same reasons. Figures 1 and 2 explain the origin of many “antitechnologies” connected with orientation of polymers. However, it is instructive to consider briefly the opposite case, when the protein is predestined to form fibres or webs. Figure 3 shows schematically (for more details see [a] or [4]) the spinning of silk or webs by silkworms or spiders. Though oversimplified, this scheme

1 m or FH

Figure 2. The inverted Fisher diagram for identical extended conformations in aqueous media corresponding to the left upper part of Figure 1. In general, such diagrams explain the second type orientational catastrophes in fibres

S. Frenkel

6

a

b

Figure 3. Schematic representation of stream-thread transition during “spinning” of natural silk or cobwebs. (a) the initial solution (in glands). Only a part of the molecules is shown, containing two crystallizable peptides in a-helical form; (b) under the influence of elongational flow (gradient +) the molecules uncoil and align in parallel; (c) due to further draw and flow a helix-to-coil transition occurs, followed by slip controlled by charged groups; (d) the last step: a coil-to-pstructure (shown by thick lines) transition occurs, the crystallizable polypeptides now assembled into crystallites by hydrogen bonding. T h e resulting microfibrillar structure with alternating crystalline and amorphous regions is optimal for “natural” or textile needs, since it combines high tenacities (the number of the tie chains is high) and flexibilities

gives a further insight in the role played by the configurational information in orientation and jixzng of the oriented state. In the case of fibroin 18 [a], it is sufficient to know that the fibroin chain consists of four “crystallizable peptides” containing only four out of 20 possible aminoacid residues. Just this “quartet” - glycine, alanine, tyrosine and serine - is coded genetically and has a special significance for the rheology of “spinning” p e r se and for the subsequent fixing of an optimal fibrillar order. Such polypeptide can form both a-helical conformation and the “pleated sheet” P-structure with a cooperative system of interchain hydrogen bonds, making this structure practically insoluble in water [6]. The remaining 12 amino-acids forming the “non-crystallizable” peptides are also “chosen” specifically to play their role in the second stage of “spinning” and to provide flexible amorphous segments between crystallites, containing practically 100 percent of tie chains (in ordinary synthetic

Problems of the physics of the oriented s t a t e of polymers

7

fibres, also consisting of sequences of crystalline and amorphous parts, this number rarely exceeds 20 percent; see also [S]). The initial state of fibroin molecules in the 30 percent aqueous solutions in the silkworm’s or spider’s glands is a coil with rigid &-helicalsegments. In contrast to technological spinning, neither silkworms nor spiders press out this solution through their spinnerets (an entomological term, now adopted by technology), but glue a little drop on some twig or leaf and then, by appropriate movements, draw the necessary portion of the slightly viscous liquid from the glands. In this way a longitudinal flow is generated, with its main feature being the ability to uncoil and orient flexible chains along the flow lines. But in our case, even after complete uncoiling and alignment, the &-helical parts of the chains still remain under stress. Now serine and, to a lesser extent tyrosine are ready to play their genetically predestined role. Polyserine in general enables the formation of a stable a-helix in aqueous solution and polytyrosine, and being diphilic is also not very stable and easily undergoes a helix-to-coil transition. Just this happens after uncoiling of fibroin molecules. The weakened ahelical parts undergo, due to stretch, such a transition, and since drawing pertains, they undergo the second transition into the antiparallel @form, thus providing the rigid crystalline parts of the primary microfibrils. To form a fibre with sufficient strength and flexibility, it is necessary to provide some slip of individual chains in order to attain the optimal spatial packing of microfibrils. This is effected due to an interplay of charged groups in the non-crystalline peptides. After a certain longitudinal and spatial configuration of these groups is attained due to slippage, the electrostatic forces prevent any further slip, and the remaining water which was ejected continuously from the stream during this sequence of events is further ejected in different amounts in the cases of silk or web since the latter must be for some time wet, glutinous, and elastic. Thus, the entire spinning “program” (including the (Y - p transition and the electrostatic control of slip) and the fibre properties are “written” in the primary structure of fibroin by means of linear coding (now the term “linear memory” gets more sense), which is just the detailed (discrete) configurational information In the natural silk industry the main and most energy consuming and ecologically harmful process is connected with the unwinding of cocoons in an atmosphere of heated steam. In addition, about 30 percent of the protein is lost during this procedure due to tearing of the filaments. The corresponding purely economic losses are also considerable. Attempts to improve the situation were made repeatedly, starting in the thirties, but with little success due to the same reasons causing Ferretti’s failure. Certainly the consequences were not so catastrophic, but the artificial silk obtained from natural fibroin in a process of the same type as rayon spinning never could be compared with natural silk, speaking both of mechanical and textile properties. ~

8

S . Frenkel

There is no more need to explain that here again the cybernetic law for linear polymers was violated: the configurational information dictated quite a different technology and, being misused, led to poor fibre properties. 1.2. Principal routes to the formation of uniazially oriented structures in polymers In the late sixties [9], considering in general the principles of organization of the orientational supermolecular order and using biological analogies (encompassed, as I understood much later, by the methodology of molecular cybernetics), I mentioned three principal routes: (1) Direct generation. This includes either biochemical growth, as in the cases of wool, hairs, cotton fibres, etc., or a one-stage, stream-thread transition in a solution or melt subjected to elongational flow. The biorheological process of the formation of silk or web from fibroin is an extreme and most special and instructive case of direct generation controlled genetically. Certainly, all biological cases of growth are also controlled genetically, but here the configurational information defines the properties of ready biological fibres, being “grown” simultaneously with the very fibres. In all cases of direct generation in living systems, the energy expenses are very low. One can say that genetic information replaces a part of the energy needed to form fibres, the processes being close to self-organization. Later we shall consider what direct generation for synthetic polymers means. (2) Assemblage. I would not risk to assert that this mode of formation of highly oriented conjunctive tissues consisting mainly of fibrillar proteins of the collagen group is realized in living organisms, but in vitro it can be readily observed as reconstruction of collagen fibres from a solution of tropocollagen or even primary gelatin. The intermediate three-stranded tropocollagen helix obtained as a result of disintegration (without chemical destruction) of coiled-coil multicord collagen fibres (usually from tendons) reconstitutes in coiled “cables” characterized by helix axes of growing order resulting from consecutive coiling of helical microfibrils around one another [lo]. The thus reassembled “cables” are indistinguishable from the native ones. It seems that in such case of “pure” assemblage, no energy is needed at all. In reality, however, the process involves direct and reverse phase transitions (for instance, reconstitution is attained only in very cold aqueous media; only tropocollagen is stable on heating and on further heating onestranded, non-ordered molecules of primary gelatin are formed as a result of a helix-to-coil transition. In the case of fibroin, a multiple phase transition also occurs. This is of great importance, showing that configurational information controls the dynamic or static phase transition and can therefore be introduced in thermodynamic expressions. This is in agreement with Shannon’s theorem:

Problems of t h e physics of the oriented s t a t e of polymers

9

information can be expressed in negative entropy terms, and later we shall proceed accordingly. (3) Rearrangement. This method corresponds t o common technologies as well as to habitual physical procedures of obtaining linear polymers in a n oriented state. Usually rearrangement (or/and repacking), as an orientational process involving molecules of biopolymers, is much more energyconsuming in comparison t o the two preceding ones - and this is just a purely physical (or cybernetical) reason why it is rejected by living nature. T h e increase of energy is directly related t o a misuse of the initial structural information (configurational information being certainly just a part of the latter, specific for polymers). Though the following approximate cybernetic invariant, being a common base (or “common denominator”) for algorithms (in the broad sense of this word), defining such different processes as evolution of life, technology, generation or transformation of energy, etc., can be introduced in a more rigorous manner, the preceding discussion allows t o postulate i t , the proofs, when necessary, being always available [4] :

I xt

N const.

(1)

Here I represents the initial structural information contained in a system, and t is the sum of expenses (energetical, economical, properly technological, etc.) necessary for the processing, i.e., the transformation of the initial system (in the simplest case - a raw material) into industrial goods. By means of Eq. (1) for the analysis of orientation phenomena in polymers and the respective technologies one can easily define two extreme situations. If I is very high (+ co),practically no expenses are needed (t -+ 0) and something very close t o self-organization can be achieved. In the other O ) , the process of manufacturing consists just in ‘(pumpextreme case ( I ing in” a definite amount of information into the starting material and the expenses are high. Cases of desinformation leading to “antitechnologies” are readily derived on rigorous analysis and concretization of the general expression (1).Obviously the case I ---* 00 and t + 0 corresponds t o a n optimal technology [4], the present fibre high technologies still being far from it (though, certainly, closer than routine technologies, rapidly becoming obsolete). In what we call Life the extreme case t -+ 0, I + 00 dominates, I being mainly the genetic information. In the early sixties, defining the essence of structural mechanics of polymers (and including technologies in this definition coming back t o the early sixties), the late Prof. V . A . Kargin said (in several personal communications and discussions) approximately the following: “All possible physical and mechanical properties of polymers are coded in their molecular structure. But they are realized on the level of the supermolecular structure that can vary widely depending on the mode of treatment of a given polymer.” Obviously, this definition expresses the same cybernetic approach I try to -+

10

S. Frenkel

present, and some recent modifications in terminology (such as “different levels of structural organization” or “supermolecular orientational order” instead of “supermolecular structure”) do not matter substantially. Now, keeping in mind that Eq. ( l ) ,being a postulate, requires a specification in every particular analysis [4], we can now consider purely physical and some technological problems that I avoided in [l].The fact that a quite different methodological approach will lead to essentially the same conclusions is instructive in the sense that when dealing with non-linear dynamics of polymers, it is often more appropriate to use a “sum of circumstantial evidence” rather than t o attempt a direct representation of multidimensional trajectories in the space of states. In [l]this “sum” was presented using the thermokinetic formalism, the shifts of state diagrams or statistical distribution curves representing two-dimensional cross-sections (involving explicit or implicit parameters partly replacing the omitted coordinate axes) of the multidimensional trajectories of change of state (or attractors [4,11]).This summing up of two-dimensionnal plots in [l] also represents the essence of the systemic approach to phenomena under consideration [la]. Molecular cybernetics and the invariant (1) provide another basis for use of the systemic approach to the same purposes. 2. Configurational information and orientation phenomena in synthetic polymers 2.1. Direct generation of orientational order from solutions and melts. Orientational hardening, orientational crystallization, and orientational catastrophes This subsection deals only with flexible chain polymers for both purely physical and technological reasons. As we have seen, “biological spinning”, though genetically controlled, involves longitudinal flow - a rheological process enhanced by a high amount of detailed configurational information and including, as the first substantial step, the uncoiling of the initialfibroin coils having the primary and secondary structure necessary t o achieve and fix the stream-thread transition. In the mid-sixties we tried to reproduce this process in vitro using a simple scheme shown in Figure 4 and lithium bromide solutions in dimethylformamide or acetone as solvents. Certainly, even then we understood that a part of the initial information would be lost (the a-hellical blocks in these solvents becoming disordered coils), but it was tempting not only to reproduce nature but also t o try a spinneret-free fibre technology. The sequence of events readily observed visually resembles to some extent that shown in Figure 3. After attaining the conditions of stationary elongational flow (these conditions depending on the fibroin concentration and angular velocity w of the rotating cylinder, or the longitudinal gradient f), one could gradually increase w . At a certain moment an opacity

Problems of the physics of the oriented state of polymers

p

11

0 2

(p

A /--I --

-‘-

I

.-

111

IV

Figure 4. Schematic representation of the first type (rheological) orientational catastrophe. T h e catastrophe proceeds in the same manner with fibroin and P M M A solutions (in different solvents). T h e liquid thread (step I) is generated by a glass stick, the free end of the stream being “glued” to the surface of the slowly rotating cylinder. Then, by adjusting the angular velocity, a stationary longitudinal flow is established; the further steps are obvious

appears in the part of the liquid stream in the vicinity of the cylinder. On further increase of w the “opacity front” moves downward, i.e. in the direction opposite of the direction of flow, attains the surface of the solution in the vessel and then gradually expands in its volume. Simultaneously a dense fog appears around the drawn stream; it is formed by microdroplets of solvent ejected from the stream undergoing the transformation into a highly swollen thread continuing to eject the solvent. The opacity in the vessel spreads practically over the entire solution, the volume transformation being of the solution-gel type. Finally, the orientational catastrophe occurs: practically all the polymer is torn out of the vessel, in the form of a stable swollen gel, by a thin (ca. 50 microns in diameter) swollen thread. A rough estimate of its strength amounts to 0.5 GPa. The “opacity front” is in reality a solidification (dynamic glass or phase transition) front, and, as was understood much later, the linear and then spatial expansion of the transition is characteristic particularly of a d y n a m z c phase (or “behavioural”, according to Prigogine) transition occurring in a dissipative structure and connected with a bifurcation (for details and different graphoanalytic formalisms see [ 11). Unfortunately, during that time we were obliged to deal with more technical matters involving high thermal and mechaiizcal resistance of synthetic fibres, and could not study the structure of the fibrils obtained in this manner. However, I suppose that the initial information I (Eq. (1)) was somewhat misused, which should have affected the structure. This assumption is further supported by the fact that the rheologzcal sequence of events in the case of poly(methy1 methacrylate) subjected to a similar treatment, was quite the same despite that the statistical configurational information

12

S . Frenkel

contained in atactic PMMA chains was of low quantity and value. The substantial difference between fibroin and PMMA was distinctly observed if a sufficiently long part of the swollen filament between the cylinder and the gel bulk was stored under isometric conditions (for the description of the apparatus see [S]). Certainly, the solvent continuously evaporates upon storage. In both cases, just as one could predict, the internal stresses in the threads were increasing. In fibroin filaments, this process ceased without any damage; on the contrary, the PMMA filaments “exploded” at some moment, with only a fine powder remaining in the measuring apparatus. Substantially later an analogous but more drastic event was discovered on polyacrylonitrile (PAN, a poorly crystallizable polymer) or atactic polystyrene (PS) fibres obtained at very high draw ratios either from a dilute solution (PAN) or from a melt (PS) of almost homodisperse and very high molecular weight samples (lo6 for PAN and lo7 for PS) [13]. Except that very high draw ratios were attained, the fibres were obtained in an almost normal fashion and were thoroughly dried. Their mechanical properties were quite unusual, tenacities and Young moduli at liquid nitrogen temperature being correspondingly 1.5 and more than 12 GPa for both polymers, decreasing by approximately 40 percent at room temperature. In liquid nitrogen a large part of a loaded fibre exploded, again turning into fine powder instead of undergoing mechanical failure at a localized cross-section. Upon storage at room temperature, free (i.e. unloaded) fibres also disappeared after a certain time T which can be correlated with S. N . Zhurkov’s kinetic (or thermofluctuational) concept of failure ([14]; see below). It is essential for the following discussion that the process of failure encompasses the whole system. In other words, instead of an Arrhenius type equation involving some local activation energy one must write a more general expression: T

= TO exp(G(c)/kT)

(2)

G being the Gibbs free energy of activation depending on internal or external stresses u. Though it is obvious that this second type orientational catastrophe is due only to internal stresses, we should analyze in more detail their origin (or, to be more precise, the origin and nature of the metastable state - in terms of classical thermodynamics - of these superoriented systems). Moreover, this is necessary since the behaviour of superoriented, crystallizable polymers is quite specific though even then a third type orientational catastrophe is possible, as discovered first by A. Pennings (in parallel with another discovery: see below) and having some technical and technological implications. Though I tried from the very beginning to escape a compulsed autoplagiary, here I am forced to present a series of graphs accompanied by several

Problems of the physics of the oriented s t a t e of polymers

13

paragraphs repeating one section of [l].I should come back to physics in the proper sense of the word, but my final comments will differ substantially from those presented in [l] and will include some technological principles based on the molecular cybernetics approach. To make this intention more comprehensible, let us reconsider the “technologies” of silkworms or spiders in connection with the main, or first rheological catastrophe. If special measures are not taken, it can occur in ordinary solution or melt spinning, involving either a spinneret or a n extruder. Instead of pressing the spinning solution or melt through the spinneret or nozzle, it can happen that due t o erroneous technological conditions, the solution or melt is drawn out of the apparatus. Not only the dose control is thus perturbed (the technology a priori is not based on biorheological principles) but a more dangerous perturbance can occur. T h e same solidification front considered above can enter through the spinneret or nozzle, expand in the volume of the spinning solution or melt and simply block the process. Other cybernetic implications in technology will be considered below (in [l]I tried to avoid them since pure physics or physical chemistry in principle cannot provide a truly scientific foundation of technology if not supported by general and molecular cybernetics [4]) in some details, including a brief analysis of some astounding omissions of dynamic or statistical factors or their most essential combinations. As mentioned in [2], though the detailed configurational information is much more complex than the usually averaged statistical information in man made synthetic polymers, just this information and its possible uses are less understood and more difficult t o decipher, thus hindering the progress of high technologies. Such averaged characteristics as stereoregularity (i.e. crystallizability), flexibility, ability to form intrachain noncovalent bonds, ability t o form mesophases, etc., can partly be predicted even before the synthesis, but need verification by presently well known methods [1,8,14].However, a more complete deciphering requires special physical experiments dealing either with the orientation processes per s e or with properties attained a t different degrees of orientation. Obviously one has t o start with molecular mechanisms, as in the above considerations, when comparing fibroin and noncrystallizable flexible chain polymers. The method of diagrams used in [l] (keeping in mind t h a t these planar diagrams are two-dimensional cross-sections of the dynamic multidimensional space of states) is appropriate to this purpose. Moreover, if one or two parameters affecting mainly the free energy or entropy, or other functions of state under given particular conditions are considered, one can proceed with the systemic analysis in the form of “summarizing circumstantial evidence”, the later giving a deeper insight in the essence of different processes of purely physical nature. Here the complementarity principle does not reflect the intervention of the operator or device in the process under study; it reflects just the “division of a whole into parts”,

S. Frenkel

14

being one of the systemic analysis approaches. This specific approach is inappropriate in studies of life or nature of intellect [la], but it is very useful in physical studies. Let us start with individual chains [1,15] and consider a longitudinal flow that can be generated on sucking the solution between two coaxial capillaries. Treating a physical experiment as a key for deciphering some part of configurational information, we have to denote the longitudinal gradient as the “main deciphering parameter”. Now, what can be stated a priorz? (1) If the chain is flexible, it is able t o uncoil and simultaneously align in the flow direction. The difference between the longitudinal and shear flow is of special importance. If we use the classical W. Kuhn’s dumbbell model for a coil (Figure 5), the difference can be seen immediately. In the first case, a positive feedback is created: the higher the uncoiling ratio p = h / L ( h being the end to end distance of the coil and L the contour length of the chain) , the stronger the stretching force proportional t o ?, enhancing further uncoiling. In the case of sufficiently long chains, both internal and external (rotatory) Brownian motion can be suppressed. Therefore, at sufficient molecular weights, pure uncoiling and orientation should take place, their extent being readily measured by following the streaming birefringence [16]. A shear field produces rotation by itself [16] and though a continuous uncoiling as predicted by Peterlin is, in psinciple, possible at the limit M + 00, it was never unequivocally observed. (2) If the chain is rigid and rod-like, and sufficiently long, it should be aligned due to orientation only, but such results were not observed so far, despite that these chains can form spontaneously a nematic mesophase [S]. (3) The worst case is when the chain is semirigid (as in cellulose deriva-

+

Figure 5. Kuhn’s dumb-bell model in a longitudinal hydrodynamic field. The mechanism of establishing a positive feedback is obvious. On increasing the distance between the spheres, the force drawing them apart ( i x . uncoiling the initial random conformation) increases

15

Problems of the physics of the oriented state of polymers

tives) and contains a limited number of Kuhn’s preferential statistical elements (segments). (This part of information is very essential! When this number is less than 13, an overall behavioural transition occurs [8,17].) Such chains still have a conformation of a slightly asymmetrical coil but due t o both thermodynamic and kinetic rigidity they resist uncoiling, and it can happen that the necessary gradients would be attained only after turbulence starts. Figure 6 [18] shows experimental data for flexible and semirigid chains. The rhomboidal shape of the rotational Brownian motion is not fully suppressed, and therefore, a 100 percent orientation is not attained. Figure 7 [19] shows the influence of N . The coil-extended chain transition is very sharp at large N and it is clearly a first order (dynamic) phase transition (strong hysteresis of dynamic origin and conformational relaxation times increasing with N ) . Another indication of the phase nature of the transition is the reversible disappearance of the birefringent “thread” or rhomboid on increasing temperature or decreasing +. At smaller N values ( N = 13) the transition degenerates into a second order one, the hysteresis disappearing. Further, the dashed line has a typical shape of a van der

h

C

Figure 6. The birefringent region in the gap between coaxial capillaries: (a) schematic representation; (b) polystyrene solution; (c) cotton cellulose solution in cadoxene

S. Frenkel

16

Y

--lo --loo

-- 1000 -- 10000 - - ,

’

AS

K

Figure 7. T h e dynamic phase transition of high molecular weight polystyrene. Note the binodal A “rotated at 90’”

Waals binodal for entropy [20] turned as a whole at 90”. At last, the negative sign of the entropy changes is of special importance. Following Shannon’s theorem, it confirms that upon uncoiling, structural information is gained (or released), thus establishing a direct connection between the approaches adopted in this chapter and in [1]. The additional configurational information collected from the methods of elongational flow together with the longitudinal streaming birefrigence is important both for the physics of orientational phenomena and (partly in retrospective) for discriminating obsolete processes (where 1 in the invariant (1) is misunderstood or neglected). I have to mention here the so-called “flair effect” first discovered by Keller’s group and repeatedly observed in my department by Brestkin’s group. The effect consists in a sudden expansion at attaining a certain (“second”?) critical gradient ;f still long before turbulence arises, of the birefringent “thread” into the volume. Now we can conclude immediately that it is the same first-type orientational catastrophe described above but on a quasi-unimolecular level since the solutions are very dilute (in terms of Debye’s fundamental criterion [q] x c 5 1) and, as was shown by Brestkin (using luminescent “tracers”), the concentration within the “thread” or “rhomboid” is practically the same as in the adjacent unperturbed solution. Further, since in fibroin the configurational information predestinated the fixing of the finite state, and since the sequence of the events was the same with PMMA solutions fully devoid of information leading to fixing, and, at last, since the “flair” effect is reversible with respect to ;f, one can conclude finally that the main (first type) orientational catastrophe is of

Problems of t h e physics of the oriented state of polymers

17

Figure 8. A part of Figure 7 now presented as a bifurcation of the

I

0

1x1

P-parameter, IzI being an arbitrary external uncoiling parameter (4, draw ratio, draw rate, etc.), P’ M 0,25. 1 - the thermodynamic branch, 2 - the nonthermodynamic branch (in Prigogine’s terminology)

a n essentially rheological nature and is due t o a positive feedback between uncoiling and changes in the geometry of flow. Let us consider Figure 7 together with Figure 8, selecting a very high value for N , the other extreme being the critical one equal t o 13. T h e sharp transition shown by line 2 represents a typical bifurcation considered in the theory of dissipative structures, the system of non-interacting chains being transferred from the thermodynamic t o the non-thermodynamic branch and forming a new phase consisting of still non-interacting parallel chains, and being a stationary dissipative structure. (4) T h e situation is changed if some additional primary information is added, for instance if the chains are regular and can crystallize. In his first presentation of experiments of this type (Budapest, 1976), Keller dealt with a polyethylene solution in xylene. In this case, at some critical combination of concentration, temperature and gradient, the “thread” fell out of the solution as a small (though macroscopic) fibrillar crystal. In Prigogine’s terms, this is an example of a dissipative structure undergoing a bifurcation simultaneously with a phase transition which is “ordinary” in the sense that there is no more need t o “pump in” energy t o keep the resulting system stable. In my terms it is purely orientational crystallization. It should occur in a drawn melt, but now we should take care of critical p values and of entanglements. (5) Entanglements. At some critical concentration depending on M (or N ) , sufficiently long flexible chains form a spatial network of entanglements, substantially increasing the viscosity. It was a common opinion in 1976 that they are necessary for the direct generation of orientational order, the “nodes” providing the continuous transfer of draw. However, a t present it is quite obvious that uncoiling (Figure 5) is due t o the longitudinal gradient rather than t o the force. Therefore, increasing viscosity and hindering uncoiling, entanglements hinder orientation as a whole. This can be readily proved by experiments involving elongational flow: if the product [q] x c is sufficiently higher than unity, the thin and well drawn “thread” becomes blurred and either undergoes the “flair” effect or simply becomes unstable due t o reasons already discussed. T h e corresponding birefringence before

+

18

S. Frenkel

this happens indicates a degree of orientation which is substantially lower than at [q] x c 5 1. T h e technological consequences of these observations are evident. (6) One more feature of elongational flow connected with t h e energy of covalent bonds in t h e chains was predicted yet by 3. Frenkel [21] and can be readily understood from Figure 5. T h e hydrodynamic force necessary to tear the chain into two parts is inversely proportional to M 2 (or N 2 ) a n d rupture occurs practically in t h e middle of the chain. This prediction was confirmed both by Keller’s group and our group [22]. Its implications for the theory of failure under load and technology are, again, quite obvious. (7) Critical p values. Due t o internal Brownian motion, flexible chains change their conformation continuously, the distribution function for /3 being of the same shape as Maxwell’s distribution in the kinetic theory of gases. Under static conditions, the most probable value of p is

(p) =

(iN)-lf2

(3)

which in the case of N = 13 leads to p* = 0.25, the asterisk indicating t h e critical value. Under dynamic conditions in a drawn melt or solution, the bifurcation most probably occurs just at this p value [l,S]. It follows t h a t in an optimal orientation process from solution or melt, after attaining p” and t h e occurrence of bifurcation, t h e drawing stress can be decreased considerably. Then the stress-strain curve would take a n

E

Figure 9. The expected stress-strain ( E ) curve for a self-elongating system with “negative longitudinal viscosity”. The dashed curve represents an ordinary deformation curve, the plateau region corresponding either to creep or to rubber-like elasticity

Problems of the physics of the oriented s t a t e of polymers

19

unusual shape shown in Figure 9. But this prediction was confirmed so far only for self-elongating systems and described in terms of “negative longitudinal viscosity” [23]. Now it is time t o consider condensed systems (concentrated solutions and melts) where the relatively simple molecular mechanisms of direct generation are complicated by intermolecular interactions of different extent and nature. In the preceding discussion some implicit insight in these processes was already made. The origin of both types of orientational catastrophes and orientational crystallization can be better understood using the thermokinetic approach [l] and considering “phase diagrams” (quotation marks are used to remind once more that planar phase or kinetic diagrams should be treated as two-dimensional cross-sections of a multidimensional space of states). In Figure 10 the formalism of “deformation of the binodal” is shown. In addition to the legend, this figure needs some comments. When a hydrodynamic field is imposed to the solution, the configurative point A, corresponding to the unperturbed state, due to uncoiling (which is equivalent to an increase of rigidity and t o a decrease of solubility, or increase of the Flory-Huggins interaction parameter x [S]), is situated under the “dome” of the shifted and deformed binodal, and phase separation should occur, leading under dynamic conditions (a drawn stream) to ejection of the dilute phase. However, it is gradually also engulfed by the stream, and practically the pure solvent remains outside the swollen thread. The difference between the information-rich fibroin (or any crystallizable polymer) and information-poor PMMA becomes evident if we introduce, in addition to binodals, the crystallization lines. They are shifted upward irrespective of the binodal type, so that the configurative point A can be situated below the crystallization line, and the oriented state will

(concentration of polymer)

%

Figure 10. “Deformation of the binodal” - the dynamic change of the coexistence longitudinal flow is imposed. The thin lines L1, Lz represent the crystallization ( “liquidus”) curves shifting upward with increasing 4

curve when a

S. Frenkel

20 C

G

C

AG

2

a(orF)

T a

b

Figure 11. G, T and G, u (or F ) “phase diagrams”. A - amorphous melt, CN compelled nematic phase, C - crystalline phase. The dashed line (a) corresponds to overcooling either of a regular or irregular (non-crystallizable) polymer. The set of line 2 is the same as in DiMarzio theory for rigid chains. AG is excess energy “pumped in” by stretch. The thin lines A’ both in (a) and (b) correspond to noncrystallizable polymers. They can be only overstretched without formation of an intermediate compelled (CN) dynamic nematic phase, further transformed into fibrillar ECC. The thorough investigation of the excess energy (arrow in (a) allows one to understand the stabilization of ECC or the orientational catastrophe, depending on the regime)

be fixed. However the concentrated gel on the right extreme of the binodal for PMMA can turn to be sufficiently kinetically stable (especially if the field is imposed at high rate, and a spinodal phase separation occurs). The free energy vs. temperature or stress (in polymers stretch is equivalent t o positive pressure when a liquid-gas equilibrium is considered) diagrams (Figure ll) also require some additional comments. The shift of the lines in the G, T diagrams and the appearance of a compelled nematic phase due to drawing of the melt* reflects the “pumping in” of the external energy, making their effective internal energy higher, i.e. increasing their dynamic rigidity and compelling them to behave as equivalent rigid chains. The latter, as it is well known [3,8], can form a nematic phase spontaneously. For instance, the upper set of the curves in Figure ll(a) coincides with the DiMarzio [24] phase diagram for rigid chain polymers. The same is observed with G , a (or F ) diagrams, and the shift of the lines downward corresponds to increasing temperatures. The disappearance of the ordered, nematic and crystalline phases reflects the fact that they cannot exist anymore at given temperatures, regardless of the rates of strain or stresses (or forces) - not necessarily because of the start of thermal degradation, but very possible due to the failure of the drawn

+

~

‘The same holds for solutions since they always can be treated as “dilute melts” [20]

Problems of the physics of the oriented sta te of polymers

21

melt or solution. At last, there exist “purely thermodynamic” conditions under which a compelled ordered phase, in spite of continuing compulsion (stretch), still melts [25]. The information did not figure explicitly in these considerations. However, it appears immediately if we analyze the most probable crystalline morphologies. The curves in Figure l l ( b ) are more convenient for such an understanding. The lower curve corresponds solely t o an amorphous phase that can be overdrawn until it is ruptured. The intermediate set corresponds t o stress-induced (isothermal - this holds for all sets of curves) crystallization leading t o the formation of folded chain crystals (FCC) not very advantageous in fibres if the aim is to attain high tenacities and moduli. The upper set corresponds to properly said orientational crystallization, the latter resulting from a nematic phase with uncoiled (“compulsively rod-like”) chains and leading to the formation of extended chain crystals (ECC) , very favorable in superfibres [l]. The upward shift of the lines in the G , T diagram reflects the same events. However we can now go into more detail concerning information, fixing of the oriented structure, overcooling simultaneous with overstretching, and second type orientational catastrophe An inherently disordered (atactic) polymer can form neither a crystalline nor a spontaneous liquid crystalline phase (nematic, due to rigidity only); the exceptions are very rare. However, on stretch (at a sufficient rate of strain, to avoid backward relaxation into the coiled state) it can readily form a compelled nematic phase with extended chains. But in contrast to ECC, as clearly seen in Figure l l ( a ) , this state should be unstable even at low temperatures. As shown by the arrow in the G , T diagram, after orientational crystallization the “pumped in” energy is released in the form of latent heat (enthalpy) of crystallization. Thus the oriented system must be stable. However, on overstretching followed by overcooling (dashed line) of an irregular polymer, the compelled nematic phase remains a high energy one with no other means to release the excess energy than to explode. Usually the explosion does not occur immediately, and the corresponding lifetimes of such superoriented systems depend on the energy of interchain interactions and consequently, on the molecular weight. To proceed further with information and limiting conditions of formation of a dynamic mesophase, we can consider a spatial summation of Figures l l ( a ) and (b). Such an operation reveals an elementary step of what was called “the sum of circumstantial evidences”, and just this step does not need a developed spatial imagination necessary when dealing with a multidimensional space of trajectories. In our particular case we can still limit ourselves to a two-dimensional cross-section of a three-dimensional quadrant (being also a cross-section) u ,GI T , its plane making an angle of less than 90” with both G , u and G , T planes. For example, let us rotate the G , T plane around the G axis. u appears again in the thus modified

S. Frenkel

22

T Figure 12. The G, T “phase diagram” as a non-orthogonal cross-section being at some angle with respect to the G-axis of a three-dimensional 6 ,G, T cross-section of the space of states. The critical point a* shows the thermodynamic limit of existence of an ordered (CN) phase. However: if the rate of strain i. is taken into consideration, a purely kinetic limit of elongational flow can occur due to a quasi-brittle rupture of the drawn melt or solution

G, T diagram as a “hidden” parameter but with quite different geometrical results (Figure 12). The upper set of lines can now attain a form pointing to a decrease of the entropy instead of its increase, i.e. production of information, since in classical thermodynamics S = -dG/dT. But here we deal with partial derivatives, the free energy being approximated as a function of two variables T and u. As already mentioned, the information is “pumped in”, together with energy, when the melt or solution is drawn. Of course, in Figure 11(a) the shifts of “phase lines” are also due to the same implicit parameter n. The availability of more sets of lines in Figure l l ( a ) allows the obtaining of the same result as in Figure 12, and even to find a hint of a critical point (shown explicitly in Figure 12) over which only a molten phase can exist. In contrast to melting-crystallization equilibrium in ordinary liquids or solids [20], this critical point is a physical reality for flexible chain polymers, as proven for a particular system - collagen natural fibres swollen in water ([8] or [9]). The technological implications of this data are evident; however some purely kinetic parameters should be taken into account. This will be made briefly by the end of this chapter, and for more details see [l]. 2.2. Assemblage; liquid crystalline polymers The ability of macromolecules to form liquid crystals is coded in two ways. Both ways suggest a similarity of orientation processes and biological (self-)

Problems of t h e physics of t h e oriented st at e of polymers

23

assemblage, though some limited expenses ( t in Eq. (1)) are still required. One route to self-organization is connected with rigidity, and the first corresponding theories were proposed, in somewhat different terms, by Flory [26] and DiMarzio [24]. Though DiMarzio’s theory leads t o a G,T-phase diagram already discussed (Figure l l ( a ) ) , Flory’s approach is more relevant from the standpoint of configurational information. This averaged statistical information was expressed explicitly in the form of a “flexibility parameter”

f = ( z - 2 ) e - E / k t / ( 1+ ( z - 2 ) e - E / k t )

(4)

z being the coordination number (6 in Flory’s theory) of the (pseudo-) lattice, and E - the energy of formation of an “irregular” bond (the “regular” one corresponding t o the trans-conformation in vinyl chains). Thus f represents the molar fraction of “irregular” bonds predestinating the overall conformation of the chain. Strictly speaking, E corresponds t o the kinetic flexibility (or rigidity) and this uncertainty in the definition of f led t o criteria1 errors discussed in detail in [l]. In the case of E + M, f + 0 which corresponds t o rigid rods, and for them Flory developed a quite correct theory of formation of a nematic phase (this was the only case considered by DiMarzio, though he did not discuss explicitly the influence of the solvent) and predicted a very peculiar coexistence diagram, the prediction being brilliantly verified some 15 years later. The critical concentration of the appearance of the nematic (“ordered” or tactoid in Flory’s terms) phase is equal to (p;

8 2 = -(1- -) P

P

(5)

p being the axial ratio of rod molecules approximated as cylindres (Di-

Marzio considered other shapes leading to similar results). These are very well known data, and I presented Eq. (4) in order to “translate” (or “transcript”) it in information terms and t o introduce the notion of osmotic traps, which was not discussed widely though it allows t o eliminate Flory’s error (by the way, the only known t o me) with a numeric estimate of the critical value of f for semirigid macromolecules. The idea is visualized in Figure 13 [8]. I prefer this presentation since it does not involve pseudolattices and uncertain coordination numbers, though we can keep the energy E as an essential znformative parameter. But we treat it as the energy of formation of one effective bend in a primarily extended chain. We can start with rigid rods. On chaotic packing there is no choice how to eliminate the osmotic traps and t o decrease the free energy of the solution. The only way would be to “victimize” the entropy. In the case of rods, where we cannot divide the entropy into conformational and configurational terms, we victimize just the configurational entropy or,

S. Frenkel

24

Figure 13. The osmotic traps (schematic representation) showing the ”choice” between disorder (left) and order. L is the average contour length of semirigid

*

chains, E is the energy of formation of one bend, is the gradient of the dT chemical potential

in other words, directly realize the configurational information, packing the rods in parallel. More difficult is the case of semi-rigid chains, irrespective of the number of Kuhn’s segments in them. Here a choice arises: the chains can undergo multiple bending, turning into more compact coils or t o uncoil, making again possible a parallel packing. Obviously, the gradient of the chemical potential directed inside the osmotic traps should rise with the concentration cp2 and now the choice becomes unavoidable. Flory supposed (though in the first of the two papers [26] he did not treat the matter sufficiently rigorously, basing his reasoning on some data connected with self-elongation of preoriented fibres or films, see [S]) that entropy is “victimized” , gradually involving both its conformational and configurational (packing) parts, and at the end of this process the system achieves again the state shown in the right part of Figure 13. In spite of possible high kinetic rigidities, this should occur at a critical value f* = 1 0,63 (= 1 - - . . .). In this case no more solvent is present, and the system, e given kinetic possibility, must become nematic spontaneously. However, f* = 0 , 6 3 means that the length between chain bends comprises less than two elementary units which is an obvious absurdity. In reality the “bending distance” should approach the length (or degree of polymerization) of a Kuhn’s segment or at least of the persistence length (being in value a half of Kuhn’s segment [16]). This leads in full agreement with experimental data to f* x 0,05. The value is purely empiric but quite reasonable since it means that the axial ratio of a chain part corresponding to Kuhn’s segment or the persistent length varies from approximately 10 to 6, which is the limit of validity of Eq. (5). (Finding his error with f*, Flory adopted in his further works just the criterion connected with the

Problems of t h e physics of t h e oriented st at e of polymers

25

“local” axial ratio). After the nematic state is attained, the system has a domain structure, each domain being characterized by its director [27] and a great number of chains. To obtain a uniaxially oriented system, a slight draw is required t o make all the directors parallel and thus to eliminate the boundaries between the domains [28]. This is just a case when I in Eq. (1) is high and therefore t is low, the entire orientation process resembling mechanicaly induced self-organization. Coming back to DiMarzio’s form of representation (upper set of curves in Figure l l ( a ) ) , one can readily see that it involves the part of internal energy responsible for rigidity, E , as a fraction of the overall free energy G. Coming back to Flory’s coefficient f and paying no more attention to ( z - a), we can immediately see that the origin of the energy E does not influence the positions of the phase lines in Figure 11(a). It can be a kind of additional external energy Ae. If the “natural” energy E =. E O of a rigid or semi-rigid chain equals the effective sum €0 Ae, the positions of the “phase lines” should coincide. This is one of the forms of expressing the “equivalence principle of thermokinetics” [S] . In mesogenic polymers, with mesogenes in the main chain or in the side groups, the implication of configurational information is even more evident and needs no further comments. Modern polymer chemistry allows t o assemble chains containing a limiting number of units, their sequences predestinating the overall degree and character of liquid crystallinity (see ~91).

+

2.3. Reconstruction

The matter is considered in detail in Chapter 2 of this book. However, I would like to add the following: (1). The information given in Eq. (1) appears here also. For instance, the results of multistep hot drawing (thermomechanical recrystallization) strongly depend on the initial state. It is practically impossible t o rearrange a system initially consisting of large spherulites or lamellar crystallites. However, if it contains small and imperfect crystalline morphoses, t decreases substantially, and even at the first step one obtains better orientational order and thermomechanical properties. ( 2 ) . The free energy of activation or the local activation energy of failure Uo is of particular informational importance; it is considered in the next section. During thermomechanical recrystallization, one must avoid, a t each step, draw energies higher than Uo. (3). In its essence, thermomechanical recrystallization is a complex dynamic process including as its main component a multistage FCC -+ ECC phase transition, treated erroneously by myself in the past ([as],second paper) as improbable without intermediate melting.

26

S. Frenkel All three routes considered in this section can lead to the formation

of structures with fully extended chains containing ECC. However, the invariant I x t z const works in different ways, which becomes especially

obvious in the search of optimal technologies. 3. Failure under load

Keeping in mind the nature of the second type orientational catastrophe, we can avoid senseless discussion on the “correct formula” describing the kinetics of mechanochemical failure of oriented polymers [14,30]. We can start with the following a priori assumptions. They are obvious and therefore need no proofs. (1). The process is delocalized. Then one should simply use Eq. (2) in its general form and apply to it Le Chatelier-van’t Hoff principle, i.e. one should state that G

G ( o ) ,and

dG < 0, G being the free energy do

-

of activation, and o the external (due to load) or internal stress. One can further write G(o)in the form of Taylor or McLaurine series and, if possible, limit oneself to the first derivative (though just this presumption requires

dG do

thorough analysis) and write - = y; Eq. (2) then turns to

y having the dimensionality of volume and containing the information on the localization or delocalization of the cross-section of failure. Nothing can be said a priori about the time TO though, as pointed out by J . Frenkel [20] and more recently by Bartenev and Ratner [8, 301, since Go and y can encompass a substantial part or the entire volume of the oriented system, TO should not necessarily be equal to the lifetime of an atom in its equilibrium position in a real crystal (or in a liquid). In amorphous or nearly amorphous (PAN) superoriented fibres, the dangerous initial structural defects are most certainly delocalized along the orientation axis, and the very occurrence of an explosion supports J . Frenkel’s interpretation of G(o) or Go. (2). The oriented fibre or film has the usual long period structure with alternating crystalline (it does not matter whether they are of ECC or FCC type until we start dealing with y) and amorphous regions. Obviously, the latter are weak parts not only because they are amorphous but mainly due to the tie chains deficiency [14]. Thus it is now more reasonable to correlate 7 with the homogeneity of the oriented system and to ascribe the elementary act of failure to a rupture of one covalent bond. If the energy

Problems of the physics of the oriented sta te of polymers

of its thernial degradation is

(10

27

we can rewrite Eq. (6) i n Zhurkov’s form

UOnow being the activation energy in Arrhenius’ sense, and TO M sec being a logical assumption still needing, however, a rigorous verification. Now, Zhurkov’s equation holds better with respect t o the sense and value of the parameters T O ,U O ,y for simple solids; in the case of polymers some obvious anamorphoses [14,30,32] often show anomalies (the so-called shift of the pole), which can be due t o misinterpretation of parameters, very long range extrapolations (since it is difficult t o observe directly lifetimes T of less than 10-1 sec), or some extent of delocalization a t very high or very low crystallinities when one has to substitute UOby Go. (3). T h e case of high crystallinities in ECC and extended chains in the amorphous regions is of special interest since it is connected with the structure and properties of superfibres obtained by high technologies. In contrast to ordinary technologies involving FCC and correspondingly a large tie chain deficiency (their relative number being at least less than 20 percent), the number of tie chains between ECC regions is close t o 90 percent or even more. However, if this number is close t o 100 percent or if the fibres themselves are continuous ECC having only chain ends as defects, a peculiar third type orientational catastrophe occurs; it is less dramatic than the first two types, but fully delocalized and proceeding a t a low rate. At the Budapest Europhysics Conference in 1976, A. Pennings presented a very elegant method of obtaining polyethylene fibrillar single ECC, several kilometers long, from dilute solution a t a low rate. T h e validity and reliability of these results were out of question, as it was shown by different methods. As to the method providing ECC growth, today it deserves t o be defined as a dynamic epitaxial ECC growth (the epitaxy extending on such immence lengths). T h e tenacities and moduli of those as spun “single crystals” were of the order of 10 and 200 G P a , respectively. However, a low rate loss of these unique properties was observed on storage. It had nothing t o do with low rate relaxation processes in superoriented fibres with FCC, widely discussed by I. Ward. In Pennings’ case the process consists in gradual, delocalized (with respect to the entire length) spontaneous ruptures of chains; the rate of these multiple ruptures decreasing with time and leading t o an increase of the longitudinal concentration of defects and correspondingly to a decrease of the mechanical properties of crystalline fibres. Nevertheless, the work of Pennings under discussion and the very method of dynamic epitaxial low rate growth of ECC remain among the most brilliant achievements in the physics of orientation phenomena in polymers (see also Chapters 10 and 15). However, the course of events dictated by nature itself cannot be changed. Very large ordinary single crystals, even diamonds (i.e. covalent crystals), can exist only at a very high pressure

28

S. Frenkel

since thermal motion always needs to be equilibrated by structure. As it follows from J . Frenkel’s concept of liquids and real crystals [20], under equilibrium conditions they must contain an equilibrium volume fraction of elementary defects (“holes” according to J. Frenkel). At storage under normal conditions very large ordinary single crystals can explode [8], and this is a prototype of an orientational catastrophe in a three-dimensional body. Well, something very similar happened with Pennings’ superlong “unidimensional” crystals, though, fortunately, without an explosion since no excess energy was stored. The thermal motion leading t o this spontaneous degradation is specific for superoriented polymers and will be briefly considered in the next section. However, t o generalize the three possible mechanisms of stress induced spontaneous failure, we have to treat an energy distribution, classical or quantum, in terms of fluctuations statistics. A somewhat fantastic (in shape) curve of fluctuations energy distribution is given in Figure 14. The shape is of little importance since only the high energy “tail” is of interest. “Pumping in” external energy or simple loading (which is the same) shifts the curve, and in the region of the ‘(tail” the probability of occurrence of very high energy fluctuations increases substantially. For obvious reasons this probability is inversely proportional to the expectation time T of such a damaging fluctuation (localized or comprising the entire volume). Therefore, we obtain equations of Zhurkov’s type though differing (continuously, mind it! The misunderstanding of this fact led to very heated discussions between Ratner and Zhurkov’s school - see [l]or [30]) in the cases of localized and delocalized (second and third type orientational catastrophes) failure.

T’

Td

T

Figure 14. T h e shift of the fluctuations distribution curve on loading. Td is the energy of thermal fission of a chain bond, T’ is the average temperature of the system. The ”tail” (the shaded part of both curves) is important

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The first case needs additional comments. Kausch reports (also in [l]) a very fine estimate of the extent of elastic energy release in an elementary act of rupture of one strained chain. (The expectation time for this event is given by the distribution curve in Figure 14). This released excess energy is quite sufficient to start a chain reaction of rupture of other bonds in the corresponding cross-section of the fibre (’lmicroexplosion”, following Zhurkov) . This very fine interpretation allows Kausch t o explain simultaneously two puzzles: (1) Why in general the failure under load is localized at a certain (though unpredictable) cross-section - if elementary chain damages proceed at random? (2) Why the expectation time for macroscopic rupture of a loaded fibre into two parts or for explosion is of the same order as the time for one critical fluctuation? Kausch’s approach eliminates both imaginary paradoxes but needs just one comment [l].The notion of elastic energy for such a quantummechanical object as a macromolecule is somewhat dangerous since in some particular cases it can lead to disagreement with the law of conservation of energy. Therefore, it seems more appropriate and even more comprehensible to attribute the energy distribution to a phononic gas [l] (it does not matter that phonons are quasi-particles; they can be treated as carriers of thermal energy). Paradoxically (since we deal with qaasz-particles), it even allows a better visualization (!) of the situation. Phonons are Bosons, and therefore, their number is not constant and can increase in accordance with the Bose-Einstein statistics [31]. Moreover, they can multiply in the same manner as neutrons in nuclear chain reactions or as the Auger showers occur. The rupture of one bond by a high energy phonon generates, on average, at least more than one phonon, so that the coefficient of multiplication is > 1 which is necessary for a branched chain reaction. This approach changes practically nothing in Kausch’s reasoning but eliminates the inconvenience with the elastic energy. However, it also needs some additonal considerations (connected with Debye temperatures, see [l]). To summarize, the above brief discussion shows that Zhurkov’s kinetic concept of failure stating that the mechanical rupture under load is not an event but a process, characterized by a lifetime r and being in the case of polymers mechanochemical in nature and stimulated by high energy thermal fluctuations, contains no contradictions and meets no difficulties when a rigorous treatment is needed. The reasons for discussions are rather imaginary and connected only with the “canonical” formula (7), which, as I tried to show both here and in [l],is not at all necessary to prove the correctness of the physicalconcept. However, a deeper insight in this formula is necessary when numeric data are needed for engineering calculation or prognostication [30].

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4. S o m e specific p r o p e r t i e s of s u p e r o r i e n t e d p o l y m e r s

Since this book deals mainly with general properties of oriented polymers, I shall consider briefly some rather unusual properties “decoded” on superorientation, irrespective of the method by which it is attained (see Chapter 15). As very ingeniously mentioned by L. P. Myasnikova, superoriented polymers become closer in their properties t o ordinary solids considered in solid state physics, losing many “typically polymeric properties” but attaining new ones that should be attributed to ”long chain solids”. (1) To start with, most dynamic crystallographic properties, and first of all, the types and growth mechanisms of large defects become similar t o those in ordinary real crystals (see Chapter 2). (2) Some “anomalies” of quantum nature appear. They are directly related to A. Pennings’ effect discussed in the preceding section. Superoriented fibres demonstrate a “negative linear expansion coefficient” having nothing in common with normal shrinking. It is due to generation of a special mode of transverse (with respect to the chain axes corresponding to the macroscopic orientation axis) vibrations of high amplitude. By themselves they can be sufficient for a moderate shortening of superfibres. In the case of very long fibrillar ECC, these vibrations can accumulate along the fibrillar axis in the form of a gradual increase of amplitudes and, consequently, of energies. The same energy distribution curve as in Figure 14 makes unavoiably an increase in energy, sufficient for a sporadic and nonlocalized rupture of chains. This effect is essentially non-linear in nature and in non-linear dynamics it should be expressed in terms similar t o the famous “butterfly effect” (see [ll])with which any treatment of modern non-linear dynamics usually starts. (3) Two other quantum effects are observed by Bronnikov and Vettegren [32]. They consist in the coincidence of Debye temperatures for torsional and bending vibration modes (as revealed from IR or Raman spectra) with temperatures of /3- and a-transitions treated as relaxational (kinetic) transitions and being such in reality [8]. Thus it seems that the quantum transitions connected with Debye temperatures for specific vibration modes, being real phase transitions, “trigger” the corresponding kinetic transitions. If this is true, it can change the whole concept of transitions (in Boyer’s sense) in polymers, both with fundamental and practical consequences. The latter may consist in a new interpretation and treatment of both creep and rubber-like elasticity. (4) Finally, I would like to mention one more “inversion”; it is the inversion of Poisson’s coefficient in some transverse (to the orientation axis) crystallographic directions observed on stretching of superfibres at very high stresses. The very experiments of this type become possible with superfibres only, since the applied stresses substantially exceed the tensile strengths of ordinary fibres.

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Just because superfibres do not undergo failure at stresses of the order of several GPa, some tie chains shift along the orientation axis, thus locally damaging the order in unit cells which is readily observed by X-ray diffraction. 5. Technological implications They are more or less obvious, and only direct generation requires some additional comments. In this respect Pennings’ dynamic long range ECC epitaxial growth, also belonging t o direct generation methods, is instructive from both molecular and general cybernetics points of view. Certainly, the “longitudinal butterfly effect” could be predicted and therefore, the purely technological efficiency of this very ingenious method could be reconsidered. (1) Statistical configurational information. For any flexible chain polymer the predestination to form fibres must be checked (the check comprising both rheology and final stability) using graphs similar in sense t o the two representations of the Fisher diagram. A more careful check must discern the stable oriented systems and stationary or metastationary dissipative structures, the latter always being connected with compelled anisotropy. (2) Synthetic fibres of “third generation”. This problem has two aspects. First, natural fibres are still better for textile purposes than the purely synthetic ones. Using modern methods of molecular design one can probably “construct” macromolecules serving as real substitutients of the corresponding biopolymers. Second, as mentioned by Elias [ 3 3 ] , the industry of natural fibres is neither economically nor ecologically as favorable as is the common opinion. Therefore the use of natural fibre-forming polymers (especially keratin of bird feathers which is very abundant and in most cases completely lost as a byproduct of the food supply industry) in artificial spinning processes can turn to be quite prospective. Certainly, one should not forget the configurational information. There are no problems with fibroin or collagen, but to dissolve keratin one has to rupture its disulphide bonds and in general to “efface” its structural information on the fibrillar level [a]. However, this disadvantage can be overcome using “tricks” developed long ago by technologists to obtain twocomponent (on the fibrillar level) fibres using special spinnerets, allowing to combine in one fibre two subfibres having a thin longitudinal boundary and consisting of polymers with different thermal expansion, response to humidity, etc. At last, there is always a possibility to modify globular proteins (for example, by treatment with monoiodoacetic acid) and to shift them along the Fisher diagram in the direction of fibrillar proteins. (3) General cybernetic consideration. For the obtaining of superfibres, polymers of very high molecular weight are needed. But then one has to

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remove the entanglements, both for rheological and purely structural reasons. This is achieved by starting the process with a crystalline mat and extending it as a first step to draw ratios of the order of 6. Then the necessary temperature (Section 2) is applied and the process proceeds at a high rate of strain to high draw ratios (of the order of 100 and more). Since the viscosity of the melt is still sufficiently high, the entanglements after the first stage of extrusion (and they are certainly absent in the initial crystalline mat) simply have no time t o occur. Purely kinetic and thermokinetic considerations are of great importance when a mathematical model of the technological process is considered. The possible errors connected with omission of shifts of the system shown in Figures 10 and 11 and occurring not only with ”phase lines”, but also with distribution curves (Figure 14) or purely kinetic curves (rate of crystallization vs. temperature), are discussed in detail in [l] and, earlier, in [34]. The main error in all previous unsatisfactory attempts t o proceed with orientational crystallization to high extents consisted in the neglect of these shifts, but the main failure was the neglect of the fact that purely orientational crystallization must be an isothermal process realized at temperatures higher than the static melting temperature with subsequent cooling when a 100 percent transition to a nematic state is achieved. If this condition is violated, a strand of spatial carcass of ECC containing only a low (less than 20 percent) fraction of the melt (or solution) is formed and by its mere formation hampers subsequent drawing. Probably other methods can be applied to avoid entanglements but the performance of orientational crystallization close to the “critical” temperature (Figure 12) necessarily follows from the molecular cybernetics laws. However, on the other extreme, the danger of the “butterfly effect” exists, and it also should be taken into consideration. A shorter range “butterfly effect” in some rigid chain polymers can explain the “strange fact” that mesomorphic fibres produced from them are better with respect to tenacity and thermomechanical stability than the crystalline ones. 6. General conclusions and summary

The above consideration can be summed up in the following manner.

6.1. What is clear? In physical and physicochemical qualitative essentials, almost all becomes clear when the molecular cybernetics approach is added t o the common ones. In particular, different sources of uncertainties related t o complementarity and relativity also become evident. They were discussed in detail in [l],and here I shall only remind that the complementarity, in addition to

Problems of t h e physics of the oriented s t a t e of polymers

33

the general Bohr’s principle, arises from the necessity of separate analysis of different planar (or three-dimensional) cross-sections of the multidimensional space of states, and their summation is not always possible with the methods developed so far. The relativity has a kinetic origin and was demonstrated in [l](see also [S]) by the notion of “arrow” (or needle) of action. This notion applies to physics in general, but due t o long response times in polymers, it is especially useful to analyze different processes taking place in them. In addition, time dependent variables (including time derivatives of thermodynamic parameters), which can affect the “normal” course of “phase lines” as well as the final states, are of great importance. There is, however, a purely thermodynamic uncertainty connected with the coexistence of FCC and ECC and leading to an inherent impossibility to define an ”equilibrium melting temperature”. Finally, in the short time between writing this chapter and [l],the “grand paradox of Gibbs-DiMarzio” was understood. The difficulty, as correctly stated in [l],consists in the possibility to start with Eq. (4) and t o achieve a second order transition into nematic state by a simple decrease of the temperature. The transition, if attainable, would be of a second order simply due to its continuity. However, the ordinary glass transition will make a phase transition at low temperature, involving uncoiling, kinetically impossible. Nevertheless, the amorphous fibres undergoing the second type orientational catastrophe, though having the same morphology that would occur at Gibbs and DiMarzio temperature T2 (lower by about 50’ than T,), are in reality a frozen nonstationary dissipative structure, and therefore the analogy is erroneous. 6 . 2 . W h a t is incomprehensible?

The most difficult part in the present discussion was connected with different Debye temperatures for different vibration modes. The very problem of the dependence of Debye temperature on orientation needs profound consideration. For instance, is the Ti1 transition (again higher by about 50’ than T, [37]) also triggered by unfreezing of a certain vibration mode, or, in other words, by trespassing one more Debye temperature? The number of vibrational modes of polymers is very high. Why are only torsional and bending modes of such specific importance? And last but not least, if we adopt the notion of Debye temperature for different vibration modes, what will be the fate of phonons? They are quasi-particles and Bosons, and irrespective of temperature they must have a Bose-Einstein distribution. But then, what means a multitude of Debye temperatures for different vibration modes [32]?

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S. Frenkel

6 . 3 . W h a t n e e d s bettei- .uizde~stairdiizgY

Since we discuss here only problems mentioned in this chapter and partly in [l],I would like to concentrate on one, both fundamental and probably applied problem. It starts with the necessity of a deeper insight into compelled anisotropy as a form of a stationary or metastationary dissipative structure. The detailed properties of such long-living oriented structures are poorly understood. The problem in itself is very interesting for modern physics and particularly for non-linear dynamics. However, there is a very tempting prospect of adopting such structures for lasers. Lasers on dyes introduced between the parallel chains of liquid crystalline polymers can be lasers p e r s e or laser filters (in general, the use of liquid crystals as laser filters to generate higher harmonics, i.e. to change the frequency or wavelength, is well known). But what will happen if one uses a compelled rubber-like nematic of the polydiethylsiloxane or polyphosphasene type [as]? Could one produce in such a manner a laser or filter with a continuous tuning in? Of less importance but still of both fundamental and practical value are two other problems recently stated experimentally [35,36]. The first problem is directly related to compelled anisotropy, appearing in an elongational flow of a mixture of two semirigid chain polymers giving separately a rhomboid pattern (Figure 6) or no observable birefringence at all. But the mixture even with a very low content of the minor component (1 or 2 percent of cyanoethylcellulose, the other component being cellulose triacetate, in a mixed methanol-dichloromethane solvent) provides a clearly observable elongated birefringent pattern. Probably, though this needs further analysis, the effect is due to the segregation (its quantitative measure being the segregation parameter X A B , A and B corresponding t o the different incompatible polymers, and X A B being in other terms polymer-polymer Flory-Huggins interaction parameter). It is known that X A B increases with the temperature or stretching stress (or i.).With spun fibres of such a mixture a 100 percent self-elongation and orientation are observed. Probably in solution the initial state is emulsoidal [20], and just the quasi-droplets are responsible for birefringence, its immediate source being the form-effect. What happens within the droplets in the course of their deformation? Probably, the entropy is “victimized” again but now this has nothing to do with osmotic traps, and the uncoiling is due to segregation, Both theoretical and experimental analysis present no apparent difficulties, but their need is obvious. The second effect deserves an illustration (Figure 15). At first glance it is a tremendous anomaly of Zhurkov’s law. However, the left, ascending, or “reinforcing” branch has a lot in common with compelled anisotropy, the active media being ejected from the fibre in the same surrounding liquid.

Problems of the physics of the oriented state of polymers

35

Figure 15. T h e “anomaly” of Zhurkov’s law for flexible chain fibres in active media (solvent or diluent). mo - the initial stress. The left (“anti-Zhurkov”) branch reflects some repacking (formally meaning a substantial decrease of y in Zhurkov’s formula) and must be of the same nature as orientional hardening of drawn solutions with ejection of the solvent. Dashed lines show the uncertainty of behaviour (the “bifurcation region” according to Vaykhansky). It is of interest that for a rigid-chain fibre a normal maximum is observed, without discontinuities or uncertainties [36]. This is one more puzzle that can be added to Subsection 6.3

T h e descending, “Zhurkov’s” branch needs no comment a t all. What really needs understanding is the intermediate region where the critical point should appear (Figure 12, or [8 and 91). One can treat the uncertainty (instead of a smooth maximum) either in the terms of J . Frenkel [20] when he considered the possibility to apply the van der Waals equation for melting, or in more modern terms, since a large scatter of data is characteristic of this region, t o conclude that here the system becomes a metastationary or non-stationary dissipative structure with high probabilities of different bifurcations. All this could appear as a less important special case, but from the technological point of view it becomes very important, providing a very simple method for a substantial reinforcement of fibres. T h e related puzzle is even more intriguing: with rigid molecules of polyparaphenyleneamidobenzimidazole,the overall effect of the abrupt increase of strength and modulus is of the same order of magnitude, though the physics involved should obviously be different. To finish, it could happen that only f o r me a part of the above problems is comprehensible, the other incomprehensible, etc. I often ask my younger co-workers to be quite frank with me if I advance some “strange”

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or “ m a d ” idea. T h i s t i m e , however, 1 simply h a d n o t i m e t o discuss t h i s text with m y aids, a n d therefore I limited the conclusion to apparently obvious formulations of some solved a n d unsolved problems.

Acknowledgements Here I wish to mention the names of the late Prof. V. B. Baranov, who for a long time was my main aid and generator of ideas and of my coworkers Professors B. M. Ginsburg, L. N. Korzhavin, Yu. N. Panov, Yu. V. Brestkin, G. K. Elyashevich, 0. V. Romankevich, Drs. V. I. Gromov, K. A. Gasparian, N. G. Belnikevich, L. S. Bolotnikova, S. A. Agranova, T. I. Volkov, A. A. Shepelevsky and S. V. Bronnikov. The enlightening discussions with my friends from the Ioffe Physico-Technical Institute, Russian Academy of Sciences, among whom I am pleased to name Dr. L. P. Myasnikova, Professors S. N. Zhurkov, V. A. Marikhin, A. I. Slutsker, V. I. Vettegren and V. A. Zakrevsky, are most gratefully acknowledged. T h e same should be addressed to my friends from abroad, Professors A. Pennings, A. Keller, I. Ward, and A. Ziabicki.

References 1. S. Frenkel, to be published in the special issue of Progress in Colloid and Polymer Science containing the main lectures presented on the 25-th Euro-

2.

3.

4. 5. 6. 7.

8. 9. 10. 11. 12.

physics Conference on Macromolecular Physics - Orientational Phenomena in Polymers, 1993 S. Frenkel, “Polymers. Problems, Prospects, Prognoses”, in: Physics Today and Tomorrow, edited by V. M. Tuchkevich, Nauka, Leningrad 1973, pp. 176-270 (in Russian) A. Yu. Grosberg, A. R. Khokhlov, “Statistical Physics of Macromolecules”, Nauka, Moscow 1989 (in Russian) S. Frenkel, I. M. Tsygelny, B. S. Kolupaev, “Molecular Cybernetics”, Lvov University Press, Lvov 1990 (in Russian) S. Frenkel, “Macromolecule” , in: Encyclopedia of Polymers, Moscow 1974, vol. 2, pp. 100-133, (in Russian) M. V. Volkenstein, “Molecular Biophysics”, Nauka, Moscow 1975 (in Russian) A. Blumenfeld, “Problems of Biological Physics”, Nauka, Moskow 1977 (in Russian) G. M. Bartenev, S. Frenkel, “Physics of Polymers”, Khimia, Leningrad 1990 (in Russian) Editor’s supplement 11 to the Russian translation- Ph. Geil, Polimer Single Crystals, Khimia, Leningrad 1968 See, for example, K. Kuhn, Kolloid Z. Z. Polym. 182, 93 (1962) For an exellent comprehensive treatment of modern non-linear dynamics on the “non-fiction level”, see Jason Gliek, “Chaos”, Penguin books, USA 1987 Arthur Koestler, “The Ghost in the Machine”, edited by Picador, Pan Books, Ltd., 1975

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13. S . L . Dobrecov, V . A . Salnikov and S. Frenkel, Acta Polyrnerzca 31, 448

(1980) 14. V. R. Regel, A. I. Slutsker, E. E. Tomashevsky, “Kinetic Nature of Strength of Solids”, Nauka, Moscow, 1974 (in Russian) 15. A. Keller. In the same issue as [l] 16. V. N. Tsvetkov, V. E. Eskin and S. Ya. Frenkel, “Structure of Macromolecules in Solutron”, edited by C. Crane-Robinson, bart., National Lending Library for Science and Technology, England 1971 17. L. Z.Vilenchik, S. Frenkel et al., Acta Polymerica 36, 125 (1985) 18. Yu. V. Brestkin, S. Frenkel et al., Polymer Science 34,386 (1992) 19. Yu. V. Brestkin, Acta Polymerica 38,470 (1987). 20. J. Frenkel, “The Kinetic Theory of Liquids”, Dover Inc., NY 1955. 21. J. Frenkel, Acta Phisicochimia USSR 19,52 (1944) 22. (a) J. A. Odell, A. Keller and A. J. Muller, Colloid Polym Sci. 270 307 (1992); (b) Yu. V. Brestkin, S. Frenkel et al., Visokomol. Soedin. A31, 506 (1989) 23. A. K . Evseev, Yu. N. Panov and S. Frenkel, A d a Polymerica 34,381 (1985) 24. E. A . DiMarzio, J . Chem. Phys. 35,658 (1961) 25. Yu. Godovsky, In the same issue as [I] 26. P. Flory, Proc. Roy. SOC. 351,351 (1956) 27. P. de Gennes, “Physics of Liquid Crystals”, Russian edition, Mir, Moscow 1977 28. S. Frenkel, J . Polym. Sci. 44,49 (1974); ibid., Polym Symp. 58, 195 (1977) 29. A. Yu. Bilibin, V. V. Zuev, S. S. Skorokhodov, Makromo!. Chem., Rapid Commun. 6 , 601 (1985) 30. S. B. Ratner, V. P. Yartsev, “Physical Mechanics of Polymers”, Khimia, Moscow 1992 (in Russian) 31. J. Frenkel, “Statistical physics”, Academic Press, Moscow-Leningrad 1948 (in Russian). German translation: Statistische Physik, Akademie Verlag, Berlin 1957 32. S. V. Bronnikov, V. I. Vettegren, S. Frenkel, J . Macromol. Sci., Phys. B-32, 33 (1993) 33. H. G . Elias, “Mega molecules”, Springer Verlag, Berlin-Heideberg 1987. Russian edition: Khimia, Leningrad 1990 34. G. K. Elyashevich, S. Frenkel, in: Orientation Phenomena in Solutions and Melts of Polymers, Khimia, Moscow 1980 (in Russian) 35. B. F. Kukovitsky, PhD Thesis, Institute of Macromolecular Compounds, RAS, St. Peterburg 1993 36. L. Vaykhansky, S. Frenkel et al, Text. Res. J . 62, 356 (1992) 37. R. F. Boyer and J. B. Enns, in: Order in the Amorphous “state” of Polymers, Plenum Publ. Co., NY 1987, p.221

Oriented Polymer Materials StoykoMaterial> Fakirov Oriented Polymer Copyright 0 2002 Wiley-VCH VerlagPolymer GmbH &Materials Co.Fakirov KGaA Oriented Stoyko & Co. KGaP Copyright 0 2002 Wiley-VCH Verlag GmbH Stoyko Fakirov Copyright 0 1996 Hiithig & Wepf Verlag, Huthig GmbH

Chapter 2

Structural basis of high-strength high-modulus polymers

V. A. Marikhin, L. P. Myasnikova

1. Introduction Melt-crystallized or solution-cast semicrystalline polymers processed from quiescent melts or solutions have poor mechanical properties due t o formation of a hierarchy of morphological units (folded chain crystallites, lamellae, spherulites, etc.), interconnected by so-called tie molecules which can be dangling or taut. For this reason, only a small amount of molecular chains in an unoriented polymer bear an external load. This complex morphology causes the difference between polymers and conventional solids. In order to force all macromolecules “to work” on loading, one should extend and align them in one direction. Then it can be expected that the mechanical properties of this well oriented bulk polymer will be close to those calculated theoretically for the individual macromolecules. The production of such a perfect system is, however, a hard task. Various approaches are used to the achievement of a parallel alignment of macromolecules. In general, there are two principal posssibilities: (i) to prealign flexible molecules in a mechanical field (flowing solution or extended melt) and let them crystallize in an extended state, and (ii) to allow flexible molecules to crystallize into a folded state from quiescent melt or solution and then to try to unfold them by solid-state deformation. The first approach, involving flow-induced crystallization of dilute solutions [1,2], extensional flow of melt [3], high-speed spinning [4], etc., has been intensively developed and studied by many authors [l-71. The other

Structural basis of high-strenght high-modulus polymers

39

approach is widely used in industry and is known as drawing or strain hardening which includes conventional drawing of unoriented polymers [8-121, hydrostatic and direct extrusion in the solid state [13], quench-rolling [14] and solid-state coextrusion as well [15]. Long-term experience of various researchers concerned with producing polymers of enhanced mechanical properties have indicated that ultimate characteristics cannot be reached using the first approach only. Drawing should be used as the main or at least as an additional technique for polymer strengthening. The highest values of tensile stength and elasticity modulus, close to their theoretical estimates, have been obtained for gel-crystallized UHMWPE drawn over a hundred times [16,17] and for UHMWPE samples crystallized from stirred dilute solution and subjected to multi-stage zone drawing [18] (see Chapters 11-15). Thus the clear understanding of the drawing mechanism is absolutely necessary for the establishment of the proper route to high-strength and high-modulus polymers. In this chapter we shall consider the rearrangement of the supermolecular stucture during drawing, the formation of the microfibrillar structure and its plastic deformation, the structure-kinetic approach t o the enhancement of the mechanical characteristics by deforamtion, and some other properties of the oriented and ultra-oriented polymers. 2. Structural transformation in semicrystalline polymers on stretching

2.1. Deformation mechanisms at small strain

It is well known that long-chain molecules, if left on their own, crystallize in the form of lamellae within which they are folded. In a bulk isotropic polymer, the latter are arranged randomly or radiate from a centre comprising spherulites. The lamellae consist of folded crystallites and are sandwiched by disordered regions (often called erroneously “amorphous”) involving taut and gangling tie molecules, cilia and chain loops. The chain segment length distribution in interlamellar disordered regions is usually broad [19], though it is significantly affected by the crystallzation conditions. The structural heterogeneity leads to a nonuniform stress distribution in the polymer bulk, as the tensile stress is applied. Due to the significant difference in the elastic modulus, the crystalline and disordered regions show a different response when loaded. The latter deform at first, the external load being transmitted to crystallites by a small number of taut tie molecules. Moreover, the deformation mode depends dramatically on the orientation of the tensile axis with respect to the chain direction and to the normal of a fold plane. In an isotropic bulk polymer this orientation varies from point to point within the crystalline lamellae in the spherulite. Numerous deforamtional modes can operate simultaneously in a stretched

40

V . A . M a r i k h i n , L. P. M y a s r i i k o v a

polymer and the initial morphology plays a significant role in the deformation process. For the mentioned reasons it is difficult to study the deformational modes operating in a bulk polymer on stretching; the majority of data used for establishing the deformation mechanism has been obtained on model samples: single crystals [20-261, “two-dimentional” spherulites [27,28], extremely thin films with thickness of less than 100 n m [29-301 and bulk polymers with a texture of single crystal [31-331 (see also Chapters 10 and 11). It is known that polymer structure, whatever its initial type, is rearranged on drawing into a microfibrillar structure, which is usually accompanied by neck formation. The study of the model samples has shown that interlamellar slip and lamellar separation precede this rearrangement, as do different modes operating inside the lamellae. These are the chain slip and chain tilting [22,25,27,28,30,34,35],(i.e. intralamellar slip), the twinning of polymer crystallites [27,28,36,37] and the martensitic transformations [20,27,28]. Interlamellar slip is induced by shear stresses, acting in the planes parallel t o the large faces of the lamellas. The stresses normal t o them cause elastic deformation of disordered layers, which varies with the density of kinks and results in lamellar separation. Interlamellar slip contributes mostly to the deformation of bulk samples. Intralamellar slip is induced by shear stresses in the crystallographic planes parallel to the chains and has two basic modes: longitudinal slip along the chain and transverse mode which is normal to it. Large distance slip can occur only in the direction parallel to the fold planes. The real crystal structure can limit the possible slippage planes, as in the case of nylon-6 where the slip can occur only over the planes parallel to those containing hydrogen bonds. Chain tilting is another possible deformation mechanism, that proceeds via multiple slip along the chains. The slip inside lamellar crystals seems t o take place through the dislocation motion [19,39]. The driving forces acting on the dislocations are produced by shear components of the applied stress field. The mechanically induced twinning is due to shearing of planes parallel to the mirror plane between a parent crystal and a twin in a definite direction. The mirror plane contains the polymer chain which is thus left undistorted. Mechanical twinning is a process which proceeds by the migration of a twin boundary through the crystallite. T h e remaining parts of the crystallite shear mutually. This minimizes the defect energy, as compared to the rotation of the whole crystal. The twinning polymer crystallites, by analogy with low-molecular crystals, should also involve the motion of a specific dislocation. Other deformational modes operating in polymer crystals are the phase transformations, for instance, from the orthorhombic to the monoclinic

41

Structural basis of high-strenght high-modulus polymers

phase, or the martensitic phase transformations of various geometries (11 or Iz).These modes can be realized by a simple heterogeneous shift of the molecular chains. The correlation between the operation of separate deformation modes (including twinning, slip and martensitic phase transformation) with fold geometry in polyethylene single crystals has been studied in detail by Alan et al. [38,41]. It had been found that stretching the four 110-domains single crystals in the direction of their long diagonals (along the a-axes, perpendicular to fold planes) by 5-10% leads t o (110) and (110) twinning while that in the direction of short diagonals (along the b-axes, perpendicular to fold planes) results in phase transformation of the orthorhombic lattice to a monoclinic one (Figure 1). Shear deformation occurring via these deformational modes (as well as via molecular slippage and tilting) is small and usually does not exceed 10 to 20%. The main operative deformational mode is determined by the criterion of resolved shear stress. The calcuations of the critical shear stresses (CSS) appropriate for the operation of one or another deformational mode have been carried out for samples with a texture of single crystals [33]. The CSS values determined on compression PE samples at room temperature appeared to equal 14 MN/m2 for martensitic 12 transformation, 14,5 MN/m2 for (110) twinning, 12 MN/m2 for (110) (010) slip, and 15 MN/m2 for a slip in the (001) direction. Tensile experiments give a smaller value for intralamellar slip (9 MN/m2) , while the stress appropriate for interlamellar slip is high enough (50 MN/m2). It is worth noting that these estimates may change significantly depending on deformation temperature and rate. Owing to more diversified orientation relationships between polymer chain axes, the lamella surfaces and the tensile axes, additional intralamellar deformation modes have been detected in experiments with "two-

7

1

l I trans.

,'

monoclinic

0'

CI

a

w

repealed twinning

\

b

Figure 1. Dependence of the operative deformation modes for fold sectors A (a) and B (b) of 110 polyethylene single crystal

V . A . Marikhin, L. P. Myasnikova

42

dimensional” spherulites. In particular, the twins which cause the chain axis to rotate (the so-called “c”-twinning [37,42]) appeared to operate in polymer spherulites. The (310) twinning] which was not distinctly observed in single crystal experiments] was identified in spherulites as an intermediate stage of deformation [27]. The nucleation sites of (310) twins were suggested t o be the high-energy dislocations or the faults in folding which are absent in single crystals. Unlike single crystals [20-231 and ultrathin films [25,26], the two-dimentional spherulitic samples can be plastically deformed without distortion of the lamellar structure up t o a higher strain level (up to 60% in the meridional and diagonal regions and up to 20% in the equatorial regions)] which is easily explained by a large contribution of interlamellar slip and separation [27,28]. The same deformation modes operate in bulk spherulitic samples. The sequences of the intralamellar deformation processes occurring through different operational modes lead to distortions of the lamellae and formation of microfibrils. It is very important to clarify at which level of lamellar deformation the irreversible rearrangement into the microfibrillar structure starts and how it occurs. At the present stage of research one finds a large scatter in these estimates. 2.2. Folded-extended chain solid phase t r a n s i t i o n in the neck

region The most widespread model of unoriented structural rearrangement on drawing of semi-crystalline polymers is that proposed by Peterlin [44-461. According to Peterlin, the transformation of stacked lamellae of the original sherulitic or lamellar structure into microfibrils of the final fibrous material is a discontinuous process taking place at the numerous micronecks positioned at the cracks of lamellae. During micronecking, folded chain blocks are broken off from the lamella, turn by their c-axes in the draw direction,

-

IF-

Figure 2 . T h e Peterlin model of structural rearrangement during drawing

Structural basis of high-strenght high-modulus polymers

43

and are incorporated in the microfibrils which, therefore, consist of alternating crystalline and amorphous regions (Figure 2). Taut tie molecules, originating from partial chain unfolding during separation of the blocks, bridge the amorphous layers and connect the blocks, and in this way a new structure is formed from the remnants of the starting one. In an alternative approach, the rearrangement of an unoriented structure into a microfibrillar one is considered as a recrystallization process. The hypothesis about polymer melting during necking due t o the expected dependence of the crystallite melting temperature on orientation towards the applied orienting forces was proposed in the early fifties [47,48]. It was also suggested that the work of plastic deformation for the destruction of lamellae can be converted into heat and can lead to a temperature rise up to the melting temperature. The true drawing temperature calculated by Peterlin on the assumption of adiabatic local heating in the destruction zone of the lamellae of linear PE stretched a t a draw rate of 0.5 cm/min appeared to be much lower than its melting temperature even upon hot drawing, and for this reason he rejected the idea of recrystallization [49]. The study of the thermal effects in the necking of PE, PP, PVC and PCA by means of an infrared camera has shown that a t least 85% of the mechanical work done on the specimen during necking is converted into heat but the temperature rise even at a very high draw rate is insufficient for complete melting [50]. However, all the experiments pointing to a significant but insufficient temperature rise on necking [50,51,52]did not give an indication of the temperature achieved on a molecular level during deformation. At the same time, a lot of experimental facts suggested a complete destruction of the initial crystalline structure on necking, including a change in the long period [53-571 , decrease in crystallinity and density, observed in PCA [57,58],PVA [59,60], PS [59], polychloroprene [61], P E T [62], etc., as well as the change in the crystal modifications [63,64,65]. By electron microscopic obserations of the critical transformation of various unoriented supermolecular structures into microfibrillar ones (Figure 3) in various polymers, Marikhin concluded that these transformations had a recrystallization nature [66], Further studies confirmed and further developed this concept [10,11,67,68,69].In our opinion, deformation occurs through a stress-activated solid phase transition from folded to extended chain crystals by unfolding folded macromolecules in narrow zones of lamellae at the boundary between predeformed (through the deformation modes described in Subsection 2.2.1) and necked material. Deformation starts when the fold tilt attains its critical value [70]. It remains still unclear, however, whether unfolding occurs when a crystal stem separates from another one in succession or this process takes place in the bulk of a t least one molecule. The latter case requires local melting. Note that the enhanced molecular mobility can be affected not only by heat generation but also by a reduction in the melting temperature due to the negative stresses arising in disordered regions in the vicinity of crystal faces [48,71].

V. A . Marikhin, L. P. Myasnikova

44

C

d

Figure 3. Rearrangement of various initial structures into a microfibrillar one. Spherulites of nylon-6: (a) E = 35 %, replica, TEM; (b) E = 30 %, thin film, TEM; (c) lamellae of melt-crystallized PE, microneck, replica, TEM; (d) lamellae of gel-crystallized UHMWPE, E = 15 %, thin film, SEM

However, the observed dependence of yield stress on the so-called “parameter of intrachain melting cooperativity” , (the latter appeared to be equal

Figure 4. Necking of gel-crystallized UHMWPE film during drawing: (a) scanning micrograph of deformed film, (b) a model of its structural transformation, original lamellae (I), deformed lamellae (dl), nematic structure (n), microfibrils (mf). T h e arrow indicates the draw direction.

Structural basis of high-strenght high-modulus polymers

45

1.o

0.8

0.6

0.4 0.2

0.0 Figure 5. Change of t h e thickness (d) and width ( b ) of gel-crystallized UHMWPE films with draw ratio X to the stem length in unoriented polymers [72]) makes, in our opinion, the first process more probable. Nevertheless, the enhanced molecular moblity is also necessary in this case. Unfolded molecules seem to be unable to form statistical coils because they experience the action of orienting forces. Therefore, unfolding will be followed by the formation of the nematic phase (unfolded molecules being oriented in the draw direction) rather than of the true melt phase, and stress-induced crystallization giving rise to microfibrils. The idea of unfolding was brilliantly supported by experiments with gel-crystallized UHMWPE films [67] which have a structure similar to that of single crystal mats (Figure 4) (see Chapter 15). The orienting forces operate normal to the molecular stems in the folding planes. This favours the simultaneous unfolding of macromolecules on necking, which is expressed in a drastic drop of the film thickness while the lateral size reduces slowly and gradually with the rise of the draw ratio (Figure 5). By the assumption of chain unfolding, the estimates of the thickness decrease on necking are in good agreement with experiment. The difference in the width and thickness change in melt-crystallized samples is less pronounced due to the random lamellar orientation with respect to the draw direction. As for the nematic phase, it is likely to be present in a definite range of temperatures and rates of drawing. There is no experimental technique to detect it in the intermediate stage of drawing but the existence of liquid crystalline order was observed on extrusion of a PE melt [73,74] and in a polyolefin mixture [75]. The generation of LC phase on drawing is more readily attained with flexible chain polymers containing benzene rings [76]. The model proposed by Harrison [77] in the late eighties is of a similar nature. In his view, however, deformation occurs through a stress activation transition to the melt phase, and the “randomization” of macromolecules

46

V . A . Marikhin. L. P. Myasnikova

in the neck region does not require a temperature rise up to the melting temperature. Over the last decade, a number of experiments have been performed in order to estimate the true local temperature rise on the molecular level on drawing. Hendra [78] considered a content of monoclinic phase modification in drawn linear PE, determined by vibrational spectroscopy as a sensitive molecular level thermometer, and indicated that temperatures in the vicinity of the melting point can be generated by drawing at strain rates and temperatures typical of commercial practice. This conclusion seems doubtful because the transition from the orthorhombic t o the monoclinic phase can occur even at temperatures lower than the melting one. More appropriate results were obtained in a SANS study [79] on cocrystallized deuteurated and protonated P E samples with isotropic segregation. The samples were then either deformed in compression or melted and rapidly cooled. In either case there was a significant loss of segregation indicating that deformation involves extensive molecular rearrangement such as that occurring during melting. It is clear that the mechanism of structural rearrangement is influenced by both the structural parameters of the starting material and the drawing conditions. A similar technique w a s used to study the melting during necking in a series of polyethylenes over a range of drawing temperature [80]. The segregation of previously well mixed, unsegregated blends of hydrogenated and deuterated P E on necking was indicative of local melting. It was shown that at lower drawing temperatures there is no evidence for any local melting. Some local melting during necking occurs at a drawing temperature above 70-90°C (depending on the polymer molecular weight.) The former contradicts, however, a conclusion concerning the molecular mobility in the neck during drawing at low temperature, deduced from the change in X-ray long period. To explain this contradiction, the authors suggested that: (i) the crystalline blocks which are broken away and rotated into a microfibril (in accordance with Peterlin’s model) lose their regular stacking, so that the X-ray diffraction signal is smeared up;

(ii) the thinnest lamellae (there will be crystals of differing thickness) escape the breaking up stage and are simply rotated and aligned, thus contributing to the observed reduction in the measured long period and intensity at low drawing temperatures. Since the authors observed no significant changes in the overall properties when the deuterated molecules were segregated on drawing, they concluded that the changes in the shape of individual molecules are similar to those which occur without segregation. The last conclusion appears to be questionable. The change in the overall properties was not, indeed, observed at the stage of necking, when the properties are poor. But one can suppose that it will be pronounced at further drawing when the structural defects originating from necking will prevent the ultimate properties to be attained. To conclude, in the extreme

47

Structural basis of high-strenght high-modulus polymers

cases (low drawing temperature, high molecular weight polymer, large morphological units with well pronounced boundaries) of drawing through a neck, the molecular mobility can be small and the rearengement of the initial structure can occur in accordance with the Peterlin model. In most cases, however, local melting does occur in the neck. 2.3. Micro- and macrofibrillar structure in oriented polymers and its plastic deformation

The microfibrils are not the only morphological units replacing the initial polymer structure. There are other fibre-like entities, macrofibrils, with transverse sizes larger by at least one order of magnitude than those of microfibrils (Figure 6) (see also Chapter 5). The macro- and microfibrillar structure of polymers was thoroughly studied by Peterlin [8l]. He considered macrofibrils as aggregates of microfibrils formed from cleaved lamellae. However, he did not take into account the other levels of structural hierarchy. We belive that microfibrillar aggregation is controlled by the presence of larger structural units in a starting polymer, e.g. spherulites [69]. The transformation of an initial spherulitic structure into a microfibrillar one occurs within every individual spherulite, the boundaries between them remaining intact. Thus, the spherulites are transformed into spindle-like macrofibrils with narrowing

a

b

C

Figure 6. Scanning micrographs of the macrofibrils in oriented PE at different draw ratios (DR): DR = 6 (a); DR = 18 (b); DR = 50 (c)

48

V. A . Marikhin, L. P. Myasnikova

Figure 7. Spindel-like macrofibrils arising from PE spherulites, replica, T E M . T h e arrow indicates their narrowing ends

ends (Figure 7). The deformed spherulites with recrystallized inner structure give rise to specific small-angle polarized light scattering patterns [82,83] and are observed not only in an electron microscope [10,84] but even in an optical one [85]. In the absense of spherulites their role can be played by, for instance, stacks of lamellae, as in the case of gel-crystallized samples, in which the lamellae themselves are aggregated into leaf-like entities of several micron size. Oriented amorphous polymers also reveal a macrofibrillar structure, although the starting polymers are always structureless. Only in this case a pure tendency of anisometric units to aggregate [86] is pronounced. In all other cases it is masked by the presence of initial structural units with weak boundaries. Formation of micro- and macrofibrils is completed after the neck propagation through the deformed sample, and further stretching of a polymer material occurs through a plastic deformation of the fibrillar structure.

49

Structural basis of high-strenght high-modulus polymers

microfibrils

a

n-

a

a macrofibril

C

b

Figure 8. Scheme of macrofibril formation: initial spherulites (a); recrystallized spherulites giving rise to macrofibrils consisiting of microfibrils, the latter being indicated by arrows (b); change in the macrofibrillar shape with drawing (c) Various polymers exhibit different drawability after melting, e.g. nylon can be stretched as much as 2-3 times while PE - 10-20 times. Microa n d macrofibrillar slippage contributes primarily t o this process. T h e former is visualized by a change in t h e shape of the macrofibrils with drawing, distinctly seen in Figure 6 a n d shown schematically in Figure 8 (the microfibrillar slippage can also be deduced from the observed constancy of the X-ray long period and of the transverse sizes of microfibrils on drawing [10,11,87,88].T h e latter can be inferred from a comparative analysis of t h e sample deformation and t h a t of recrystallized spherulites. We have found t h a t macrodeformation, especially at t h e early stages of drawing, typically precedes microdeformation (Figure 9) , which implies a macrofrillar slip. One can assume t h a t slippage of both micro- and macrofibrils should be governed by their connectedness with each other, as well as by the den-

12

10 8 c

E 6

3

4 2 I

I

10

1

I

20

I

DR macro

Figure 9. Relationship between macrodeformation and deformation of spherulites D J p h (DR,,i, = l/R, where 1 is the average length of the microfibrils, R is the average diameter of the initial spherulites) for PE of different M,: 50,000 (a); 100,000 (b); and 290,000 (c)

V . A . Marikhin, L. P. Myasnikova

50

sity of their packing. We suggest that on necking the molecules crossing the boundaries between the neighbouring spherulites are transformed into intermacrofibrillar tie molecules, and the molecules connecting the stacks of lamellae in the spherulites give rise to intermicrofibrillar tie molecules. Then, by varying the amount of the molecules in the starting materials

b

a

a

C

d

C

b

d

Figure 10. SAXS pattern and microfibrillar models of the oriented samples: drawn gel-crystallized UHMWPE film with DR = 50 (a); melt-crystallized PE film of M, = 100,000 with DR = 25 (b); melt-crystallized UHMWPE film with DR = 3 . 2 (c) and DR = 8 (d)

Structural basis of high-strenght high-modulus polymers

51

through changing the crystallization conditions or selecting polymers of various molecular weight, one can change the polymer drawability. The amount of tie molecules is known t o increase with the molecular weight of polymers and with the crystallization rate due to an increase of the socalled wrong folds [89-911. Indeed, PE samples of lower M, show a larger discrepancy between macro- and microdeformation than that of higher M, crystallized under the same conditions (Figure 9). Furthermore, the discrepancy decreases with the draw ratio because of increasing density of fibrillar packing which hinders interfibrillar slippage. The dependence of microfibrillar slip on the amount of interlamellar tie molecules in the starting polymer is evidenced by the difference in the SAXS meridional scattering from gel- and melt-crystallized drawn UHMWPE, as well as from quenched and slowly crystallized drawn PE samples of various M, (Figure 10). Interfibrillar tie molecules inhibit the microfibrillar slip, and an increase of the orienting load is required for further drawing [92]. This leads to an increasing skew of crystallites due t o activation of intracrystalline slip [67, 681. The SAXS pattern from drawn gel-crystallized UHMWPE samples exhibits conventional meridional streaks even at a high draw ratio (Figure lO(a)), suggesting that there are a few interfibrillar tie molecules (if any) in these samples and they present no difficulty for slippage. In melt-crystallized PE of moderate molecular weight, their quantity is

I!

CRYSTALLITE

....

...... ......

I .....

.... ...... ...... .....

CRYSTALLITE

Figure 11. Model of a disordered microfibrillar region proposed by Marikhin (89). The tie segments are formed by crankshaft type conformers ( 1 ) ; trans-conformers (2); GG-conformers (3) and TGT-conformers (4)

V . A . Marikhin, L. P. Myasnikova

52

larger than in solution-cast samples, which leads to a certain skewing of the crystallites at the last drawing stage. This can be concluded by the transformation of meridional streaks into the boat-shaped SAXS reflexes (Figure 10(b)). The SAXS patterns from the melt-crystallized UHMWPE samples display four-point scattering even at the early stages of drawing, which suggests a large amount of interfibrillar tie molecules (Figure 10(b,c)). Calculated from the X-ray patterns, the skew of crystallites can attain 60 degree in the ultimately drawn samples (Figure 10). At the same time the transverse sizes of the crystallites remain unchanged or change only slightly with the draw ratio. Even more dramatic changes occur on drawing in the disordered regions. At present, there are different concepts of the structure of intrafibrillar disordered regions [10,46,92-961. The interpretation of experimental results depends significantly on the accepted model. The models differ primarily in the hypothetical structure of disordered intrafibrillar regions (amount of tie molecules and folds). We believe [89] that the majority of chains in these regions are the chains of different length with a conformation of the crankshaft type (Figure 11). The major conformational defects are 2G1 defects, in the classification of Pechold [97]. During drawing, the tie molecules become gradually equal in length due to the migration of kinks through the crystallites under the action of tensile or shear stress. The kinks of opposite signs annihilate. It is generally accepted that the distribution of external load over the disordered regions is extremely nonuniform. For the evaluation of the real number of load-bearing tie molecules, the IR absorption band shift under load (Figure 12) can be used [98] (see Chapter 4). From the shift magnitude it is possible to define the stresses acting on the conformers of differ-

1.2 .4 Y

5

t

UII

1.0

d 2 0.8 c"

.-0 0.6

75

3 0.4 %

g 0.2

0.0

940

950

960

670

cm-'

Figure 12. Shift of the IR absorption band at 975 cm-I in polypropylene under a load of 0.8 GPa

Structural basis of high-strenght high-modulus polymers

53

ent structures. These studies, in combination with structural investigations [99], have shown that in typical flexible chain polymers (PP, P ET, nylon6, etc.) with relatively low strength-to-break, there is only about 3-10 % of the total number of tie chains that can bear loads greater by an order of magnitude than the average microscopic stress. IR data indicate that with increasing draw ratio, the concentration of irregular segments lowers and the structure of disordered regions becomes more homogeneous. This reduces the overstresses on the tie molecules since an increasingly larger number of tie segments takes on the external load. The concept of the possible stress distribution over the molecular segments in the disordered regions can also be inferred from the broad-line NMR study of oriented P E samples of various draw ratios [100,101], from which the length distribution function of the segments in the disordered regions is obtained (Figure 13). It was shown that with increasing draw ratio from the neck (DR of about 7) up to a draw ratio of about 30, the number of short segments grows, while that of long segments decreases. The difference in the tie segment lengths becomes small. However, since these segments still contribute to the narrow component, they are much longer (by 20-30%) than the distance between the crystallites in microfibrils that act like microclamps. By a further increase of the draw ratio, the narrow component in the NMR spectrum often disappears, so it becomes difficult to find the length distribution of tie molecules. In any case, this type of spectrum indicates that the macromolecular segments become more and more extended and uniform. In accordance with other models, drawing results in a tautening of the tie molecules in the disordered regions, which homogenizes the stress distri-

W(I),arb. units

Es' ,1mT, a

1.2

0.0

.o 1.1 1.2

l/lml,,

b

Figure 13. NMR spectra (a) and the tie molecule length distribution function W(2) for drawn samples of varying draw ratio: DR = 7 (curve 1); DR = 16 (curve 2); DR = 20 (curve 3 ) ; DR = 30 (curve 4)

V . A . Marikhin. L. P. Myasnikova

54

0.8 -

/" 0

I

arb. units Figure 14. Dependence of the tensile strength of HDPE samples on the fraction of the shortest segments bution over tie molecules. But still there is a discrepancy in the suggested mechanisms of deformation and in the estimates of the amount of the tie molecules. According t o Peterlin, the number of tie molecules does not exceed 25-30%. Furthermore, the plastic deformation of a fibrillar structure is supposed to result in the extension of interfibrillar tie molecules via pulling them out of microfibrillar crystallites (which increases their volume fraction), and in the gradually increasing protrusion of crystalline segments through each disordered region. However, calculation of the load bearing chain fraction in commercially drawn HDPE from our NMR data (Figure 14) has shown that it is large (not less than 50%) even for samples with a relatively low strength (0.8 GPa), which is possible only on the assumption of the Hess-Hearle fibrillar model with a large number of tie molecules. The study of the reversible deformation of oriented P E samples also confirms this model [l02]. The Peterlin model makes it difficult to explain the frequently observed reduction of the intensity of SAXS meridional reflexes at the last stages of drawing. As is known, this effect in SAXS may be caused mainly by the reduced difference in the electron density of the ordered and disordered regions. Large variations in the long period value as well as the absence of sharp boundaries between the crystallites and the disordered regions also influence the SAXS maximum but to a lesser extent than the levelling off the electron density. The latter is difficult to suggest if the fraction of tie molecules is small. An attempt has been made [96] t o explain the drop in the meridional SAXS intensity with the draw ratio by assuming a gradual decrease in the amount of microfibrils because of transformation of some of them into interfibrillar tie molecules. In this case the interfibrillar regions should become stronger. However, our observations [lo] and the available

Structural basis of high-strenght high-modulus polymers

55

GPa

0.5 0.3 0.1.10

20

h

Figure 15. Dependence of the transverse tensile strength (c)of oriented HDPE films on the draw ratio

data [lo31 suggest the contrary. The strength in the direction transverse to the drawing decreases with the draw ratio (Figure 15). This is obviously due t o scissions of interfibrillar tie molecules during the microfibrillar sliding. Thus, the number of interfibrillar tie segments decreases rather than t o increase. This process is particularly well pronounced at the pre-rupture stages of drawing. It is accompanied by the formation of longitudinal pores between the fibrils which is implied by the diffuse equatorial SAXS scattering (Figure 16). The assumed reduction of the amount of microfibrils contradicts the constancy of the transverse crystallite sizes and the invariable electron microscopic image of the microfibrils as well. Thus, the drop in the meridional SAXS intensity should be attributed to the perfection of the intrafibrillar disordered regions, their density becoming almost equal to that of the cryst allites .

a

b

C

Figure 16. SAXS patterns from HDPE films of different draw ratios: X = 7 (a); X = 16 (b) and X = 28 ( c ) .Note the appearance of the equatorial diffuse scattering a t the pre-rupture stage of drawing ( A = 28)

56

V . A . Marikhin, L. P. Myasnikova

The question arises as to which degree of order can be attained on drawing and whether the longitudinal order-disorder alternation can disappear completely, giving rise to continuous needle-like crystals. This question was extensively discussed in the literature [104-1081 and will be considered in detail in Section 6. Plastic deformation of the fibrillar structure is always accompanied by molecular scission. As we have already mentioned, the interfibrillar molecules are the first t o break because of overstressing during the slippage of micro- and macrofibrils. The probability of scission of the interfibrillar molecules, however, differs from zero during the entire drawing period, since the thermal fluctuation mechanism of fracture manifests itself under conventional drawing conditions, and stress is distributed nonuniformly over the tie molecules. The molecular scissions can be detected by the ESR and IR techniques [11,109-1111 (see Chapter 4). An analysis of the intensity of certain absorption IR bands allows the calculation of the molecular scission concentration in the sample investigated. A typical dependence of the scission concentration on the draw ratio is shown in Figure 17. It is seen that mechanical destruction occurs during the entire drawing process. The breakdown of a chain in a disordered region can lead t o a chain reaction and destruction of the whole disordered region [112,113], giving rise to submicrocracks. The latter aggregate into microcracks of larger sizes and when their concentration reaches a critical value, the main crack propagates through the sample and breaks it up. By changing the drawing temperature and rate, one can suppress or stimulate the mechanical destruction. An increase of the drawing rate or a decrease of the drawing temperature _ -

I m

I0 E

60 40 -

20 2

0

4

8

12

16

20

h

Figure 17. Concentration of molecular scission accumulated during drawing in PE films of different original structure as a function of draw ratio (A): slowly crystallized perfect large lamellae (1);spherulites crystallized from quenched melt (3); rapidly crystallized small imperfect lamellae (2)

Structural basis of high-strenght high-modulus polymers

57

suppresses the micro-Brownian mobility of the chain segments in the disordered regions, which results in their vitrification and more probable rupture [114]. 2.4. Drawing arrest and fracture of oriented polymers

Plastic deformation of the fibrillar structure consists not only in the overcoming of van der Waals bonds between the molecules but it is inevitably accompanied by scissions of covalent bonds. Rupture of interatomic bonds in a loaded polymer was first detected by ESR from the appearance of free radicals [log] and was also deduced from IR [11,12,109-1121 and X-ray data [log]. Molecular scissions are registered in the oriented samples during the entire drawing process. We assume that the interfibrillar molecules break first, since they prevent micro- and macrofibrillar sliding. The probability of scissions of nonuniformly stressed interfibrillar molecules, controlled by a thermal-fluctuation mechanism [113], also differs from zero. The external force and temperature monitor the parameters of breaking fluctuation, hence the probability of its generation. The increase of the drawing rate and the decrease of the drawing temperature suppress the micro-Brownian mobility of the chain segments in the disordered regions, which results in their vitrification and more probable rupture [114]. The morphology of the starting polymer also affects the intensity of mechanical destruction [ 10,11,110,111].The typical S-shaped curve of accumulation of molecular scissions with the draw ratio differs significantly for quenched and slowly crystallized PE samples, as well as for PE samples of different M, (see Figure 17). A further discussion of the fracture mechanism should involve the transition from the rupture of individual molecules to formation of the main crack leading to the eventual breakdown of an oriented sample. About two decades ago, a two-stage mechanism of submicrocrack formation has been proposed [log]: at first, a thermal fluctuation breaks one molecule, then the remaining molecules in a given disordered region are ruptured through radical-chain reactions for a very short time. Recently [115], a new hypothesis has been put forward on the assumption of a gigantic fluctuation, which is bound t o embrace the entire disordered region. In both cases fracture should occur as a microexplosion that decays at the borders of the neighbouring microfibrils. The amount of submicrocracks grows gradually with the draw ratio, as revealed by X-ray and light-scattering studies [112]. They are accumulated in the samples long before the breakdown, however their concentration is saturated and even at the pre-rupture stage of drawing it is not, typically, as high as it should be to satisfy the concentration fracture criteria. According to the latter, the submicrocrack accumulation turns into accelerated growth of the main crack when the mutual influence and coalescence of incipient cracks comes into action. This becomes possible when the distance between the crack tips does not exceed the double or triple of their

58

V . A . Marikhin, L . P. Myasnikova

size. Such a requirement can be met if the cracks are distributed uniformly throughout the volume, but then an extremely high concentration, as much as 1014-1016 cm-3 for cracks of tens to hundreds of A in size, is necessary, which is observed only with a number of specific (for instance, oriented and annealed) samples. Such a large “volume” crack concentration has not however been detected in a highly oriented polymer. In this case the fracture process has t o result from a drastic localization at certain sites. The dangerous sites can be located in thin surface layers of the polymer where the submicrocrack concentration can be several times higher than that in the volume [116]. Our studies have indicated, however, that the most probable sites for submicrocrack formation and coalescence in a highly oriented polymer are the kink borders [117], where microfibrils are ruptured due to a sharp bending (Figure 18). The kink bands are formed at the last stages of drawing (when all other modes of plasticity but rotational ones stop operating) due t o the release of elastic energy, stored in strongly stressed fibrillar entities at the moment of their breakdown [118-1191. The latter give rise to compressive forces acting in the direction of the microfibrillar long axes, so that the fibrillar rods in the oriented polymer lose their stability, contract sharply and form the kink band nucleus, propagating across the entire sample during further drawing. This mechanism is fairly well described in terms of the disclination-dislocation theory [120]. As evidenced by NMR studies [117], the segmental mobility of the chain in disordered regions is almost completely suppressed at the prerupture stage of drawing because of an abrupt increase of the orienting stress (though the temperature of drawing is close t o the melting temperature). Thus the phenomenon of mechanical vitrification is a fundamental reason for the drawing arrest and transition to the “solid-state” fracture

Figure 18. Microcrack formation on the boundaries of kink bands

Structural basis of high-strenght high-modulus polymers

59

mechanism. I t has been established for highly oriented PE samples that the concentration of kink bands correlates with the concentration of microfibril ends. This is another confirmation of the important role of the starting material structure. 2.5. Alternative mechanisms of drawing

An alternative approach to the understanding of the orientation processes on drawing is to consider the deformation of the entanglement network by ignoring the supermolecular structure [121-1281. In this approach, the macromolecules are supposed to form a transient network with entlanglements acting as friction centres or nonlocalized junctions (see Chapter 16). Savitskii concluded from his reorientation experiments [lag] that the macromolecular network is not destroyed during drawing or reorientation, but is the major factor controlling the mechanical behaviour of flexible polymers. He assumed that rearrangement of the initial networks occurs in such a way that the macromolecular orientation grows in the draw direction together with increased density of tie molecules over the cross-section of an oriented sample without a change in their amount [130]. A network concept was also elaborated by Smith et al. [123-1271. It was used to interpret the difference in the drawability of melt- and solutioncrystallized PE samples [123-1281. This concept apppeared to be useful for the interpretation of oriented polymer shrinkage [131], which was attributed to the persistence of the initial network on drawing. In the kinetic model for tensile deformation proposed by Smith et al., a polymer solid is represented as a loose network of entangled chains, tied together through numerous weak van der Waals bonds (Figure 19). The latter represent the crystallinity that imparts the initial stiffness to the material. It was stated that on drawing, the bonds are broken and the tie chains are deformed and allowed to slip through entanglements; use was made of a Monte-Carlo pro-

Intermolecular

Figure 19. Dense system of polymer chains. T h e heavy black circles represent entaglements loci, and the dotted lines denote the van der Waals bonds

60

V . A . M a r i k h i n , L. P. M y a s n i k o v a

cess based on the Eyririg chemical activation rate theory [126]. The model ignores the possible influence of the crystalline phase on the deformation process past its initial stage. To examine the effect on the deformation behaviour of the entanglement spacing, i.e. of the number of statistical chain segments between entanglements, the stress-strain curves for various entanglement spacing factors (4) were calculated. The spacing factor was taken as the (Me)melt/(Me)sol ratio, where (Me)melt is the approximate molecular weight between entanglements in a melt of linear P E macromolecules and (Me)sol is the approximate molecular weight between entanglements in a PE solution that increases with dilatation. (Me)melt is supposed t o be about 14 statistical chain segments [132] if special steps are not taken t o reduce the entanglement density through e.g. performing polymer synthesis at low temperature or in highly viscous media in order to equalize the rates of crystallization and polymerization, thus reducing to a minimum the amount of entanglements in the as-polymerized material [133], or through repeated extrusion, which favours disentangling [134]. Calculations have shown that the maximum draw ratio, which could be attained in the absence of slippage (i.e. in the case of affine deformation), is inversely proportional to 4.The calculated ratios appeared to be in good agreement with the experimental values observed for drawn UHMWPE samples produced from PE solutions of different concentration. Some differences have been, however, noted between the calculated and experimental stress-strain curves, including the discrepancy between the predicted and experimentally observed stress levels and strain hardening. Savitskii et al. [128] have also attributed the high drawability of solution-crystallized UHMWPE samples to the reduced entanglement density resulting from the disentanglement of macromolecules in solution. Both theories give close estimates of the critical concentration of a polymer solution in which the interpenetration of macromolecular statistical coils provides the necessary entanglement density for attaining the maximum draw ratio. It was emphasized that the predicted ratio agreed with the observable one not only in the absence of slippage but also when the mechanical destruction during drawing was suppressed. The latter is possible only under carefully chosen drawing conditions [128,135]. The effects of temperature and elongation rate on the drawing behaviour have also been discussed in terms of entanglement spacings, van der Waals bond breakage and thermally activated chain slippage [136]. Application of this model to the drawing behaviour of semicrystalline linear PE has shown that for each molecular weight there exists an optimum temperature or elongation rate window within which maximum drawability occurs. Simulations carried out at constant elongation rate by varying the deformation temperature demonstrate that increasing molecular weight leads to higher temperatures for optimum deformation. Calculations for a given molecular weight indicate that the optimum drawing temperature shifts towards higher values with the increase in the elongation rate, and vice versa.

Structural basis of high-strenght high-modulus polymers

61

Experimental results for almost monodisperse PE with M, = 125,000 were found to be in qualitative agreement with the theoretical predictions. The observed tendencies fit also the general experience in drawing. A quantitative agreement has been found, however, between the theoretical and experimental values of the maximum draw ratio only. Unlike the maximum draw ratios, the predicted and observed optimum temperature or rate windows differ significantly. In our opinion, the coincidence of predicted and observed maximum draw ratios together with the quantitative agreement between the calculated and experimental deformation behaviour for some melt- and solutioncrystallized P E samples is insufficient to consider the simple network models as adequately describing the complex process of tensile drawing. The coincidence of the attained draw ratios may be merely formal. It is well known that one and the same polymer can be drawn up to the same draw ratio under various conditions, and shows different strenghts. This is due t o the different contribution of strain hardening and mechanical destruction to the drawing process, as we pointed out in the previous section. The above models totally neglect the molecular scissions that play an important role in the drawing arrest (i.e. in attaining the maximum draw ratio) and affect the achieved mechanical properties. Neglection of the contribution of the crystalline phase and, which is very important, of the conformation structure of folds and tie molecules to the plastic deformation is also a weak point of the entanglement theories. This explains the observed discrepancy between predicted and experimental curves. We believe that the extraordinary drawability of solution-crystallized UHMWPE is caused precisely by the regular folding of macromolecules in crystallites and by the small amount of interlamellar tie molecules. The former provides a synchronous unfolding and formation of very strong microfibrils with intrafibrillar tie molecules close in length, the latter facilitating lamellar rotation in the direction appropriate for the drawing. The high drawability of disentangled single crystal mats [137] produced from solutions below the overlap concentration cannot be explained in the frame of network theories either. It is unclear how the dramatic loss of drawability in solution-crystallized samples occurs after heating for a time too short for “re-entangling” by reptative motion [138] , the only motion providing macromolecular diffusion. Furthermore, the explanation of the neck formation at the early drawing stage in the frame of the network concepts presents much difficulty. Nevertheless, the entanglement model, which has neglected many recent data for the sake of simplicity, is very useful for getting a general notion about polymer behaviour. Those who advocate the entanglement concept and those who consider the deformation behaviour of polymers as a two-phase system depending on morphology, differ primarily in terms. The assumption of long-term and short-term entanglements (the former are crystallites and “trapped” entanglements, the latter are entanglements easily disentangled through dissolution or in mechanical fields) [139] brings to-

V. A . Marikhin, L . P. Myasnikova

62

gether the different approaches. This is a matter of definitions. The trapped entanglements may represent, for instance, conformational defects of the rotational type that cannot migrate through the crystallites. Clusters of unremovable defects are accumulated on the crystallite boundaries and deteriorate the mechanical properties of polymers. A further progress in our understandings of polymer behaviour on elongation requires the development of the defect theory, the study of defect localization and the search for appropriate techniques for the removal of defects.

3. Deformation-induced strengthening of semicrystalline polymers 3.1. Structural kinetic approach t o the enhancement of polymer characteristics b y deformation

Impressive advances in the preparation of UHMWPE with a strength of 510 GPa and a stiffness of 150-200 GPa, comparable to theoretical estimates [17,18,135,137,140-1431, have recently been made by combining the drawing technique with gel-spinning, surface growth technique, solid-phase extrusion or by using single crystal mats subjected to two-stage drawing (see Chapter 15). However, conventional drawing most commonly employed in industry for strengthening flexible-chain polymers solidified from the melt produces samples with stength and elasticity modulus that do not typically exceed 0.8-1.3 and 5-20 GPa, respectively, though higher parameters have been achieved with lab-scale samples in numerous cases [9,12,144-1461 (see Chapters 10-14). Therefore, the search for an optimized drawing procedure is still a pressing problem. One approach to the improvement of drawing is based on the analysis of physical and chemical processes occurring during orientation (see Section a), using notions of the kinetic nature of strength of solids [ 12,92,110,113,147].

<

Figure 20. Schematic representation of the structure of disordered regions in the lamellae. A - regular folds; B - loose loops; C - tie molecules; D - double folds; E - cilia

63

Structural basis of high-strenght high-modulus polymers

Table 1 . Structural characteristics of unoriented H D P E samples Specimens

Tcryst, L , OC

HDPE, M, = 7 x HDPE, M, = 1 x HDPE, M, = 7 x HDPE, M, = 1 x

nm

I,, nm

20,

91

92

93

% g=2.5 g=1.4 g = 1

94

lo4

-95 23.0 11.5 50

0.215

0.102

0.245 0.438

lo6

-95 21.0

9.5 45

0.265

0.092

0.108 0.535

lo4

+120

37.0 18.5 50

0.142

0.033

0.608 0.217

lo6

+120

33.5 16.8 50

0.212

0.096

0.272 0.420

L is the long period (derived from SAXS data); 1, is the length of a disordered interlamellar region; w is the degree of crystallinity (calculated from the SAXS data);

= 2.5;

q1

is the fraction of macromolecules forming loose loops with degree of coiling

q2

is the fraction of macromoleculesforming slightly extended tie molecules with degree of coiling = 1.4;

93 is the fraction of macromolecules forming fully extended tie molecules (y

= 1)

having double or triple fold length; q4

is the fraction of macromoleculesforming regular folds.

In this approach, drawing is regarded as a superposition of two simultaneous and competing phenomena: (i) strengthening achieved through the alignment of macromolecules along the draw direction due to structural rearrangement and (ii) loss of strength due to thermofluctuation-induced scissions of chemical bonds in the molecular backbones under the action of orienting stress. Scissions accompany the entire drawing process, starting with the initial stage of stretching. The loss of strength can also result from relaxation and annealing effects in the oriented state. Since the lifetime of a loaded sample depends exponentially on the temperature and the applied stress, it is especially important to take into account the effects of loss of strength when polymers are oriented a t high temperatures. In a number of studies, the temperatures used a t the final orientation stages even exceeded the melting point of the polymer in the unoriented state [121]. We have shown that the specific features of the molecular and supermolecular structure have a decisive effect on the kinetics of strengthening and the loss of strength. The relationship between these competing processes a t each drawing stage determine the resulting characteristics of the oriented polymer. It has been found that an efficient way of governing these processes is the formation of an optimal supermolecular structure of the polymer in the starting material [12,68,69,92,111,114,147,148] (see Chapter 14). Using the

V. A . Marikhin, L. P. Myasnikova

64

0.08

'

1

-100

-50

0

50

100 TCr,-C

Figure 21. Dependence of the tensile strength of PE samples on the crystallization temperature T,, model of rearrangement of a folded lamellar structure into a fibrillar one as a result of molecular unfolding (Section 2.3), one can a priori assume that the ultimate mechanical properties might be inherent to the microfibrils produced by the drawing of an individual single crystal along the folding plane normal to the crystal stems under optimal conditions. We doubt, however, that the mechancal properties of such microfibrils observable only in the election microscope [149] could ever be measured. Nevertheless, drawing experiments with a PE single crystal mat have revealed fairly high physical and mechanical characteristics of oriented polymers [137], despite the random orientation of single crystals with respect to the draw direction. The situation becomes even more complex for polymers quenched from the melt. Instead of an ideal folded lamellar structure, spherulites are normally formed, with small lamellae stacked on one another and radiating from the spherulite centre. Some crystallizable and rapidly cooled polymers can be frozen in a fully amorphous state (e.g. PET) and form a network-like structure (see Chapter 14). It is important that in the case of crystallization from the melt the folded lamellar surface is more rough than that of a single crystal, because of the large number of loops of varying length and numerous tie molecules connecting the neighbouring lamellae [150]. Since the thickness of lamellae, their transverse dimensions, the degree of crystallinity, the structure of the interlamellar amorphous layers and other characteristics can be appreciably varied by varying the crystallization conditions [10,149-1551 (Figure 20, Table l), one can expect that the physical and mechanical properties of both unoriented and oriented polymers will depend on the supermolecular structure of the initial materials. Indeed, it has been found (Figure 21) that the tensile strength (measured at liquid nitrogen temperature of 77 K t o avoid elongation of the unoriented sample during the test) depends on

Structural basis of high-strenght high-modulus polymers

65

the initial supermolecular structure. The strength of the PE samples with a fine spherulitic, fine lamellar structure produced by quenching from the melt (Figure 22) is twice as high as that of samples with a well-pronounced lamellar structure (Figure 23) obtained by crystallization from the melt a t a slight supercooling [12,144]. It is important to note that the difference in strength between quenched and slowly crystallized unoriented PE samples (measured at 77 K) due t o the different crystallization conditions leads to the difference in the mechanical properties of the final material. In other words, the higher X = ( I - l o ) / l o , the higher Aa = gq - ccr in absolute units (Figure 24) [12,68,69,87,92,101,110,111,117,144,147,148,156,157]. The degree of crystallite orientation and the orientation of macromolecular segments in disordered (amorphous) microfibrillar regions that characterize the strengthening, and the concentration of macromolecular scissions during drawing that characterizes the loss of strength have been studied as dependent on the draw ratio (DR) by WAXS, SAXS, IR, DSC and NMR techniques [9,10,15,16,18-21,28-331 in order to find the structural features responsible for this behaviour of polymers (see Chapters 3,4,6,8,9,10).The thermal properties were also studied. The data obtained indicate that the physical modification can substantially affect the processes of stregthening and loss of strength. It can simultaneously enhance the former and weaken the latter, allowing the production of stronger and stiffer polymers (Figure 25). A favourable effect is achieved through the foramtion of a finespherulitic, fine-lamellar structure with an isotropic distribution of defects (tie molecules, cilia, “wrong” folds ) in the interlamellar space during rapid crystallization from the melt (Figure 22). An external orienting stress is distributed in this case more uniformly throughout the sample microvolumes, thus lowering the coefficient of chemical bonds overstressing and minimizing the mechanical destruction of the oriented polymer. The probability of submicrocrack formation is reduced, leading to relaxation of the extended chains. A particular obstacle in the production of high strength and high modulus materials from melt-crystallized polymers is the formation of vast lamellae when crystallization occurs at a slight supercooling (Figure 23). It was found that they are connected mainly by fully extended macromolecular segments which unite into short fibrous crystals [152-1551 and, like nails, keep the lamellae together. Rearrangement of the initial structure in the neck region cannot proceed as uniformly as in the previous case. A large number of molecular scissions detected by the IR technique (Figure 25) during necking (at DR = 7-10) is, obviously, a consequence of fibrous interlamellar tie ruptures. The drawing process is adversely affected by the appearance of an anisotropic a-axis structure which is often observed with processing in strong shear fields. A negative role is also played by the increase in the molecular weight of the processed polymer because of generation of a large

66

Figure 22. Surface replica of a quenched P E film (Tqu= -95 " C )

V . A . Marikhin, L. P. Myasnikova

Figure 23. Surface replica of a slowly crystallized PE film (Tcr= 123 "C)

L

Figure 24. Relationship between tensile strength u and draw ratio X for quenched (0)and slowly crystallized (e) P E films

number of interlamellar tie molecules. Thus, by modifying the superrnolecular structure of semicrystalline polymers through the variation of T,, [12,144], molecular weight [11,148,158-1601, the number of side chain groups [161] and cross-links

67

Structural

20-

~o/o-o-o

O /

Figure 25. Dependence between molecular segment orientation (cos' 0) in disordered regions (a) and the concentration N of molecular scissions (b) on draw ratio X for PE quenched at T, = -95OC (0) and for PE slowly crystallized at T,, = 123OC ( 0 )

[162], etc., one can influence fairly efficiently the kinetics of both processes, i.e. strengthening and loss of strength. It has been found that one can choose such temperature and stress conditions of drawing and form such an initial structure that strengthening could be made most efficient, and the concurrent process of loss of strength could be suppressed. However, t o fulfill these requirements in the entire range of the draw ratios, drawing should be carried out in several stages, with a proper choice of temperature and stress for each stage, as well as of optimum molecular weight and molecular weight distribution.

3.2. Physical criteria f o r the optimization of the drawing process Since drawing is a basic technique of commercial production of polymer films and fibres, its modification aiming at the enhancement of the me-

68

V . A . M a r i k h i n . L. P. M y a s n i k o v a

chanical properties is a topic of great interest. The proper choice of the drawing stages and of the temperature-rate regime at each stage is quite important. The technological process typically involves two stages. In high-speed spinning, this process seems to proceed even in one integrated stage. The drawing temperature is one of the most important factors strongly affecting the type of X = f(udr) dependence. Drawing of amorphous polymers (e.g. PET) is usually carried out at a temperature higher than the glass transition one but lower than that of yielding, i.e. in the viscoelastic state. Polymer deformation in this state is described in terms of the statistical theory of viscoelasticity as an affine extension of the entanglement net in the entire range of draw ratios [127,128,164]. For semicrystalline polymers the drawing temperature Tdr is also varied within broad limits at the initial stage, though in some cases it is believed that Tdr should be close to the temperature of a-relaxation in crystallites [146]. The drawing rate is another parameter essential for the strengthening. Since there are no generally accepted facts for the choice of the rate at each drawing stage, it varies significantly in different technologies. The major factor determining the choice of different temperature-rate regimes of drawing is, therefore, the achievement of high productivity and reliability of processing. The potential of the drawing technique, however, is not yet exhausted. We suppose that it can be successfully modified by taking into account: (i) the thermofluctuation theory of stregth of solids [113]; (ii) the influence of the starting material morphology on the deformation strengthening; (iii) the exponential dependences of relaxation, thermal and mechanical destruction in polymers on temperature and stress; (iv) the deterioration of mechanical properties resulting from structural changes upon annealing, which may occur both at the last stage of the drawing and during additional thermal fixation; (v) the increase of the crystallite melting temperature under loading; (vi) the delay of relaxation and annealing processes in the loaded polymers. Drawing involves two entirely different steps, i.e. (i) neck formation accompanied by a drastic rearrangement of the initial structure into the microfibrillar one. It occurs through a transition from a statistical coil or folded molecules into extended ones (Figures 3 and 4) and (ii) plastic deformation of the newly formed macro- and microfibrils (Figure 8). It is quite clear that the drawing temperature and orienting stress will differ at various steps of drawing and will be determined by the respective physical processes. We believe that it is extremely important to choose properly the conditions of necking, because the fibrillar structure that will subsequently determine the properties of ultraoriented polymers, is formed precisely at this stage [10,11,66,164]. It has been found [76,162] that the temperature-rate regime at the stage of neck formation is fairly well elaborated. It is desirable that an oriented fibrillar structure with a nematic

69

Structural basis of high-strenght high-modulus polymers

character of chain packing could be formed in the neck region. This greatly facilitates the removal of conformation, dislocation and disclination defects during subsequent plastic deformation of the fibrillar structure and leads t o an effective perfection of the disordered regions in microfibrils, enhancing the polymer properties. The nematic chain packing can evidently be achieved by stretching even flexible chain polymers. For amorphous polymers, Tdr can be lower than T,, for semicrystalline polymers it can be close to the a-relaxation temperature. One should keep in mind that a transition to this state can occur only at a definite tensile stress. In a continuous technological process, this is achieved only at definite and fairly low drawing rates. For these reasons, it is unlikely that the polymers with enhanced mechanical properties can be produced through high-speed drawing. Considering the plastic deformation of fibrillar structures, it is important to clarify (i) whether it is necessary to perform drawing in several stages, (ii) what temperature and stress conditions should be created at each stage and (iii) in what way transition from one stage t o another should proceed. Plastic deformation is often performed in one stage at constant temperature and tensile stress. However, it has been found that high strength, high stiffness, long lifetime of the samples and stregthening stability can simultaneously be achieved only in the regime of zone drawing performed in 3-4 stages. To reduce the probability of molecular scissions during drawing, the samples should be kept in the heating device for a limited time of less than 15% of the lifetime T = TO exp(U0 - y a / b T ) , derived from the kinetic theory of solid strength [113]. This requires the use of local heaters. Drawing a t the stage of plastic deformation of the fibrillar structure is typically carried out a t a temperature TjF higher than that (T;,) at

Figure 26. Schematical dependence of the tensile strength (A) for PE films under various conditions (see text)

( m ) on

the draw ratio

V . A . Marikhin. L. P. Myasnikova

70

0' 0

10

20

30

Figure 27. Dependence of tensile strength (u)on draw ratio (A) for HDPE of M, = lo5 drawn a t 373 K (curve 1); at 373 K up to X = 7 and a t 383 K u p t o the arrest of drawing (curve 2); a t 373 K up to X = 18 and at 393 K u p to the arrest of drawing (curve 3)

the necking stage. However, it remains still unclear a t what draw ratio the temperature should be raised and t o what extent. T h e choice of suitable Tdr along with the optimum drawing rate influences the mechanical properties of the final product. T h e latter are described by the dependences u = f ( A ) and E = f(X). T h e available data can be shown schematically by three types of curves (Figure 26). The dependences of the type I indicate t h a t the temperature-rate conditions of drawing are chosen in such a way t h a t mechanical destruction does not play a decisive role in the entire range of draw ratios. However, both dependences often have a plateau (Figure 26, curve 2) or bend (Figure 26, curve 3). The deviation from the linear relationship starts at smaller A' for polymers that undergo a more intense mechanical destruction. An increase in TAf leads t o several effects [162]. First, it is possible t o reach higher draw ratios, changing the stengthening efficiency, by extending the linear portion of the u = f ( A ) dependence with the same slope k = Aa/AX (Figure 27 dashed part of line 1). This will lead t o higher strength and elastic modulus. Furthermore, by raising TAf a t a certain A' one can increase the strengthening efficiency (curve 2 in Figure 27) by finding a suitable orienting stress. : f can be repeated several times, so that the Drawing with increasing T final Tdrcan be even higher than T,,, of the undrawn polymer due t o a rise of the melting temperature of the crystallites in the stressed state. However, because of the intensification of mechanical destruction with raising temperature and orienting stress, the dependences of strength and modulus on the draw ratio a t the last drawing stage eventually form a plateau (curve 2, Figure 27) or drop abruptly (curve 3, Figure 27). A steep slope in the curve a ( A ) is sometimes observed at a much lower draw ratio (curve 1,Figure 28).

71

Structural basis of high-strenght high-modulus polymers

Figure 28. Influence of drawing temperature ( T d r ) on tensile strength for H D P E with M, = 2 . lo5 drawn a t 373 K up to X = 13 (curve l ) , at 393 K u p t o X = 13 and at 393 K up to the arrest of drawing (curve 2)

I

10

20

h

Figure 29. Dependence of modulus of elasticity (E) on draw ratio (A) for H D P E with M, = 2 . l o 5 drawn at 373 K (curve l ) , a t 373 K u p to X = 13 and at 393 K up to the arrest of drawing (curve 2)

This can also be efficiently corrected by increasing Tdr and through the proper choice of the drawing rate (dashed line 2, Figure 29). In spite of a n insignificant increase in the strength in this case, an almost two-fold rise of the initial modulus can be attained at the pre-rupture draw ratio, which can be of great practical interest (compare lines 1 and 2 in Figure 29). When drawing is carried out at Tdr higher than T,, it is necessary t o use antioxidants and try t o avoid annealing that begins t o manifest itself at 20-30 K below T,, thus leading to significant structural changes for fractions of a second [166]. Thus, the general approach t o the optimization of the draw-

72

V. A . Marikhin. L. P.

Myasnikova

ing technique includes: (i) the choice of suitable molecular characteristics of the polymer to be processed, including its molecular weight, molecular weight distribution and the number of side chains; (ii) the formation of an optimum morphology by varying the conditions of crystallization from melt or solution; (iii) the choice of an optimum temperature-rate regime for each drawing stage. Much attention should be focused to the regime of neck formation] since the optimum values of both parameters lie in a very narrow range. It is highly desirable that a nematic structure ensuring subsequent preparation of polymer films and fibres with the highest possible mechanical properties be formed at this stage; (iv) carrying out the plastic deformation of the fibrillar structure in several stages with a stepwise increase of Tdr and b d r ; (v) when choosing the temperature-rate regime of drawing, the sharp exponential dependences of relaxation, annealing, thermal and mechanical destruction on Tdr and orienting stress should be taken into account. At high Tdr an antioxidant should be used; (vi) the use of local heaters to greatly reduce the time of keeping the polymer at an elevated temperature. 3.3. Optimal molecular weight and molecular weight distribution

A distinguishing feature of polymers, in particular of polyolefins, is that their molecular weights (M,) and molecular weight distributions (MWD) can be varied within a broad range by varying the conditions of synthesis. It is possible to change M, by 3-4 orders of magnitude and MWD by a factor of 20-50. Therefore, it is important to find M , and MWD that would be optimal for the preparation of high-strength, high-modulus polymers. It is known that the best properties can be achieved only for ultrahigh molecular weight (UHMW) polymers (M,> lo6) processed from gel [17] or solution [140] since they cannot be produced through conventional melt extrusion with subsequent drawing of a melt-crystallized polymer due to the extremely high viscosity of the melt. Since the commercial production of UHMW films and fibres by the melt-technology faces problems, the focus is currently on polymers with relatively low M,, for instance, HDPE with lo5 < M , < 3 x lo5. M , and MWD affect significantly all stages of polymer processing owing to their influence on the rheological properties of the melt, on the polymer ability for fibre formation, nucleation, crystallization and M, fractionation during solidification, on their drawability, tensile st,rength, impact strength, etc. Lab-scale melt-crystallized drawn samples of some polymers (HDPE, PP, POM) with a high Young’s modulus (about Etheor/3) were obtained at a high draw ratio, but their tensile strengths often turn out to be low (0.4 GPa for HDPE [9]). It is quite clear that the best model polymer for the study of the M, and MWD effects on the properties is HDPE because of a wide variation of its molecular characteristics. In the experiments we used samples with 5 x lo4 < M , < 3 x lo5 and 2 < Mw/Mn < 50, i.e. the HDPE samples

Structural basis of high-strenght high-modulus polymers

73

that are of major interest for commercial production by melt technology. Narrow strips (0.5 mm wide) of pressed films (30-50 micron thick) were drawn to different DR by a multistage zone drawing technique [12,144,1581601 (see also Chapter 13). To avoid additional stretching of the samples during the tensile strength measurements, the tests were carried out at 77 K. According to the kinetic theory [113], the strength of P E at room temperature is lower by a factor of 2 than that at 77 K, which was confirmed by direct measuraments of ultimately oriented polymers. It has been found that high DR (up to 20-30) can be achieved for all samples (Figures 30 and 31). The dependences of the tensile strength on the draw ratio exhibit two distinct regions: (i) a linear relationship up t o DR < DR,, and (ii) saturation or even drop of the tensile strength with draw ratio at DR > Dcr. One can see that both M , and the polydispersity of PE affect the length of the linear portion of the curves (viz. magnitudes of DRcr)and the slope K = Au/AX, in other words, they crucially influence the strengthening efficiency. For the majority of samples, the highest achievable strengths (measured at 77 K) and elastic moduli (measured at room temperature) vary in a broad range: from 1.0 up to 2.2 GPa and from 35 up to 70 GPa, respectively. High strengths and moduli cannot be obtained simultaneously for all M , and MWD. In most cases the high strength samples do not necessarily exhibit a high modulus and vice versa. This refers primary to the samples with tensile strength/DR dependences having a plateau or a drop at high DR. The effect of the loss of strength, leading to a decrease in the tensile strength, is much more pronounced in these samples. Data analysis [158-160,1621 has shown that the highest efficiency of

t O:,

10

20

30

Figure 30. Dependence of the tensile strength (c)on the draw ratio (A) for HDPE with M, = 80 x l o 3 , M,/M, = 6.5 (curve 1); M,., = 105 x l o 3 , M,/M, = 6.0 (curve 2); M, = 185 x l o 3 , M,/M, = 5.2 (curve 3); M, = 270 x l o 3 , M,/M, = 5.8 (curve 4)

74

V . A . Marikhin, L. P. Myasnikova

1

Figure 31. Dependence of the elastic modulus ( E ) on the draw ratio (A) ~, for HDPE with M, = 80 x lo3, M,/M, = 8.9(0); M, = 90 x l o 3 , M,/M, = 10.0 ( x ) ; M, = 150 x lo3, M,/M, = 10.0 (A); M, = 200 x l o 3 , M,/M, = 10 - 1 5 ( 0 ) ;M, = 2 9 0 . l o 3 , M,/M, = 9.1 (0)

strengthening is achievable for the samples with a moderate polydispersity M w / M nof about 5 to 7. They are characterized by the highest strengthening coefficient “I?, which means that fairly high mechanical characteristics can be achieved at lower DR. This is certainly of interest for commercial production. Figures 30 and 31 also show that the best results with melt-crystallized drawn HDPE were obtained for M , = lo5 and Mw/M,, = 5 to 6. The tensile strength/DR dependence remains linear in this case up to DR = 30 - 35; as a result, the highest strengths (3.0-3.2 GPa measured at 77 K, or 1.5-1.6 GPa measured at 330 K) and moduli (70 GPa) can be achieved simultaneously. The elastic modulus was determined from the stress-strain curve obtained under stepwise static loading at room temperature and deformation of about 0.1%. The observed differences in the deformation and strength can be explained if one takes into account the specific supermolecular structure that is formed in the PE samples during rapid quenching (supercooling AT = T, - T,, = 100-150 K, rate of crystallization V = 103-104 nm/s, crystallization time of about 0.5-0.05 s. Under these conditions, the resulting supermolecular structure is fine and comprises spherulites of 5-7 microns in diameter which are built up of stacks (about 0.5 x 0.5 x 0.5 p m in size) of at least 10-15 small lamellae 30 nm thick connected by tie molecules (Figure 22). This structure is formed due to homogeneous multiple nucleation, as shown by various techniques [152-1551. The data analysis led us t o the conclusion that the effect of molecular weight fractionation during crystallization [151] results in the formation of lamellae from the molecules with elevated M,, while the low-molecular weight fraction ( M , < l o 4 ) is pulled out and localized at the boundaries between the stacks both in-

Structural basis of high-strenght high-modulus polymers

75

side the spherulities and between adjacent spherulities. It follows from the model of recrystallization during the spherulite-fibrils rearrangement (see Section 2.3), that the quantity and length of interlamellar tie molecules determine the characteristics of interfibrillar tie molecules in the oriented polymer. The former play a dual role. On the one hand, they transfer the applied orienting stress from one fibril (limited in length) to another, thereby promoting the formation of shear forces and improving the perfection of disordered regions. Therefore, the greater the amount of tie molecules, the higher the local shear forces, in other words, one gets a more perfect structure and more efficient strengthening. Indeed, the strengthening coefficient K for the initial part of the tensile strength vs. DR dependences grows with increasing M , [158-1601 (Figure 30). Moreover, the highest initial values of K were observed for melt-crystallized P E samples with M , of about 1 million [148]. For gel-crystallized PE samples K is substantially lower (by a factor of 2-3) and high tensile strength (6-7 GPa) and modulus of elasticity (150-100 GPa) can be achieved owing to their extremely high drawability (DR is up to 200). However, these tie molecules play also a negative role, preventing the slippage of fibrils during further drawing. This leads to skewing of crystallites in microfibrils (which is derived from four-point SAXS patterns [87]), increased mechanical destruction [110,111,144] and intense formation of kink bands [118-1120,147,167], limiting the ultimately attainable draw ratios and mechanical properties: the melt-crystallized P E samples of M , = 1 x lo6 cannot be stretched more than by a factor of 10-12, and their tensile strength/DR dependences reach a plateaux or exhibit an abrupt drop starting at fairly low DR. The low-molecular weight component of the MWD plays an equally important role. Its plasticizing effect has been described in [l68]. Molecules with M , of about lo3 form extended chain crystals [151] that have a lowered T, (up to 380 K for PE) and low critical resolved shear stress along all the crystallographic directions. Therefore, the low-molecular weight component can indeed act as an effective structural plasticizer upon high temperature drawing by facilitating the slippage of microfibrils. However, if the fraction of this component is large, slippage will occur at lower orienting stresses, insufficient for the efficient ordering of disordered regions. As a consequence, one gets lower values of tensile strength and Young’s modulus (Figures 30 and 31). Since an increase in polydispersity leads to a larger fraction of the low-molecular weight component, its effect manifests itself most readily in the samples with low M , which, as follows from the data reported in [152-1551, have a few (if any) tie molecules between the fibrils. Thus, the optimal values of M , and MWD can be found, though M , and MDW affect deformational strengthening in a contradictory manner. It is likely that an optimal relationship between the content of the lowmolecular weight fraction and amount and length of the tie molecules connecting microfibrils can be achieved in the P E samples with M , of about

76

V . A . Marikhin, L. P. Myasnikova

l o 5 and MWD of about 5-6. Though the coefficient K is not the highest for this material (Figure 30), the tensile strength/DR dependences remain linear up to DR = 30-40, allowing high strength and modulus to be achieved simultaneously.

4. Mechanical properties of highly oriented polymers Fibres and films of highly oriented polymers possess exceptional stiffness and strength in the draw direction. The real values depend on the chemical structure of a polymer, its molecular weight, molecular weight distribution and molecular orientation attained during drawing. Furthermore, the interpacking of micro- and macrofibrils together with their inner structure, which are controlled by the morphology of the starting material, also influence the mechanical behaviour (see Chapters 10-15). Despite the great progress in producing high-strength and high-modulus polymeric materials, their mechanical properties are still below the theoretical predictions. Typically, the experimental figures are compared with strength and modulus of the individual extended molecule calculated for 0 K. It is much more reasonable, however, to compare the observed mechanical properties with those calculated for a three-dimensional defectless crystal at ambient temperature. According to Zhurkov’s theory, thermal fluctuations are the main factor controlling the mechanical behaviour of solids at temperatures differing from the absolute zero [113]. The applied load only increases the probability of fracture. It is easy to deduce from Zhurkov’s equation the expression for the real ultimately attainable strength at a given temperature T:

where CTT is the theoretical ultimately attainable strength at a given temperature T ; F is the theoretical strength at 0 K; R is the universal gas constant; TO is a constant approximately equal to the period of thermal oscillations (10-12-10-13); T is a lifetime of a loaded sample; 170 is the activation energy of fracture. The strength estimates made in accordance with Zhurkov’s theory for the samples broken for a period of about 1 s at 330 K are, naturally, much lower than those calculated for 0 K , as shown in the histogram (Figure 32) [68]; the ultimate strength of both commercial and laboratory-scale samples is lower as compared to the theoretical strength calculated for all widely used polymers under the above conditions. (For the sake of simplicity, only one theoretical level of strength is shown in Figure 32 for each polymer, though there is a good deal of scatter in the theoretical estimates.) Nevertheless, the experimental values of strength for some polymers are extremely high and are comparable with or significantly higher than the strength of conventional construction materials, such as steel and others.

77

Structural basis of high-strenght high-modulus polymers

"

PE K E U PAB

PEI

PVlzl

KIM

PP

Figure 32. Relation between the theoretical strength of different polymers calculated for 0 K (dashed lines), 330 K (solid lines) and their ultimate strength attained for lab-scale samples (dotted lines) and commercial products (waved lines)

Furthermore, the experimental data strongly depend on the conditions of testing. Typically, all tests are performed on an Instron testing machine operating in the extension mode, the extension rate being 10 cm/min. A higher rate of loading should lead to better results. The highest strength is achieved for UBMWPE fibres and films obtained by drawing of the samples prepared through surface growth [18,140] or gel technique [16,17]. In the first case [18], 13% of the as-prepared samples demonstrate a strength of about 10 GPa, which is the highest figure cited in the literature. In the second case [16], a strength of about 7 GP a is attained. Drawing of single crystal mats [137], solid-state extruded single crystal mats [141] or solid-state extruded reactor UHMWPE powder [141] also allows the obtaining of materials of very high strength (about 6 GPa). The strength of ultimately drawn melt-crystallized polymers is always lower than that of solution-processed ones because of their poor drawability. Another reason is the lower molecular weight of melt-processed polymers, which results in larger amounts of molecular ends, playing the role of defects. The processing via melt of a polymer of higher molecular weight is limited because of its high viscosity. The strongest melt-crystallized P E samples exhibit a tensile strength of about 1.5 GPa [11,159,160]. Unlike the theoretical estimates of strength, the theoretical values of Young's modulus show a slight dependence on temperature and can be compared with the experimental modulus measured at room temperature. More often, however, the experimental moduli are compared with the moduli of crystallites calculated from X-ray data (see Chapter 10). Figure 33 [68] shows a histogram of experimental moduli and the Xray moduli for the same polymers as in Figure 18. UHMWPE samples

V. A . Marikhin, L. P. Myasnikova

78

l.....

.....a

q‘ 100 50

......

FL

..... .....

......

......

Figure 33. Relation between the Young’s modulus of crystallites in different polymers measured by X-ray technique (solid lines) and the ultimate moduli attained for lab-scale samples (dashed lines) and commercial products (dotted lines)

demonstrate again the best results. The stiffness of the ultimately drawn UHMWPE samples practically attains the theoretical level equal to 220 GPa. One should note, however, that these high values are obtained typically when the modulus is calculated from ultrasound experiments. The figures obtained by mechanical testing are much lower and depend drastically on the testing speed. Young’s modulus of the same UHMWPE samples derived from stress-strain curves is only 150-160 GPa. Kevlar and POM also possess a stiffness close to that of an ideal crystal. We have attained high Young’s modulus for as-prepared P E T samples produced through multi-stage zone drawing from a specially treated initial material [76]. Sufficiently high moduli can be obtained with other polymers, too. The theoretical considerations yield a tensile strength lower than Young’s modulus by approximately a factor of 10 [169]. This relation is observed, however, for low-molecular solids only. For polymers, the experimental values of tensile strength are always lower than 0.1 of their moduli. This can be attributed to the imperfect polymer structure that influences the tensile strength stronger than the axial modulus. It is worth noting that the tensile strength-modulus relationship differs for one and the same polymer produced by various techniques. For instance, PE samples produced by solid-state extrusion from melt-crystallized billets have sufficiently high Young’s modulus, typically as high as 70 GPa, yet they have tensile strength of only about 0.5 GPa [170]. At the same time, PE samples of similar molecular weight and molecular weight distribution obtained by multistage zone drawing exhibit a similar modulus (50 GPa) but a much higher tensile strength (1.5 GPa) [159,160]. This problem was extensively discussed in the literature [171,172]. The lower

Structural basis of high-strenght high-modulus polymers

79

tensile strength of the solid-state extruded samples was attributed to their substantially larger cross-section area as compared to that of the meltcrystallized/drawn filaments, since it was established that for samples of similar sizes and similar M , and MWD produced through various technique (surface growth/drawing and gel-spun/drawing) the tensile strengthmodulus relationship is the same [172]. However, different tensile strengthmodulus data are observed for polyethylenes of approximately the same M,, but with quite different M,, values produced through drawing of meltcrystallized samples [159,160,162,172,173]. In our opinion, the strengthmodulus relationship is controlled mainly by interfibrillar packing. As it was shown in [162], the molecular weight distribution strongly influences interfibrillar slippage. Young’s modulus is usually estimated from the initial slope of the stress-strain curves (at a strain of about 0.1-0.25%) when a tested sample is under a load much lower than the breaking one. If the fibrils are densely packed or they are interconnected by a large amount of tie molecules, the slippage will not operate, and the samples under investigation will exhibit a high striffness, provided that the content of extended chains is high enough. It is known that the solid-state extruded melt-crystallized billets have a densely packed fibrillar structure consisting of imperfect microfibrils and of those from extended chains. The content of the latter is insufficient to provide high tensile strength but it is large enough to result in a high modulus. At the same time the microfibrillar structure in the zone-drawn samples is more perfect, which enables one to attain both high modulus and strength. The interfibrillar packing may also influence another mechanical characteristic of oriented polymers, i.e. the strain at break. It is known that with increasing orientation, the strain at break rapidly decreases. In solidstate extruded samples it approaches asymptotically a constant value of about 3% which is reached at a draw ratio of about 15 [174]. However, ultraoriented high molecular weight specimens exhibit an increased strain at break with increasing tensile strength [18,174,175]. For instance, some ulrahigh strength surface growth/drawn samples reveal a strain at break as high as 10-30% [18]. We believe that the increase of the strain at break is due to ruptures of interfibrillar tie molecules at ultimate drawing, which facilitates fibrillar slippage in long loading experiments. The same phenomenon may govern the creep behaviour of ultraoriented polymers. There is still a great body of ambiguities related to this problem. The crucial question is whether interfibrillar or intracrystalline slip contributes more to the creep behaviour. The question, however, is so far open to discussion and much more work is required to elucidate this problem. To conclude this very brief description of the mechanical behaviour of oriented polymers, one should bear in mind that ultraoriented polymers lose their intrinsic properties, such as e.g. flexibility, and on bending or twisting behave like conventional low-molecular solids. They can be prac-

80

V. A . Marikhin, L . P. Myasnikova

Figure 34. Formation of kink bands on bending of ultraoriented UHMWPE fibres

tically deformed through high energetical rotational deformation modes (kinking), which is typical of low-molecular weight crystals. Even a slight bending of these extremely rigid and strong samples leads to the formation of kink bands in the zone of compression, as clearly seen in Figure 34. As it was shown in Section 2.4., kinking accelerates the fracture due t o multiple submicrocrack formation on the boundaries of kink bands and localization of dangerous sites (see Figure 18). The use of ultraoriented polymers is confined, therefore, t o composites where they are applicable as reinforcing elements. 5. Thermal properties of superstrong high-modulus polymers The study of the thermal characteristics of oriented polymers can provide information not only on the temperature range in which such polymers can be used, but also on the crystal sizes, their perfection, and on the structure of disordered regions in the microfibrils (see also Chapter 6). The melting temperature T: of oriented polymers is an important thermal parameter. Here, one should differentiate between three kinds of temperature [151,176]: (i) the equilibrium melting temperature of a perfect

Structural basis of high-strenght high-modulus polymers

81

crystal of an infinite size T:, which holds valid for a crystal size of about 1 p m when the surface free energy is negligible as compared to the bulk energy; (ii) the real melting temperature TA of a metastable imperfect crystal of a limited size l,, which is smaller than the equilibrium temperature, TA < T:, and varies with l,, as in the Thomson-Gibbs equation [151]; (iii) the experimental T, corresponding to the endothermal melting temperature maximum and obtained, for instance, by the DSC technique at a constant heating rate V (K/min) = const. The values of T, for a crystal may differ considerably, by as much as 10 K , due to superheating of the crystallites (at high V )followed by their rearrangement and recrystallization (at small V )during melting endotherm measurements [176,177]. For this reason the frequently reported T, data obtained at a fixed scanning rate are reliable only for an approximate estimation of the melting temperature, because they are usually higher than the real values and are obtained under incomparable conditions. This makes it difficult to assess the contribution of each factor to the drawing process as well as to the structural and other characteristics of oriented polymers. To eliminate this ambiguity, the T, measurements should be performed with samples of a small weight by varying the heating rate, and the T, values should be found by extrapolating the linear dependences

T, = j ( V 1 I 2 ) to

V = 0.

Many authors [9,137,178-1821 have observed an increase in T, and a decrease in AT, (the melting interval) with increasing draw ratio for samples drawn from the melt, gel and single crystal mats. For highly oriented samples, the melting temperature was as high as T, N 418 K at V = 10 K/min and sometimes even T, 21 428 K at isometric heating [182]. These high values of T,, comparable t o and exeeding the melting temperatures for extended chain crystals (ECC) obtained by Porter’s and Pennings’ techniques as well as during crystallization under high pressure [9,151], have sometimes led t o the assumption of a radical structural change of highly oriented samples - formation of ECC during the drawing. However, independent WAXS measurements of crystallite size always indicated small longitudinal dimensions of the crystallites in these samples. Many authors have also noted a considerable growth of the T, values upon isometric heating of oriented samples as compared to the melting of samples with free ends. This fact was interpreted as being due to the smaller melting entropy because of a limited molecular mobility under loading [178,179]. We have pointed out above that one should obtain extrapolated values of T, in order to find the TA(X)and extreme TA values in the oriented state. Such studies have recently been performed [156, 183-1853. The objects under study were P E samples with M , = (0.1 - 4.5) x lo6 kg/kmol in the form of fibres, films, filaments or thin rods prepared by the six wellknown techniques listed in Table 2. In the general case, the draw ratio varied

V. A . Marikhin, L. P. Myasnikova

82

Table 2. Thermal characteristics of oriented PE samples produced in various ways

I I1 I11 IV V VI

X

M,

Preparation technology Surface growth technique with subsequent multistage zone drawing (MZD) MZD of gel-crystallized films MZD of gel-crystallized fibres Solid-state extrusion of single crystal mats Solid-state extrusion of melt-crystallized billets MZD of melt-crystallized films

T L , K AT;, K

1.5 x lo6 2.5 3.5 x lo6 200 1.5 x lo6 150

414.0 414.0 415.0

4.5 x lo6 300

417.5 0.05-0.07

lo5 lo5

25 30

408.0 409.0

0.40-0.50 0.05-0.07 0.04-0.05

1.8 0.30-0.40

from 2.5 to 300. For the sake of comparison, an initially isotropic P E (DR = 1) was also measured. Table 2 lists M,, the ultimate draw ratio attained by each technique, the mechanical, structural and thermodynamical data for the samples under investigation. The degree of crystallinity w, = AH,/AHk and the free energy of the interfacial end surfaces of crystallites y were found from the generally accepted correlations [151].The longitudinal lo02 and transverse l l l o sizes of the crystallites were calculated from the broadening of the X-ray diffraction peaks, and the long period L was found from SAXS. These data were compared with the strength c and the static modulus of elasticity E of the samples. Figure 35 shows the endothermal melting peaks obtained for an initial P E sample and for those oriented to different degrees by various techniques. The dependences of measured T, versus the heating rate are shown in

4

I

A I I I

411

411 415.5

Figure 35. DCS thermograms of PE drawn to various ratios: X = 1 (curve 1); 30 (curve 2); 60 (curve 3); 150 (curve 4) and 300 (curve 5). T h e samples are produced by the technique VI (1,2), I11 (1,2) and IV (5). Heating rate 0,3 K/min

Structural basis of high-strenght high-modulus polymers

83

Figure 36. Table 2 shows the true values of T; and AT; for PE samples ultimately oriented by six techniques. Let us analyze the observed effects. Melting of polymers is typically characterized by spreading of the phase transition when ATm is 10 K or more, and by the reduced temperatures Tm < T:. The Tm value depends on the crystallization conditions. As shown in Figure 35 this is valid for an isotropic PE but as the draw ratio increases, T, grows and the endothermal melting peak becomes higher and narrower. As the orientation degree of P E grows, the experimental Tm(V1/2) dependences are shifted toward higher temperatures almost without changes in their slope. Deviations of these curves from linearity are observed only at the initial stages of drawing at low draw ratios, i.e. when the fibrillar crystalline structure being formed is still unstable. The effect of thermal lag on switching from V = 0 to V = 20 K/min is as low as 2-3 K owing to the heat conducting medium used and t o the small weight of the samples (Figure 36). In the case of ultraoriented PE the polymer crystallites melt, in fact, at a definite temperature (“at a point”). This was first observed by Berstein et al. [185]. For instance, the peak in curve 5 (Figure 35), equals about 0.05 K in width, i.e. it is by two orders of magnitude narrower than for isotropic PE. In this case the equality of T; to Tk is reached, being estimated by different authors to be 416 K [151,176]. Consequently, ultraoriented PE can melt at an equilibrium temperature and within a “zero melting interval”, i.e. similar to the melting of

+

420 -

~ - o - - o -0 o -0-0 /--•/ ..+ rn-*~-o :o :- ; o / o - o

>

.

-

34

A

f ---A=i=i-A-A-A77 410 i:/ ...~../ ..

kE

-A-A-A-A-A-~-A-A .A

15

A-4-a-A-

2 A-A-A-A-~-

400-..----

.

- -

A

6 I

A-

.-25 AA-

4.4 1.7

0 1

11 111 0 IV . V A VI A

84

V . A . M a r i k h i n . L. P. M y a s n i k o v a

crystalline solids of other classes. The achieved T, and AT; values correspond to those expected for hypothetical perfect macroscopic single crystals of PE. However, the degree of crystallinity w, of the samples studied did not exceed 87% in all cases. Another effect exhibited by ultraoriented P E samples is the appearance of two stages of melting [185] predicted theoretically by Flory [189]. They are: (i) a disturbance of the intermolecular order (decrease in intermolecular interactions); and (ii) the intramolecular transition from a straightened (trans) conformation of molecules in a crystallite to the statistical coil in the melt. As seen in Figure 35, at V = 0.3 K/min (Technique IV) a splitting of the narrow melting peak into peaks A and B with a distance between them of about 0.5 K is observed owing to the high resolution of the DSC technique used. At elevated heating rates and/or increased weights of the samples, no splitting occurs because of the instrumental broadening and overlapping of the peaks caused by the thermal lag. The appearance of the doublet peak of melting (A and B) in the DSC curves corresponds to the above two stages and is not associated with the instability of crystallites [185]. It has been found that ultraoriented samples retained the same length after passing only through the melting peak A with subsequent cooling (a decrease in intermolecular interactions). They contracted, transforming into a droplet only after passing through peak B (coiling of macromolecules). There is another explanation of the two peaks observed in the melting of fixed fibres of highly oriented PE. According to [187,188]it is a result of a transition from an orthorhombic structure of crystallites to a hexagonal one and then to a melt. This does not contradict the first assumption, because the hexagonal structure is indeed characterized by a reduced intermolecular interaction, increase in the specific volume and molecular mobility. The increase of T; in the case of the ultraoriented constrained sample up to a temperature above T: is caused by tensile stresses, emerging therein during the heating, since such a sample has a negative thermal expansion coefficient [151,176]. The above data allowed us to estimate T; and AT; values from peak B for ultraoriented samples that exhibit a melting doublet. From the Thomson-Gibbs equation I1511 it follows

T&= T i [l - 2~~(AH~p,,l,-,)-'] where 7i is the end surface energy of crystallites (- 10 erg.cm-2 for PE) [151]. Since 1002 and i l l 0 change only slightly during the drawing of P E [lo, 11,1621, the growth of T&and especially T&+ T: can mainly be due to the reduction of the free energy of the end surfaces of crystallites yi that drops to zero at the limit. This points t o an almost complete disappearance of the interfacial boundaries between the crystallite edges and the intercrystalline regions (absence of chain folding, etc.) in ultra-oriented PE.

Structural basis of high-strenght high-modulus polymers

85

A considerable increase of the draw ratio accompanied by the melting temperature T, rise contributes to the thermal stability of ultraoriented polymers, expanding their applicability. Thermal stability depends primarily on the attainable draw ratio. For instance, for superoriented P E samples obtained by drawing of meltcrystallized films (type I, DR = 20 [l89]), a 5-7% shrinkage can be detected only at fairly high temperatures (408 K) close to the melting one. For conventional, slightly oriented samples, the shrinkage at this temperature is as high as 90% or more. Ultraoriented samples produced by gel technology (type V, DR = 90) exhibit a still greater stability - a 5% shrinkage occurs only at 412.5 K, followed by an almost complete shrinkage (91%) in a narrow temperature range for a sample with equilibrium melting temperature of 413.5 K. An extreme temperature dependence of the shrinkage stress us,.has been found [189, 1901. The initial abrupt rise of us,.in a certain temperature interval (T 363-383 K for type I samples, T 398 K for type I1 samples) is followed by its drop as the temperature increases further. The shrinkage stress reaches a maximum value comparable to that necessary for orienting the samples (ui, 10-30 MPa, ui: 42-46 MPa). The increased us,in the first part of the curve is attributed t o the temperature dependence of entropy forces arising in the extended entanglement network [163]. The higher stability of ultraoriented samples, as compared t o less oriented ones, is associated with a large longitudinal size of crystallites which acts together with the entanglement network [189]. However, these concepts require additional analysis, since the interpretation of WAXS data on crystallite sizes 1002 > L is ambiguous (see next section). The remarkable shrinkage and the respective drop of X in the second part of the curve occur at temperatures initiating a high mobility of macromolecules in crystallites (a-relaxatioh). This produces a crystallite rearrangement due t o partial melting, recrystallization and plastic slippage along the chain in the crystal planes. The macromolecular packing in the crystallites becomes loose at the orthorhombic hexagonal cell transition at T, in loaded samples. This also facilitates chain slippage prior to the ultimate melting and complete shrinkage.

-

-

-

-

6. Structural peculiarities of highly oriented polymers

Since extreme mechanical properties have been attained only with ultrahigh molecular weight polyethylene, it is very important t o understand the peculiarities of the polyethylene molecular and supermolecular structure that provide a material with extraordinary characteristics and then t o apply this understanding for producing other polymeric materials with enhanced mechanical properties (see also Chapter 15). It was found that the major structural element controlling the proper-

86

V . A . M a r i k h i n . L. P. Myasnikova

ties of oriented polymers is the microfibril. The genesis and development of the microfibrillar structure during its plastic deformation was described in Sections 2.2 and 2.3. Since microfibrils have a heterogeneous structure, characterized by a periodic alternation of ordered (crystalline) and disordered (amorphous) regions, it is reasonable t o suppose that the properties of oriented polymers are primarily controlled by defects localized inside the microfibrils, i.e. by the disordered intrafibrillar regions. The structure of the disordered regions becomes more perfect with increasing the draw ratio. The question arises as t o what extent it is possible to eliminate on drawing the multiple microfibrillar defects such as gauche-conformers, dislocations, disclinations, so that t o remove the interfacial crystalline boundaries, i.e. t o approach the microfibrillar structure t o that of needle-like crystals having mechanical properties close to the theoretical predictions. It follows from SAXS studies that at high draw ratios the densities of the two regions of the long period become almost equal, i.e. this method, starting from a certain DR well below the ultimate one, is not insensitive t o the boundaries between two regions, so that the whole microfibril can formally be considered as a needle-like crystal. However, according to the data obtained by other techniques, e.g. WAXS, this is not the case. As follows from the model of microfibrillar structure (see Figure ll),the longitudinal crystallite size 1002 is typically smaller than the long period L. Usually 1002 increases with increasing draw ratio at the expense of additional crystallization of the extended macromolecular portion in the disordered intrafibrillar regions and the 1002 value becomes closer to L. The crucial question is whether the interfaces between the crystalline and amorphous regions can disappear completely, so that a set of crystallites with any size 1002 multiple to L can be formed, up t o fibrillar crystals of the ECC type. WAXS data do not allow this assumption, though such a conclusion was drawn by some authors attributing the observed reduction of the halfwidth of (002) reflexes to the excess of the longitudinal crystallite size over the magnitude of L . The routine procedure for the establishment of the apparent crystallite size was used. The generally accepted concept of crystalline bridges connecting the neighbouring crystallites (folded blocks, according t o the Peterlin model) was developed on the basis of these calculations. A method for calculation of the size distribution of these apparent crystallites was suggested by Ozerin 11911 . The formal calculation of crystallite size distribution for ultraoriented samples drawn from single crystal mats or from gel-crystallized materials has indicated that even in these extreme specimens there are a lot of small crystallites with sizes smaller than L together with crystallites with sizes as high as 5 L (Figure 37). It is thus clear that the interfaces between the crystalline and amorphous regions cannot be eliminated for the majority of long periods. This is natural, because WAXS is very sensitive t o small distortions of the order of a few fractions of an angstrom, in a coherent arrangements of atoms. It was recently mentioned [192,193] that P E disclinations with the rota-

Structural basis of high-strenght high-modulus polymers

87

15, a

I

10 -

5-

0 0

200

400

1002

,A

\

200

400

600

I,,,

A

Figure 37. A typical crystallite size distribution curve for: (a) melt-crystallized drawn HDPE with X = 5 (curve 1) and X = 30 (curve 2); the arrow indicates the long period L; and (b) drawn single crystal mat of UHMWPE with X = 400 [191] tion angle of trans-zigzag planes over 90' or 180' cannot migrate through the crystallites. Probably, just these defects are finally concentrated on the interfacial crystalline boundaries leading to the limitation of the sizes of the major portions of the coherent regions (1002 < L ) detected by WAXS. The question arises as to what represent the coherent regions of the sizes larger than L. It was established that this effect can be attributed to the purely diffraction phenomenon associated either with the contribution of one-dimensional diffraction [lo71 or with formation of coherent arrangement of the neighbouring crystallites inside the microfibrils [108]. One-dimensional diffraction is considerable if there are long portions of individual extended chains that are randomly distributed over the fibril cross-section and pass from one crystallite into another one through a disordered region or through several neighbouring long periods. A large co-

88

V. A . Marikhin, L. P. Myasnikova

herent scattering region can arise also from neighbouring crystallites that, in the case of a small difference in the lengths of the chain segments in the disordered regions, can arrange in such a way that they scatter in phase with respect to each other. This leads to a narrower 002 peak and its higher intensity, which was erroneously interpreted as an increase in the crystallite size. Since the X-ray diffraction intensity is proportional to the number of scattering atoms, we believe that the coherent crystallite arrangement has a greater contribution to the intensity of meridional peaks than onedimensional diffraction. Therefore, it is unlikely that crystallites with sizes larger than L appear during drawing, although the individual chains crossing the disordered regions between the neighbouring crystallites do also exist. Thus the analysis of diffraction patterns leads to the conclusion that in ultraoriented polymers there are neither crystalline bridges such as those suggested by Ward, nor ECC crystals [194]. These data also suggest a significant perfection of the microfibrillar structure and equalization of the tie segment lengths in disordered regions by as much as a few fractions of an angstrom. An independent information on the lengths of individual extended segments can be derived from LAM Raman spectroscopy. We have found [69] that all the drawn UHMWPE samples obtained by solid-state extrusion of single crystal mats have a bimodal trans-zigzag length distribution irrespective of their draw ratio, which was calculated from the peak position in the Raman spectra (Figure 38). The peaks were observed at 250 and 350 A for samples with DR = 5 , 9 and at 350 and 500-600 A for samples of higher DR. The second peak slightly shifts toward low frequencies with the drawing. Comparison of the calculated lengths of trans-zigzags with the parameters of the microfibrillar structure obtained by WAXS ( L = 20-

Figure 38. Length distribution of trans-zigzags in PE samples obtained by solid phase extrusion with subsequent hot drawing in an oven u p to draw ratios: X = 6 (curve I ) , 30 (curve 2), 78 (curve 3) and 102 (curve 4)

Structural basis of high-strenght high-modulus polymers

89

21 nm and I, = 4-5 nm) indicates that the appearance of two peaks in the LAM distribution may be attributed to the existence of two types of extended chains in microfibrils with lengths 11 = L I, and 12 = L lc,.. The fact that the 35 nm peak does not change its position for all drawn samples suggests that the crystallites grown during necking are preserved up t o the ultimate draw ratio together with the boundaries between them. The existence of a low-frequency peak confirms the concept of extended tie molecules crossing the disordered regions and neighbouring crystallites, and evidences for a tie molecular length distribution even in ultraoriented samples. A WAXS study of the crystallite behaviour in the high-strength P E samples [195-1961 (a = 5 GPa) under statical loading also confirms this conclusion: not more than 30% of the chains appear to be subjected to ultimate stress. This helps to gain some insight into the tenacity of these samples, which is equal to approximately one third of the theoretical predictions. At ultimate stress, the most overstressed molecules may slip relative to their neighbours at a distance of approximately c/4, where c is the P E lattice constant. As shown in Section 5, in addition to the improvement of the mechanical characteristics, the structural perfection of oriented polymers leads t o better thermal properties (to higher melting temperature and thermal stability together with smaller thermal shrinkage). Moreover, the study of the melting of oriented samples can provide additional information on the state of macromolecules in the disordered regions, because the melting characteristics of crystallites can be substantially affected by the number and conformation of tie molecules [176]. The data obtained [183-1851 indicate that the measured thermal characteristics of melting of ultraoriented PE produced through gel-technology or single crystal mat drawing correspond t o those expected for an equilibrium single crystal (TA + TA, A T 0). This is a sign for a gradual disappearance of the interfaces between a crystalline and a disordered region and a perfection of the microfibrillar structure. The estimates of the end surface energy y, obtained from the Thompson-Gibbs equation [151] also support these assumptions:

+

+

-

DR = 6 yi = 100ergcm-2 DR = 34 yi = 2 0 e r g ~ r n - ~ D R = 200 yi - 0 It is clear from DSC data that the microfibril approaches an ideal crystal. With the help of DSC, it is possible to obtain information on the parameter of intrachain cooperativity of melting [197]. Melting of a polymer crystallite starts from the defect sites at a lateral face and proceeds through the successive separation of chain portions in the direction perpendicular to the c-axis of the crystallite [151]. The shortest chain portion consisting of v monomer units that transforms as a whole from a crystallite into a statistical coil in the melt can be arbitrarily referred

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to as an "elementary act" of the process. One can find the parameter v from the halfwidth of the melting peak using the Flory relation [197]

v = 2R(TA)2/(Ac.AH)-1 Here, R is the gas constant; in the first approximation AH = AH& is the melting enthalpy. The estimates for oriented and ultraoriented P E samples show [184] that v grows with the draw ratio, this growth being much greater than that of the crystallite thickness. For instance, for the samples with a draw ratio of 34 (drawn melt-crystallized PE) v = 5.1038L and for the samples with DR = 200 (drawn gel-crystallized PE) v = 2.1048L, which means that the sizes of extended chain segments estimated by DSC are larger by several orders of magnitude than those of the coherent scattering regions derived from WAXS data. In addition, the low values of the melting interval AT; = 0.04 - 0.4 K also indicate the absence of an appreciable dispersion of the cooperativity parameter. Since v is comparable to the length of a molecule, one can conclude from DSC data that in highly oriented samples the molecules consist mainly of the straightened (trans) sections with length as high as 2.104hi, each passing through hundreds and thousands of crystallites and disordered regions (long periods). This means that a disturbance in the three-dimensional order of the intercrystalline regions should indeed be limited only by defects of molecular packing of the disclination type with rotation of the trans-zigzag plane. For this reason WAXS identifies the intercrystalline regions in ultraoriented P E as disordered ones, while DSC reveals these samples as defect single crystals (Figure 39).

Figure 39. Structural scheme of the intercrystalline regions in conventional oriented PE samples with X = 15 - 20 (a) and in ultraoriented UNMWPE fibres with X = 100 - 300 (b); Tie molecules have trans-zigzag (1); crankshaft (2); helix GG (3) or TGTG- (4) conformations or rotational (disclinational) defects (5)

Structural basis of high-strenght high-modulus polymers

91

Hence, the thermodynamic parameter v characterizes the general orientation of the majority of chains in microfibrils, so one can expect a correlation between Y and the sample strength. This is actually the case (Figure 40) of the PE samples of all production types, just except for Pennings' technique since these samples have a peculiar composite (shishkebab) structure. The crystallite connection by extended chains provides fairly high strength and modulus of elasticity, though the presence of fold crystallites leads t o significant broadening of the melting peak. The significance of this result is due to the fact that a direct correlation between thermal dynamics of melting and tenacity of oriented and ultraoriented polymers has been revealed for the first time. The mutual arrangements of microfibrils and their entanglements [lo] is of special importance in the analysis of the deformation-strength features of ultraoriented polymers. For instance, creep is the major disadvantage of drawn gel-crystallized ultraoriented P E samples. A possible reason for their high creep may be the poor packing of microfibrils because of the high porosity (up t o 50% in volume) of gel-crystallized polymers in their initial unoriented state, as follows from the electron microscopic data in Figure 3(d). In order to understand the porosity dynamics during drawing, we used the spin-probe ESR technique [198] allowing t o follow the molecular dynamics of stable nitroxyl radicals which were vapour-introduced into the samples at room temperature. In the ESR spectrum for a sample with DR = 12 (neck), slow and fast components that characterize the spin-probe rotation with correlation times 7c varying with the structure of the radicaldiffused regions were identified. Only the fast component was observed in the ESR spectrum of ultraoriented samples with DR = 100.

8 h

t

7LL

+ Figure 40. Dependence of the tensile strength of oriented and ultroriented PE samples on the parameter of intrachain cooperativity of melting u. T h e techniques used for orientation are indicated as in Figure 38

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The analysis of the temperature dependence of the ESR spectra (the activation energy of spin-probe rotation E,) and the SAXS data lead t o the conclusion that the slow component is characteristic of radical penetration into the intrafibrillar disordered regions, while the fast component is indicative of elongated pores between the microfibrils. It has been found that the porosity of samples oriented up to DR = 12 (neck) is also very high (40-50% in volume) and can be reduced only down to 20% on drawing up t o DR = 100. The change of E, and the spin-probe rotation rate indicate that the interfibrillar spacings become narrower and elongated and their transverse size cannot be less than lOA, which is the approximate transverse size of a nitroxyl radical. From the data obtained, one can conclude that the drawing of gelcrystallized UHMWPE filaments leads to the characterization of intrafibrillar disordered regions. The microfibrils become comparable in their structure to one-dimensional defective single crystals. Interfibrillar pores of these samples persist throughout the entire drawing range. This appears t o be very important t o the understanding of the discrepancy between the experimental and theoretical values of the elasticity modulus and tensile strength. It can partly be due t o ignoring the existence of pores in the calculations of the sample cross-sections. One measures only an apparent cross-section that is larger than the real one. A potential approach t o the further enhancement of the mechanical properties of this polymer material is the elimination of porosity of the drawn samples. References 1. A. J. Pennings, Makromol. Chem. Suppl. 2,99 (1979) 2. B. Kalb, A. J. Pennings, Polym. Bull. 1, 871 (1979) 3. G. K . Elyashevich, S. Ya. Frenkel, in: Orientation Phenomena in Polymers, Khimia, Moscow 1980, p. 9-13 (in Russian) 4. A. J. Pennings, M. Roukema, 33 IUPAC Intern. Symp. Macromol., Montreal, Canada (1990) 5. P. J. Barham, A. Keller, J . Muter. Sci. 20, 2281 (1985) 6. J . Rietveld, A. J. McHugh, J . Polym. Sci., Polym. Lett. Ed. 21,919 (1983)

7. V. A. Marikhin, A. I. Valtonen, V. M. Zolotarev, A. W. Mirza, L. P. Myasnikova, A. E. Chmel, Vysokomol. Soedin. A32, 11, 23, 78, 2384 (1990) 8. A. Peterlin, J . Mater. Sci. 6 , 490 (1971) 9. “Ultra-High Modulus Polymers”, edited by A. Ciferri, I. M. Ward, Appl. Sci. Publ., London 1978 10. V. A. Marikhin, L. P. Myasnikova, “Supermolecular Structure of Polymers”, Khimia, Leningrad 1977 (in Russion) 11. L. P. Myasnikova, Ph.D. Thesis, 1972, Ioffe Physico-Technical Inst., Leningrad 12. V. A. Marikhin, L. P. Myasnikova, V. A. Suchkov, M. Sh. Tuchvatullina, I. I. Novak, J . Polym. Sci. 380, 195 (1972)

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170. S. Kojima, R. S. Porter, J . Polym. Sci., Polym. Phys. Ed. 1 6 , 1729 (1978) 171. A. Peterlin, R. S. Porter, “Flow-induced crystallization”, in: Polymer Systems. Midland Macromolecular Monografs, edited by G. R. L. Miller, Gordon and Breach, New York 1979, p. 168 172. P. Smith, P. J. Lemstra, J. P. L. Pijpers, J. Polym. Sci., Polym. Phys. Ed. 20, 2229 (1982) 173. W. Wu, W. B. Black, Polym. Eng. Sci. 19, (1979) 174. W. G . Perkins, N. J. Kapaty, R. S. Porter, Polym. Eng. Sci. 16, 200 (1976) 175. P. Smith, P. J. Lemstra, J. Mater. Sci. 15, 505 (1980) 176. V. A. Berstein, E. A. Egorov, “Differential Scanning Calorimetry of Polymers”, Ellis Horwood, Chichester 1993 177. K. Illers, European Polym. J. 10, 911 (1974) 178. I. Clements, G. Capaccio, I. M. Ward, J. Polym. Sci., Polym. Phya. Ed. 7, 6939 (1979) 179. A. Peterlin, G. Meinel, J. Appl. Phys. 36, 3028 (1965) 180. B. Wunderlich, G. Gzonnyj, Macromolecules 10, 906 (1977) 181. V. I. Selikhova, L. A. Ozerina, A. N. Ozerin, N. F. Bakeev, Vysokomol. Soedin. A28, 342 (1986) 182. T. Kanamoto, T. Hoshiba, T. Yoshimura, K. Tanaka, M. Takeda, Reports on Progress in Polymer Physics in Japan 2 8 , 227 (1985) 183. V. A. Berstein, E. A. Egorov, V. A. Marikhin, L. P. Myasnikova, Preprints of IVth Intern. Symp. on Chem. Fibers, Kalinin, USSSR 1986, vol. 1, p. 132 184. V. A. Berstein, E. A. Egorov, V. A. Marikhin, L. P. Myasnikova, Int. J. Polym. Materials 22, 167 (1993) 185. V. A. Berstein, A. V. Savitskii, E. A. Egorov, I. A. Gorshkova, V. P. Demicheva, Polym. Bull. 12, 165 (1984) 186. P.J. Flory, Proc. Royal SOC., London, Ser A., 834, 60 (1956) 187. A. Pennings, A. Zwijnenburg, J. Polym. Sci., Polym. Phys. Ed. 1 7 , 1011 (1979) 188. A. Pennings, J. Smook, J de Boer, S. Gogolevskii, P. F. van Hutten, Pure Appl. Chem. 55 777 (1983) 189. G. Capaccio, I. M. Ward, Colloid Polym. Sci. 260, 46 (1982) 190. D. T. Grubb, A. Keller, Colloid Polym. Sci. 256, 218 (1978) 191. A. N. Ozerin, Yu. A. Zubov, Vysokomol. Soedin. A 2 6 , 394 (1986) 192. D. H. Reneker, J. Mazur, Polymer 24, 1387 (1983) 193. D. H. Reneker, J. Mazur, Polymer 29, 3 (1988) 194. S. N. Chvalun, Vysokomol. Soedin. A 3 3 , 508 (1991) 195. A. I. Slutsker, A. V. Savitskii, K. Ismonkulov, A. A. Sidorovich, Vysokomol. Soedin. A28, 978 (1986) 196. A. I. Slutsker, A. V. Savitskii, K. Ismonkulov, A. A. Sidorovich, Vysokomol. Soedin. B28, 149 (1986) 197. P. Flory, Proc. Royal SOC., 49, 105 (1961) 198. B. E. Krisyuk, V. A. Marikhin, L. P. Myasnikova, N. L. Zaalishvili, Int. J. Polym. Materials 22 161 (1993)

Oriented Polymer Material> Stoyko Fakirov Copyright 0 2002 Wiley-VCH Verlag GmbH & Co. KGaP

Chapter 3

X-ray diffraction by quasiperiodic polymer structures

R. Bonart

1. Introduction Since their discovery in 1895 by C. W. Roentgen, X-rays have been used for the “visualization” of bones and internal organs in living organisms and of inclusions and defects in metallic details. However, it was only after the advent of X-ray diffraction in 1912 thanks to von Laue, Friedrich and Knipping that an approach t o “fine structure” research was created, i.e. to the study of the location of atoms and molecules in solids and liquids. The relevant basics are encoded in the International Tables for X-ray Crystallography [l](see also [2]). At the first level, the basics concern low molecular weight crystals with 7 crystallographic systems, 14 Bravais lattices and 230 space groups. Nevertheless, the basic relationships are valid also for polymers and their crystallographic characteristics are summarized in the “Polymer Handbook” by Brandrup and Immergut [3]. Crystals are characterized by their Bravais lattice with the lattice translations a * c1, b ++ c2 and c * c3 in the 1-, 2- and 3-directions, respectively; by their bases, i.e. the location of atoms and molecules within the lattice unit cell; and by the external shape. The product of the three edges of the unit cell ci gives the unit cell volume of the crystal:

V,

= Vcell =

[ c I c ~ c ~= ]

clc~c3sinacosP

where cr is the angle between the 1- and 2-directions and

(1)

P

is the angle

R. Bonart

100

Figure 1. Crystal lattice axes. The 1- and 2-axes form the angle a. Angle ,B is the angle between the normals to the dotted 1-’&planes and the 3-direction. d3 is the net plane distance between the 1-2-planes

between the 3-direction and the normal t o the 1-2-plane (Figure 1). With cyclic change the same is valid for the planes 2-3 or 3-1, and their normals. To the crystal lattice corresponds a reciprocal lattice with the following reciprocal unit cell dimensions:

The cross-products c1 x c2, etc., are perpendicular to the corresponding planes 1-2, 1-3 or 3-1. Due to the equalities1.1 x c2l = c l c 2 s i n a l etc., it follows from Eq. (1) for the 3-direction that

Similar expressions can be derived for a1 and a2. For the designation of the reciprocal lattice vectors b, the Miller indices ( h ,k , 1 ) are used bhkl

= ha1 + ka2

+ /as;

with:

bhkl

= l/dhkl.

(4)

These indices are also used for the designation of the lattice planes and the net plane distances d h k l of a crystal, so that dl = d100, d2 = dolo and d3 = dool. The b h k l are situated perpendicular to the lattice planes (hkl); i.e. they have the same direction as the net plane distances d h k l . Their length is given by l/dhkl. To each reciprocal lattice point (or the reciprocal lattice vector b h k l ) corresponds one crystal reflection on the scattering pattern. A light-diffraction experiment with a model (Figure 2) demonstrates the relationship between the lattice and the reciprocal lattice in two dimensions. The scattering angles 2 e h k I appearing in the interference diagram are related through Bragg’s law

X-ray diffraction by quasiperiodic polymer structures

101

Figure 2. Light diffraction demonstrating the relationship between the lattice and the reciprocal lattice in two dimensions. The (01)-, (11)- and (21)-straight lines and their corresponding reciprocal lattice points are given

t o the wavelength X and the magnitude dhkr of the corresponding net plane distance d h k l , i.e., to the reciprocal lattice vector bhkl. The normals t o the corresponding lattice planes are at the same angle d with respect t o both the incident beam and the scattered one, and all three directions lie in the same plane. For this reason one can speak about “reflection” from the lattice planes, i.e., about a set of lattice planes being in a “reflecting position” provided that they satisfy the above conditions and vice versa, about a “reflection failure” when this is not the case. Except for the case when the interplanar spacing is too small, it is always possible to realize the “reflecting position” by means of rotation of the crystal under examination. Dealing with a fine, isotropic crystalline powder or with an isotropic semicrystalline polymer, there are always enough lattice planes in a reflecting position, regardless of the radiation direction (see also Section 4.2). Such a scattering pattern is characterized by Debye-Scherrer rings (Figure 3) with radii D h k l related to the distance a between the observation plane and the sample and t o the scattering angles 2 8 h k l by the following equation: 28hkI = arctan(Dhkl/a). Together with Bragg’s law, this equation leads to the net plane distances dhkl. In the case of powders with larger particles, the Debye-Scherrer rings can be resolved as point-like single reflections. The width of the homogeneous Debye-Scherrer rings provides a measure of the crystallite size, as proposed by von Laue. The diameter L h k l of the crystallite area (Lhkl being perpendicular to the reflecting lattice plane) satisfies the Scherrer equation:

The molecular disposition in the lattice cells determines the intensity of the Debye-Scherrer rings. Due to the extreme anisotropy of the polymer chains, one observes additional polymer-specific aspects which disobey the general crystallographic

R. Bonart

102 Observation plane

herrer Rings

tan(28 hkl) =

Dhkl --

a

Figure 3. Schematic representation of the scattering experiment leading to DebyeScherrer rings from an isotropic crystalline powder relationships. For instance, space filling seems to be more important than molecular symmetry in determining the crystal structure. Furthermore, polymers tend to form quasiperiodic, paracrystalline structures. Last but not least, the scattering at angles smaller than 2' is of particular interest since it provides information about the disposition of the amorphous and crystalline regions or about the structures resulting from demixing in multiphase systems. In the following Section 2, some general phenomenological aspects which are similar for all polymers will be discussed. Section 3 deals with the basics of the experiments, while Section 4 is dedicated to theoretical relationships, which are then applied t o simple lattice models in Section 5. One should bear in mind that lattice distortions can very often be observed with lowintensity scattering effects alone. The latter are only slightly noticeable by photographic registration and cannot be measured quantitatively by a counter. Nevertheless, even from such observations it is possible to obtain important information concerning structural peculiarities, provided that model structures are available. The theoretical interpretation by models makes sense, even when it is impossible to derive directly usable quantitative relations for the interpretation of the measurements. 2. Qualitative phenomenological aspects

2.1. Fibre diagrams While the low molecular weight crystals often belong to the cubic or hexagonal systems of most densely packed spheres, polymers are characterized by a looser hexagonal packing of rods (Figure 4). Rods can be displaced or rotated with respect to each other, along or around their axes, respec-

103

X-ray diffraction by quasiperiodic polymer structures

Polyethylene Chain cross-section

Pseudohexagonal packing

a

Unit

b-

Polyamide Chain cross-section

Pseudohexagonal

Figure 4. Pseudohexagonal packing of chain axes in the crystal structure of polyethylene (a) and polyamide 6 (b)

tively. It is relatively rare to deal with a neat hexagonal chain packing. Most often one observes triclinic, monoclinic or orthorhombic lattices] but never cubic ones. Furthermore] syndiotactic polymers crystallize partially in an extended conformation and isotactic polymers in a helical one where hexagonal lattices are observed. The chain direction or the rod axes are usually chosen as the 3-direction of the crystalline regions. Cellulose represents an exception] since, for historical reasons, the chain axes denote the 2-direction. Instead of forming irregular] powder-like aggregates] the polymeric crystalline regions form superordered structures] especially in the shape of lamellae, the chain axes being, on average, perpendicular to the lamellar top surface. The lamellae are organized in spherulites.

R. Bonart

104

Continuum and

a

Figure 5 . Continuum and molecular mechanic rotation moments k and m , respectively, acting during drawing of segmented polyurethane elastomers on the domains of hard segments. Depending on the domain shape - plate-like or rodlike - the moments act oppositely to each other (a) or in the same direction (b). The case in (a) results in a negative orientation of the hard segment axes When semicrystalline isotropic polymers undergo uniaxial drawing, the Debye-Scherrer rings reduce to arcs with width depending on the draw ratio from which the latter can be determined. In addition to the chains, the crystalline lamellae also contribute to the transfer of the forces. This is revealed particularly well in the case of low drawing by the continuum mechanic rotational moments. At the very beginning, the latter result in a negative orientation of the chains. With increased drawing, the lamellae break and disappear and the free chains orient into the draw direction. Such a antagonism between continuum and molecular mechanical rotational moments does not exist when an amorphous starting material is drawn uniaxially. Figure 5 shows the respective relations in the case of polyurethane elastomers based on diphenylmethane isocyanate [4,5]. The continuum and molecular mechanical moments act in the opposite or in the same direction, depending on whether there is a diol extender, where rod-like hard segments appear, or a diamine extender, where plate-like domains are formed. In the case of semicrystalline homopolymers, the dense lamellar packing creates additional troubles but the basic interplay between the rotational moments is still valid. Uniaxially drawn samples with chain axes in the draw direction show a fiber diagram with crystal reflections aligned in horizontal layer lines (Figure 6). The paratropic lattice planes with Miller indices (hkO) contain the chain axis (Figure 6(b)). The diatropic lattice planes (001) give reflections on or off the meridian (the vertical through the centre of the fibre pattern). The reflections ( h k l ) , ( h k 2 ) , etc., are on the first, second, etc. layer lines,

105

X-ray diffraction by quasiperiodic polymer structures

a

b

Figure 6. Schematic presentation of a fibre diagram with crystal reflections organized in layer lines (a). The equatorial reflections on the zero-layer line arise from the paratropic lattice planes (hkO) while the meridional or the off-meridional reflections arise from the diatropic lattice planes (001) (b). ci and ci are the projections of the unit cell edges on the equatorial plane

respectively. The fibre identity period c3 can be obtained using Bragg’s law (Eq. (5)) from the vertical distance between the layer lines regardless of the presence or absence of meridional reflections, i.e. regardless of the diatropic lattice planes being either perpendicular or inclined t o the chain axis. From the equatorial reflections, again by means of Bragg’s law, one obtains the distances dhko for paratropic lattice planes, and therefrom the cross section of the unit cell perpendicular t o the chain direction. The product of the fibre identity period and the unit cell cross section gives the cell volume V, (Eq. (1)). Figure 7 shows the scattering angle of the first seven equatorial reflections together with the respective b-values in the fibre pattern of a polyester based on adipic acid and 1,ghexanediol. With the b-values as distances it is possible t o construct by “trial and error” the (hk0)- or the equatorial planes of the reciprocal lattice and later to find the indices of the reflections as well as the unit cell cross section. Since in this case the edges of the reciprocal unit cell a1 and a2 are perpendicular t o each other, then the edges of the cell ci and ci are also orthogonal in 2-space. Their values are determined by the reciprocal values of a1 and a2,respectively. From the

R. Bonart

106 No

b

20

A1 21.0

0.2378;'

23.4

0.263 8;'

A2

A3 29.5

0.331 k'

A4 35.8 0.3998;'

FA& A5 37.5 0.42

fi'

A6 40.2 A7 43.1

k'

Ap

0.44fiA-' 0.477

A5

.......................

*

A7

................

.......................

--.:

C'21

a2 I I

L-

t

........,......

--+ C'l

Equatorial plane of the reciprocal lattice

Cell cross-section

Figure 7. Scattering angle, reciprocal lattice vectors, hkl-plane of the reciprocal lattice and the unit cell cross section of poly(hexanedio1 adipate). The absence of (100) and (010) reflections indicates the presence of a chain in the centre of the unit cell fact that the (100) and (010) reflections are missing, it follows that there is an additional chain passing through the unit cell centre. Although the ester groups require more space, one finds, within the measuring error, the same unit cell cross section as in the case of polyethylene [6] (Figure 4(a)). However, a limitation exists in the sense that the orientation of the CHa-zig-zag plane is not considered and also that very often it is not clear whether the ester groups in the neighbouring cells are at the same height or if they are displaced, i.e. whether ci and ci represent the unit cell edges or their projections on the equatorial plane (compare with Figure 6). Since the cross section of the polyester chains is almost the same as that of the CH2-chains, the neighbouring chains may be randomly displaced along the chain axis. This is proved for drawn segmented polyurethane and poly( hexanediol adipate): horizontal layer line bands are observed in its fibre diagram instead of definite layer line reflections. The first fibre pattern was obtained in 1925 by Katz [7] from stretched natural rubber (all-cis-l,4-polyisoprene).By that time this finding was difficult to understand in terms of crystallinity of rubber and unit cell size. The latter turned out to be too small in order to contain a full number of

X-ray diffraction by quasiperiodic polymer structures

107

molecules as in the case of low molecular weight substances. The model derived later assumes that the unit cell contains a full number of the monomer repeating units while the molecules protrude through numerous cells and even through many crystallites or crystalline regions. When crystallization is performed from very dilute solutions it is possible to build up crystallites containing a single molecule. 2.2. Crystal density, chain cross section and chain conformation

The crystal density can be evaluated approximately by assuming the number of “monomers per unit cell” and knowing the cell volume Vcell = V,. By comparison of the values with the experimental macrodensities (which are usually smaller by about lo%), one obtains the correct number of “monomers per unit cell” and then - the real crystal density p e . When the density of the amorphous regions pa is known, the volume crystallinity a of a semicrystalline polymer with macroscopic density p can be found:

a = - P - Pa Pc

- Po

(7)

The volume crystallinity should not be confused with mass crystallinity; the latter can be determined e.g. by calorimetric measurements. The amorphous regions appear in the scattering pattern as an amorphous halo. By comparison with the scattering intensity of the crystalline reflections, information about the degree of crystallinity can be obtained. Quantitative evaluation is however rather labour-consuming [8].In the case of highly drawn samples, the amorphous halo is distinguished by a certain anisotropy arising from preferential chain orientation in the amorphous areas. The quantitative evaluation of the amorphous anisotropy is also rather difficult [9,10]. In combination with the monomer length, the number of “monomers per unit cell” determines the number of chains passing the cell as well as their effective cross section. For instance, the chain cross sections of P E, poly(ethy1ene terephthalate) (PET) and polycarbonate based on bisphenol A (PC) [lla] are 18, 22 and 26 A’, respectively. The chain arrangement in the crystal depends primarily on the optimal dense packing in space [12]. The properties arising from the molecular symmetry play a secondary role, as is the case of crystallization of the helical isotactic vinyl polymers or of aliphatic polyamides with partially steric polar chains.The cross section, being uniform or non-uniform along the chain, is important for the packing in the space, as demonstrated on P C [13]. The same is valid for other polymers as well: the CHa-sequences in triclinic crystals of P E T [14] and of poly(buty1ene terephthalate) (PBT) [15] rotate out of the chain axis, either gradually or with two gauche positions, and consequently the distance between the residues of terephthalic acid becomes smaller.

108

R.Bonart

Depending on the chain conformation, axial loading acts on either (i) the intramolecular covalent bonds or rotation potentials or (ii) the intermolecular Van der Waals forces. Consequently, one observes higher or lower values of the elasticity modulus for crystals in the chain direction. A qualitative conclusion in this respect can be made even by the simple comparison of the completely stretched chain conformation and the real fibre identity period c g . More information can be gained by considering the change of the fibre identity period as a function of the macroscopic load over the sample [16]. Assuming the mechanical stress on a single chain to be roughly the same as the macroscopic stress applied t o the sample, one can semiquantitatively evaluate the crystal modulus. In the fibre pattern of stretched PBT, under load during examination, one observes new, spontaneously appearing meridional reflections instead of displacement of the load-depending reflections [15]. This behaviour is related to the fact that the initial gauche positions of the CHz-sequences are partially and non-uniformly transformed into trans positions. After removal of the load the intensity of the new reflections decreases but they disappear completely only after annealing of the sample in an unloaded state. Qualitative in nature, such experiments lead to a conclusion, even without a knowledge of the exact value of the elasticity modulus of the crystals, that any attempt to obtain high-modulus fibres or films from polymers with compliant crystalline regions will fail. 2.3. Anisotropy perpendicular t o the chain direction, planes of plates

In spite of the usually small deviations from the ideal hexagonal rod-like packing of the chain axes, the anisotropy of the lateral interaction forces leads t o formation of plates in the crystalline aggregates. Similarly to the pages of a book, these plates are very resistant to tensile or shear forces but at the same time they are easy displaceable with respect to each other. This phenomenon is frequently observed with aliphatic polyamides such as PA 6 or PA 6,6 [17]. During uniaxial drawing of amorphous PA 6, a statistically hexagonal y-modification appears, with the amide groups of the parallel chains being at the same height, resulting in formation of intermolecular hydrogen bridges statistically distributed from the right to the left hand side or in front and behind, etc. During subsequent annealing the y-modification [lS] transforms into the energetically more stable pmodification. These “modifications” represent paracrystalline states rather than displacements from equilibrium in the strict thermodynamics sence. The plate-like character of the polymer crystalline regions has a significant importance for the orientation and deformation behaviour. For instance, during the biaxial orientation of films, the plates are positioned parallel to the film plane. Thus the tensile strength in the main orientation

X-ray diffraction by quasiperiodic polymer structures

109

Draw direction

Figure 8. Position of P E T chains in biaxially drawn films. The planes of the plates are dotted

direction is determined by the chains and in the perpendicular one by the plates, while the weak interaction between the plates does not play any role (Figure 8). Due t o the longer “flow path” of the surface layer than that in the bulk, local shearing appears during uniaxial neck stretching [19]. For this reason, biaxial orientation results, in spite of uniaxial stretching. In order t o avoid destruction as a result of shearing, the plates take a position parallel t o the sample surface. In the case of fibres the plates are positioned around the fibre “skin”, protecting in this way the “core” what sometimes allows a partial separation of the skin from core. 2.4. Position sphere

The radial widths of meridional and equatorial reflections show, according t o Eq. (6), the diameter of the crystalline regions in the chain direction or perpendicular to it; for larger crystallites the reflections become sharper. The layer line reflections reveal also the effects of the longitudinal and lateral dimensions of the crystalline regions. The arc lengths of the reflections depend mainly on the orientation of the crystalline regions. Even at extreme orientation, however, they do not approach zero due to the effect of the crystallite dimensions. The position sphere and its stereographic projection can be used for the description of the general orientation states. Imagine a mathematical point-like sample placed at the centre of a uniform imaginary sphere

R. Bonart

110

Axial Average chain direction with respect to a given direction (parallel) C-axes 4

C-axes

t

I

a

(100)-Normals

(100)-Normals

*

Planar Average chain direction with respect to a given plane (parallel)

Figure 9. Position spheres for different orientations: (a) uniaxial; (b) biaxial; ( c ) uniplanar; and (d) biplanar orientation

and extend the orientation elements of interest, and especially the c3 axes and the plate normals until they reach the sphere surface. In this way one obtains a characteristic point distributiuon on the position sphere which reflects the respective orientation state. Uniaxially oriented samples where the c3 axes of the crystalline regions are mainly in the draw direction while the normals to the plates are isotropically distributed around them, show a uniaxial crystallite orientation (Figure 9(a)). An additionally introduced lateral stretching, driving the plates preferentially parallel to the film plane, i.e. parallel to both the main and the perpendicular draw directions, together with the simultaneous orientation of the chain axes and the normals to the plates, to biaxial orientation (Figure 9(b)). When an initially isotropic sample is subjected to uniaxial pressing, the result is an orientation of the chain axes perpendicular to the pressing direction. In cases when the normals t o the plates are distributed isotropically around the c3 axes, or they are preferably oriented in the direction of pressing, one speaks about uni- or biplanar orientation (Figures 9(c,d)). In the first case only the c3 axes are oriented while in the second case this is valid

X-ray diffraction by quasiperiodic polymer structures

111

for the normals to the plates, too. Furthermore, instead of chain axes and normals t o the plates, one can consider in a similar way other elements and determine their orientation [20]. The density distribution of the points of orientation on the position sphere can be obtained by sphere surface functions, in particular at uniaxial orientation, by means of Legendre polynomials. The coefficient of the second Legendre polynomial is frequently called Herrmans’ orientation measure: 1 2

f = -(3(cos2 e)

- 1)

where 0 is the angle between the orientation element considered and the symmetry axis. The degree of orientation f can be determined by means of birefringence measurements [21] or, in the case of fibres, by means of the velocity of sonic pulses [22] as well. Both techniques provide a measure of the chain orientation in both the crystalline and the amorphous regions. Therefore their comparison with X-ray measurements offers information about the orientation of the amorphous chains [23]. Both techniques have some peculiarities [19] that should be taken into account. Although being semiquantitative, the information they give is rather interesting and useful. The orientation of the amorphous chain segments between the neighbouring crystalline layers has the greatest importance with regard to the elasticity modulus or to the orientation of the crystalline regions. One has problems, however, with the poor thermal stability of those regions which can be slightly improved by special fixing processes. 2.5. Lattice distortions of the first and second hind. Distortion

parameter Polymers tend t o form mesomorphic, paracrystalline structures which cannot be strictly defined as crystalline or amorphous. This is related to the plate-like crystal construction that allows displacement of the plates with respect t o each other, as well as by possible imperfect orientation of benzene rings, side groups or other chain elements [24]. In 1932, in a study of surfactants by polarized light, Rinne has identified cr- and P-paracrystals [25], nowadays called nematic and smectic liquids [26]. Later Hosemann adopted the term “paracrystals” in order to describe statistically displaced lattices for which instead of the three lattice translations c1, c2 and c3 of an ideal crystal, the coordination statistics hloo(z), holo(z) and hool(z) for the statistically varied unit cell edges were used (Figure 10). cr = 1 to 3 refers to the corresponding coordination statistics while /? = 1 to 3 reflects the displacement direction. As a whole, one deals with nine displacement parameters which are equal to zero in the case of an ideal crystal; i.e. they do not play any role there.

R. Bonart

112

C

Figure 10. Schematic presentation of a paracrystal with statistically varied cell edges. The dislocation parameters A,, characterize near order distortion. a = 1 to 3 is related to the coordination statistics, p = 1 to 3 is related to the dislocation direction The near-order distortion is determined in paracrystals by the distortion parameter A&, without taking into account the far-field order, or in other words - whether despite the distortion of the near order a far-field order exists or whether the far-field order disappears as a result of near order distortion. The first case is observed with distortions of the first kind while the second one with distortions of the second kind (Figure 11). Non-correlated Debye-temperature-fluctuations of lattice atoms around their ideal periodic positions represent an example of a distortion of the first kind. The constant mean positions of the lattice atoms determine the far-field order, while the centres of gravity of the atoms at each moment fluctuate to a greater or lesser extent from their ideal periodic positions. Since the scattered radiation is not spectrally analyzed, the dynamics of

X-ray diffraction by quasiperiodic polymer structures

113

Figure 11. Lattice distortions of the first and second kinds. Distortions of the first kind (a) cause a diffuse scattering background. Regardless of the distortion, the existing far order can be detected in the sharp crystal reflections. Distortions of the second type (b) cause a broadening of the reflections

the lattice fluctuations does not play any role and should not be taken into account. Ideal mixed crystals are another example in this respect, since the basis of one or another unit cell varies but the lattice remains unaffected by these variations or shows only near order distortions. A similar situation is observed with cocrystallization of copolymers. The smaller the coherent region (region with a far-field order) and the quicker the disappearance of the far-field order, the broader and more diffuse the corresponding scattering maxima. Dealing with neat near order distortions, i.e. with distortions of the first kind, one observes, regardless of the distortions, sharp “crystalline” far-order reflections whose widths can be determined by Eq. (6). Eq. (2) is not valid for distortions of the second kind, since the coherent region is too small. This can be illustrated by the optical diffraction patterns in Figure 11. One has to take into account that

114

R. Bonart

the diffuse scattering background in Figure 11(a) should not be interpreted as an amorphous halo. The scattering structure reveals distortions rather than the presence of an amorphous fraction. The spot-like character of the

Singular lattice planes

a

Diffuse equatorial reflections

Figure 12. Special lattice types: (a) singular horizontal lattice planes resulting from local intermolecular interactions; (b) singular vertical lattice planes a t sufficiently constant chain cross section; (c) bent but equidistant (on average) horizontal lattice planes. Longitudinal displacements corresponding to a definite fraction of the fibre identity period as shown in (c) leads to singular lattice planes with small lattice plane distance inbetween

115

X-ray diffraction by quasiperiodic polymer structures

scattering patterns is not related to the problem discussed here, since it has another nature. The sharp reflections in the scattering patterns of copolymers or blends in the case of the expected presence of distortions of the first kind should not be considered merely as a proof of the lack of cocrystallization, even if the reflections are only slightly displaced from their ideal, distortionfree positions. In such cases much more attention should be paid t o the background and t o the transition region to small-angle scattering in order to separate the amorphous halo. Hosemann’s model of the ideal paracrystal is based on lattice distortions of the second kind. It offers a simple fitting of the nine displacement parameters (A:), = At, to the broadening of the reflections in the scattering pattern. Furthermore, the model also gives, to a good approximation, the broadening of the reflections due to the distortions. Discrepancies appear in the small-angle region and in the shape of the reflection profile. A recent model of Gaussian paracrystals is free of them [27]. 2.6. Special lattice types Lattices corresponding to Figure 12(a) are distinguished by singular lattice planes positioned perpendicular to the fibre axis and show sharp “crystalline” meridional reflections while the rest of the scattering pattern is “amorphous” because of an undefined distance between adjacent chains (Figure 13(a)). On the contrary, lattices such as those in Figure 12(b) (e.g. polyacrylonitrile belongs to this case) lead to sharp “crystalline” equatorial reflections in an “amorphous”, as a whole, fibre pattern (Figure 13(b)). The lattice in Figure 12(c) contains, in addition to the equidistant vertical lattice planes, other statistically bent, but on average equidistant, horizontal lattice regions. The vertical lattice planes lead to sharp equatorial reflec-

a

b

Figure 13. “Directional crystallization” according to Statton [28] for (a) poly(heptamethy1ene terephthalamide) and (b) poly(viny1 trifluoroacetate)

116

R. Bonart

Figure 14. Optical diffraction from a model illustrating the layer line bands of the second kind as a result of lateral broadening of the reflections

tions. The bent but equidistant lattice regions result in horizontal layer line bands (Figure 14). Considering both the polymer structures and the sometimes arising mesomorphic and paracrystalline chain packing, one can qualitatively evaluate, on the basis of the above-mentioned findings, the predominant intermolecular interactions and the related deformation behaviour. Thus, due to local lateral interactions, the parallel aligned chains in the lattice (as in Figure12(a)) should be at the same height, which is expected to lead to a a higher shear strength. During warm drawing, the complete crystallization of PET results in a number of sharp crystal reflections, while during cold drawing the fibre pattern is mostly “amorphous” , containing however a sharp “crystalline” meridional reflection [ l l b ] (Figure 15(b)). As far as the reflection arc follows a Debye-Scherrer ring, its width depends on the orientation and should not be considered as broadening of the layer line. The diffuse scattering around the equator arises from an undefined distance between the neighbouring chains, i.e. from a statistic orientation of benzene rings, while the chains related to the meridian arc, being “amorphous” as a whole, are already at the same heigth in the longitudinal direction. By careful observation one can find layer line bands in the fibre patterns of probably all polymers. In the case of PA they are of a diffuse-like nature while in other cases they appear as lateral broadening of the reflections. Concerning the layer line bands, one has to ,distinguish also between distortions of the first and second kinds. For instance, the pattern of highly stretched commercial P E T fibres frequently shows bands of the first kind on the first layer line, which, surprisingly enough, do not disappear after annealing. They possibly originate from the strained amorphous chain segments, the crystalline layers being kept apart from each other by coiled amorphous chains.

117

X-ray diffraction by quasiperiodic polymer structures

d

C

Figure 15. P E T fibre patterns: (a) amorphous oriented, without “crystalline” indication; (b) “crystalline” meridional arcs; (c) faint reflections pointed in the 2-layer line; (d) conventional fibre pattern. The third reflection in the first layer line is slightly displaced due to anomalous crystallite orientation

2.7. Small-angle scattering, fibrils, layer lattices In 1942, in their study of stretched PA 6 fibres, Hess and Kiessig observed for the first time long periods of about 100 in the chain direction and have explained them as a quasiperiodic alternation of amorphous and crystalline regions in the fibrils [29] (Figure 16(a)). The centres of gravity of the crystalline regions form, according t o Figure 16(b), paracrystalline macrolattices in the sense of Hosemann. During annealing, the crystalline regions grow t o crystalline layers spread out laterally, as shown schematically in Figure 16(c). In this case there is an increase of the layer line width of the long spacing reflections with increasing distance from the equator at which they are measured (Figure 17(c)). It follows that, in contrast to the assumption of Hess and Kiessig, they are not defined by the thickness of the fibrils according to the von Laue effect of the crystallite size (Eq. (5)), but they reflect the statistical bending cr of the crystal layers [30,31,32] (Figure 16(c)). The assumption of Hess and Kiessig is correct only when

a

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R. Bonart

Figure 16. Structure models for the interpretation of long spacing reflections: (a) original model of Hess and Kiessig; (b) further development of the model to a paracrystdine macrolattice according to Hosemann; (c) the layer lattice derived from (b)

the crystalline regions of neighbouring fibrils are not position-correlated. When such a correlation appears laterally outside the individual fibrils, one has t o take into account departures from the effect of the crystal size. Constant layer line width of long spacing reflections (Figure 17(b’)) or width increasing with the distance from the equator (Figure 17(c’)) can be used as criteria for distinguishing between these cases. In addition to the tendency of the laterally neighbouring crystalline regions to be pulled to the same height during annealing, thus forming statistically bent, but on average horizontal layers, one finds in other cases inclined crystalline layers resulting in a four-point scattering pattern (Figures 17(e,e’) and 17(f,f‘)). According to Statton [33] this is related to the necessity of space for the amorphous parts of the chains to spread laterally outside the fibrils. On the contrary, in the case of on average horizontal crys-

119

X-ray diffraction by quasiperiodic polymer structures

Paracrystalline layer lattice

C'

1 -c

-

0

-

-

I

b Random arrangement

Verttical to the fibre axes

f'

\I -

0

-

-

air= 0

-

7e

Hexagonal arrangement of crystallites

Inclined to the fibre axes

Figure 17. Schematic presentation of various structures of fibrils and layers with the corresponding small-angle scattering patterns. In the case (f) in addition to the shown structures one has to assume other ones rotated around the fibre axis

tal layers, the need of lateral space for the amorphous chain segments can evidently be satisfied by folding of chains. So far the tendency of formation of a 2- or 4-point patterns can be considered as a qualitative indication of a lower or higher degree of chain folding. One has to bear in mind, however, that a 4-point pattern can always be produced by a suitable deformation [31] and for this reason it is necessary to analyze the basic trend resulting in 2- or 4-point patterns. For instance, after uniaxial warm drawing, PE usually shows 2-point patterns while initially amorphous PET always shows 4-point ones. On the contrary, after drawing of crystalline PET one obtains a 2-point pattern. This supports the assumption that chain folding created during isotropic crystallization cannot be eliminated by subsequent drawing [32b]. Assuming that the chains, including their amorphous segments, move on the average during stretching in the draw direction, the conclusion can be drawn that in the absence of chain folding in the inclined crystalline and amorphous layers (Figure 17(f)), the chains should periodically depart leftward and rightward from the stretching direction since only in this case the available space is enough for the lateral spread of the amorphous chain segments [32b].

R. Bonart

120

3. Basics of e x p e r i m e n t s 3.1. X - r a y spectrum and absorption

In the X-ray tubes for fine structure analysis, a focused beam of electrons (after acceleration by voltage UO)meets a 10 x 1mm spot on the anode. In addition to the spectrum characteristic of the anode material, the X-rays originating therefrom bear another continuous noise-spectrum with a short wave limit at:

where e0 is the elementary charge, c is the light velocity and h is Planck’s interaction quantum. The expression in brackets gives the wavelength limit in A when the voltage is in kV. In polymer physics one works exclusively with Cu-anodes, in particular with the Cu-K, band at X = 1.54 A which is made monochromatic by means of a Ni filter and electronic discrimination or by using a Bragg reflection, e.g. on graphite single crystals. The latter reflect additionally the half-wavelength (the second order spectrum) which can result in misleading reflections. To avoid this, one has to reduce the X-ray voltage UO down to the disappearance of the interfering “half” wavelength. For instance, in the fibre pattern of stretched P E taken at a voltage of 30 kV as a X / 2 reflection of (002), a misleading reflection (001) is observed which disappears after reducing the tube voltage down to 15 kV. After passing through the sample the X-rays get weaker according to the Lambert-Beer law:

= ioe-PD = i o e - ( P / P ) P D

(10)

where io and 1’ are the intensities before and after the sample, respectively, D is the sample thickness, which, in relation t o the scattered light, has to be replaced with the radiation path in the sample (Figure 18). The exponent p =r u contains the real absorption r and the scattering coefficient u. p D is the mass per area in g/cm2, where the mass coefficient p / p derived from the mass density p appears to be an atomic property independent of the physical state of the sample and can be found in [l]. The mass-absorption coefficients of molecules or mixtures can be obtained by linear superposition of the tabulated ( p i / p i ) values of the elements i involved:

+

PIP

= x(pi/pi)(Pi/P) i

(11)

121

X-ray diffraction by quasiperiodic polymer structures

Slit

.....*i

Figure 18. Schematic representation to the definition of small-angle additional adsorption. i o - primary radiation, before the sample; i - scattered radiation; i’ - incident radiation after the sample including the small-angle scattering; i” - incident radiation after the sample with substracted small-angle scattering

In the case of PE, by applying the coefficients for C and H at X = 1.54A, ( p c l p c ) = 5.5 cm2/g and ( p ~ / p =~ 0.46 ) cm2/g

and molecular weights of 12 and 1, respectively, one obtains the following p / p value:

p/p

= [5.5 x (12/14)

+ 0.46 x (2/14)] cm2/g = 4.78 cm2/g

If for the density one assumes p = 0.96 g/cm3: p

= ( p / p ) p = 4.59 l/cm

The intensity of the scattered beam i increases with the number of the scattering centres proportionally to D. In other words, the incident beam and the scattered one will get weaker according t o Eq. (10) with increasing beam path length in the sample. For small scattering angles 20 M 0 one obtains the following dependence of the scattering intensity on the sample thickness: i=

-

io ~

e - p D

(12)

If the differential quotient with respect to D is given a zero-value, one obtains the “optimal” sample thickness: Doptirnal

=1 / ~

(13)

With the mass-weakening coefficient of ( p / p ) o = 12.7 cm2/g for atomic oxygen, the “optimal” sample thickness of polymers is in general between 1 and 2 mm. In the case of PE it is Doptirnal

= 2 mm

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R. Bonart

For chlorine-containing polymers such as polyvinylchloride (PVC) or polychloroprenes, etc. ,one has t o work with much thinner samples since (p/p)cl = 103 cm2/g at A = 1.54 A. It is important to note that the “optimal” thickness should be usually considered as an upper limit and that with thinner samples, however at longer irradiation times, one obtains a better angle resolution. If the X-ray tube is insufficiently cooled, the anode is damaged and no radiation appears, although the tube is electrically still perfect. With an increase of the voltage UO the electrons penetrate deeper in the anode and the hard noise-spectrum part increases. In the case of Cu anodes the optimal voltage is between 30 and 40 kV. Because the K-absorption edge = 1.39 A), a 0.02 m m of Ni is between the Cu K, and Kp bands (Acu-~# thick Ni foil is sufficient to suppress the ?!-, relative to the cr-band up to 1 part in 600. In this way, by means of an electron-discriminating counter, one obtains a sufficiently monochromatized Cu-K, radiation. This approach is not very effective with photographic registration, in which case a crystal monochromator should be preferred. Particularly for the small-angle area the use of scattering chambers under vacuum is recommended in order t o avoid the absorption losses and the misleading scattering background caused by air. Synchrotron radiation with a much higher intensity has been used recently as an X-ray source; at very short exposure times and by means of position-sensitive detectors it is possible to follow the kinetics of processes such as crystallization, melting, deformation, etc., in real time (see Chapters 2 and 11). 4. Theoretical relationships

The geometrical or kinematic interference theory assumes that all electrons of a scattering body reached by an incident beam emit in one and the same way secondary waves. The absorption of both the incident and the secondary radiations can be taken into account by the ad hoc introduced sample transparency T (20) which depends on the pathway in the sample and thus on the scattering angle 20. Multiple scattering and anomalous scattering are neglected.

4.1. Structure factor We consider a plane primary wave E o ( z ,t ) with amplitude Eo, frequency = 27rv and wave number factor Lo = 27rsO/A (so being a dimensionless unit vector in the incidence direction):

w

X-ray diffraction by quasiperiodic polymer structures

123

Figure 19. Principle scheme illustrating the beam pathway as dependent on the position 2 of the scattering electron, the incidence direction 80 and the observation direction 8

The electrons at position z in the field E o ( z , t )cause coherent secondary spherical waves with a phase position dependent on z

where r, is the scalar distance of the electrons to the observation point. With the unit vectors SO and s in the incident-direction and in the scattered one,

A, = ( Z . SO)- (Z . S) = z . (SO - S)

(16)

is the difference between the beam pathway and a hypothetical scattered wave at the centre (z = 0). In the case of Figure 19(a), z and s form an angle > 90' and their scalar product is negative; this is compensated by the negative sign of ( 2 . s ) . In the case of Figure 19(b), both scalar products are positive. Nevertheless, (z.s)has t o be considered as negative. Consequently, the phase position is always given by the negative scalar product of the position vector z and the scattering vector s - so

b=--

x

-

(k - k0)/27r

and thus by

where k is the wave number vector parallel to the observation direction B. A scattering body with a local electron density e(z) contains e ( z ) d 3 x electrons in a volume d3x at the position z.They emit secondary waves

124

R. Bonart

with identical phases -27rib. x , so that by integration over the electron density p ( x ) multiplied by exp{-27iib . x } the entire scattered radiation can be obtained. For the sake of simplicity one can substitute the individual distances rx of each electron to the observation point within the Fraunhofer approximation by the average value r = (rx):

J p(x)e-2*i(b.z)d3z

~ ( b) t , =- (Eo/r)fefee-'wf

(19)

00

As an absolute square, from Eq.(19) one obtains the experimentally observed scattering intensity:

where io = E i is the primary intensity at the place on the scattering body, T(b) is the sample transparency. The three-dimensional, spatial Fourierintegral of the local electron density e(z) in Eq.(19) is considered as the amplitude function:

With its conjugated complex

00

one obtains the structure factor (see Eq.(20)) as the absolute square of the amplitude function:

I ( b ) = R(b)R*(b)= IR(b)I2= IF{e(z)}12 The structure factor contains all structural parameters involved in the scattering experiment and for this reason only this factor will be considered further. The time dependence exp{-id} falls out when the scattering intensity is considered. At the same time the phase position of the scattered radiation with the imaginary part of the amplitude function is also lost. As a result, discussing an experimentally evaluated structure factor, one has to calculate the scattering by a trial and error procedure from a structure model until the measured scattering intensity and the calculated one get sufficiently close to each other. Thus the phase loss hampers the direct and clear evaluation of scattering patterns.

125

X-ray diffraction by quasiperiodic polymer structures

4.2. The Ewald sphere In a monochromatic scattering experiment with precisely defined radiation direction 80, the scattering vector b (Eq.(17)), being a function of the observation direction s, produces the locus of the surface of the Ewald sphere (Figure 20). The scattering vectors ending on the Ewald sphere are connected with the scattering angle 20 and with the wavelength X in the following manner:

2 sin 0 b= X

Primary beam Primary

a

Reciprocal lattice points

Scattered radiation

\

Goniometry

Texture goniometry

b Sample axis

Figure 20. Ewald sphere: (a) general principle; (b) reciprocal lattice points in “reflecting” and “non-reflecting” positions. By inclination of the sample axis at the angle 0 to the 1-3-plane one scans the %axis of the reciprocal space by means of the scattered intensity at 20 (goniometry). By simultaneous rotation of the sample around the inclined 1-axis one can scan the crystallite orientation in the 2-3-plane (texture goniometry)

126

R. Bonart

Thus the Ewald sphere represents the relationship between the threedimensional structure factor I ( b ) and the flat, only two-dimensional scattering intensity i(20) (Eq. (20)). Values of Z(b) outside the Ewald sphere have no significance for the scattering effect and this is especially valid for the reciprocal lattice points and the net planes which are in a “nonreflecting position” (Figure 20(b)). For the net planes in a “reflecting position” with reciprocal lattice points lying on the surface of the Ewald sphere, Bragg’s law (Eq. (5)) is valid, as it follows from Eq. (24) with b = l/dhkl. Each crystalline region of a polycrystalline material has its own reciprocal lattice and they all have the same origin b = 0. In the case of isotropic orientation of the crystalline regions, the different reciprocal lattice points with identical hk1 are distributed on concentric spherical surfaces, the intercepts of which with the Ewald sphere result in Debye-Scherrer rings shown in Figure 3. The radial width of the sphere shells grows inversely to the length L h k l of the crystalline regions in the direction of the respective lattice plane distance d h k l . With the differential following from Eq. (24)

one can thus obtain the Scherrer equation (Eq. ( 6 ) ) which is usually due to the fact that the mentioned sphere shells are cut from the Ewald sphere a t an angle 8 rather than radially. If the crystalline regions are oriented uniaxially, the reciprocal lattice points hkl with identical 1 form concentric circles in equidistant planes 1 = const which are perpendicular to the draw direction; the planes result in the above-mentioned layer line bands. When the sample axis in a goniometer is inclined at an angle 8 to the 1-3-plane’ and the scattering radiation is registered at 28, one examines the 3-axis of the reciprocal space (Figure 20(b)). If at the same time the sample is rotated in the texture goniometer around the inclined 1-axis, one obtains circles on the 1-2-plane of the reciprocal space and gains information on the orientation distribution of the crystalline regions. Since the choice of the axes is arbitrary, it is thus possible to probe the entire reciprocal space. 4.3. Pair distribution

With the integration variables x’ and x” the structure factor Z(b) (Eq. (23)) can be expressed explicitly as:

mm

After substitution of x’ = x

+ x” and d3x’ = d3x, one obtains

127

X-ray diffraction by quasiperiodic polymer structures

This contains the pair distribution which is designated further by a superscript:

-

a3

According t o the following scheme the structure factor I ( b ) is on the one hand the absolute square of the amplitude function R(b) (Eq. (23)) and on the other hand - the Fourier transform of the pair distribution of eN(x):

Vice versa, the pair distribution follows from the inverse transformation of the structure factor: F-’{I(b)} =

/

I(b)et2“’(b.”)d3b = e”(z)

(30)

The importance of the pair distribution can be illustrated in the following way. With ~ ( z ” ) d ~ xelectons ” in the unit volume d3xC“of a scattering d ~ x ~ ~ dto~ the x e(z z”)d3z body, there are e(z + ~ ~ ~ ) ~ ( x ” ) “distances” electrons in the unit volume d3x at a distance x from the first element. Since the same distance x appears at different positions in the scattering body, one has to integrate e(z + z”)p(x”)d3x”d3z over x” at constant x. The total number of all accomplished joint interelecton distances z is then given by e”(z).d3x. Actually, e - ( x ) (Eq. (28)) represents the distance density and d3x - the accuracy of determination of the distance 2. With b.x = blxl + b2x2 + b3x3 and d3x = dx1.dx2.dx3, it follows that

+

On the bs-axis, at b l = 6 2 = 0, this expression is simplified to:

Here, the double integral over 2‘1 and x2 is the projection of the pair distribution e ” ( x ) or the pair distribution of the projection of the structure e(z) on the x3-axis. The intensity changes on the meridian of the scattering pattern are also given by the projection of the structure on the respective parallel x3-axis.

128

R. Bonart

4.4. A special application example

On the meridian of the fibre pattern of a highly drawn segmented PU elastomer based on MDI and hydrazin as chain extender, one observes a weak reflection at 12 A-‘. Since its position depends on the chain extender, it can be assigned t o the hard segments. On the other hand, the hard segment length of this particular elastomer amounts to only 30 A and hard segments do not show any periodicity (Figure 21). This “controversial” situation can be solved by means of the light diffraction experiment shown in Figure 22. The neighbouring points in Figure 22a are displaced statistically irregularly up and down in the vertical direction but by a definite distance. Therefore, their projection on the vertical shows a period which results in sharp “crystalline” interference maxima on the meridian of the corresponding scattering pattern, although the point sequence itself in the vertical direction is nowhere periodic [34]. Back to the X-ray diagram considered, this observation leads to the question whether the neighbouring hard segments in the stretched PU elastomer are longitudinally displaced in an irregular sequence by 12 A above or below. If this is the case, one gets the scheme of arrangement shown in Figure 21 with formation of H-

I

I 4

Figure 21. Schematic arrangement of the hard segments in hydrazin-extended segmented PU elastomers based on MDI. The hydrogen bridges between the urethan and urea groups allow a longitudinal displacement by 12 8, of the hard segments with respect to each other

X-ray diffraction by quasiperiodic polymer structures

129

Figure 22. Light-optical model experiment. The points of the scattering model, are irregularly displaced upward or downward by a defined value which is reflected in the scattering pattern by sharp meridional reflections. Distant interferences are cut out since here only the relationship relative to the meridian is emphasized

bridges. It turns out that the 12 A reflection arises from a periodicity in the projection of the mutual arrangement of the hard segments rather than from a periodicity within the individual hard segments. 5. Simple lattice models

In addition t o the qualitative discussion in Section 2, here we shall consider in a rather simplified way point lattices with distortions of the first and second kind (Figure 11) as well as simple deductions from this analysis. In order to better illustrate the fundamental relationships, we shall start with ideal periodic lattices. The basis and the external size limitation of the lattices will be neglected as well as the intensity of the reflections and we shall concentrate at first on the point sequence on single lattice lines in l-direction. 5.1. Ideal periodic lattices

The normalized pair distribution (normalized “per lattice point”) of an ideal periodic point sequence of infinite length, with the period c1 is:

The first subscript in k l , o ( z ) is related to the axis direction and the second one to the ideal periodicity. p changes from -MI to +GO. hooo(z) = 6(z) ( p = 0) is the “distance” distribution of each lattice point to itself, hloo G h l ( z ) = S(z - c1) is the coordination statistics between the closest neighbouring lattice points, h200 = S(z - 2cl) is the distance distribution between the second next neighbours, etc. The corresponding structure

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R. Bonart

factor follows from the lattice statistics kl,o(z), through Fourier transformation, and it is called here the K-factor:

cJ

~ ~ , = ~ ~( { bk ~) , ~ (=z ) )

s(z - pcl)e-2"i(b.=)d3,

(32)

After some transformations, it is possible to show that, for the 3dimensional space, it describes a set of parallel equidistant (by l/q) planes which are placed perpendicular to the translation c1:

The other two translations c2 and c3 of the 3-dimensional ideal point lattice correspond to analogous K-factors - Ka,o(b) and K3,0(b) with the numbers k and 1. The product of the three K-factors leads to the reciprocal lattice with Miller's indices (hkl) and the reciprocal unit cell edges (Eq. (2)):

1

=-

v,

rxx

6(b - ha1 - ka2 - la3)

(34)

The cutting points of every three plane functions S(b1 - h/cl), etc., define 3-dimensional 6-functions with the weight l/(sin a cos p) where a and p are the angles shown in Figure 1. In order to work with normalized &functions S(b-ha1 - k a 2 - l ~ 3 ) , one has to introduce a factor which gives, with the product of the three edge lengths c1c2c3, the unit cell volume V, (Eq. ( 1))* 5.2. Distortions of the first hind

The above considerations are applied to a lattice with purely near-order distortions, for which a three-axial Gaussian curve displaced on c1 with variations A$ is used as coordination statistics hloo(z): h o o ( z ) = S(" - c1)

with

Dealing with purely near-order distortions, the distance distribution h ~ o o ( zbetween ) the second nearest neighbours with their centre of gravity at 2c1 shows the same variations as hloo(z):

131

X-ray diffraction by quasiperiodic polymer structures

Taking into account Eq. (33) and hooo(z) = 6(z), one obtains with = G(b) and F{hooo(t)} = 1 for the K-factor:

.T(g(z)}

C

+

~ ~ , = ~ ~( {bk )~ ( z=) (1 } - ~ ( b ) }~ ( b ) {e-2*ib.cl}p

+

= (1 - G ( b ) } G(b)Ki,o(b)-

(37)

The subscript I indicates distortions of the first kind. After a transfer to three-dimensional lattices, one obtains:

+

Z I ( ~=) { 1 - G ( b ) } G(b)Zo(b).

(38)

The ideal reciprocal lattice Zo(b) gives, independently of the present lattice distortion, sharp crystalline reflections which are weakened by a factor G( b). With increasing reflection order these reflections gradually disappear into the monotonically incrasing diffuse background 1 - G(b ). In light-optical model experiments (Figure 11) the reflection widths are given by the crystallite size, i.e. by the external dimensions of the scattering model. The slighly lower intensity of (10)-reflections as compared to that of the (01)-ones shows that in the model the variations = A& l-direction are somewhat larger than the variations At2 = A;2 in 2-direction. Dealing with non-correlated temperature fluctuations of the lattice points, G ( b ) with the temperature-dependent variations A$ = A&(T) is called the Debye-Waller factor. According to the same principle, one also finds sharp reflections which disappear more or less rapidly in a diffuse background, in the case of ideal mixed crystals where the background with b + 0 in general does not approach zero. In the case of correlated distortions of the first kind, in addition t o the zero-term hooo(z), one has t o take into account further distance distributions. This situation is illustrated by highly stretched chains displaced in the longitudinal direction as a result of an inhomogeneous force translation. When the periodicity within the chains is preserved, the lattice statistics of the non-distorted vertical point sequences is k 3 , 0 ( ~=) C S(z - rc3). With the ideal I<-factor in the 3-direction1 the lattice factor takes the following form:

Zl(b) = (1 - G(b)}K3,0(b)+ G(b)ZO(b).

(39)

Because of the multiplication in the first term, the diffuse background is limited t o only the horizontal layer lines. Thus the layer lines appear. The space between the layer lines is free of background. Crystalline reflections G(b)Zo(b)are placed on the broadened layer lines (1 - G(b)}K3,o(b),their width being determined by the effect of the crystallite size.

132

R. Bonart

In case that entire lattice planes are displaced with respect to each other, as in aliphatic polyamides, one finds a “background”

which, because of the multiplication by Kz,o(b)K3,o(b)is limited only on discrete straight lines in the layer planes 1 = const of the reciprocal lattice. It follows that the “background” arising from distortions is irregularly distributed over the entire reciprocal plane (hkl), forming however rod-like areas perpendicular to the distorted lattice planes as is the case of e.g. doubly oriented polyamide 6 [19] or highly drawn P E T [13].

5.3. Distortions of t h e second kind In the case of distortions of the second kind, the variations of the distance distributions hpoo(z) increase according to Gauss law of the expanding error being proportional to IpI. Thus we have the transform {gpoo} = G,OO= GIPI, and:

Hpoo(b)= F{h,oo(z)} = {G(b)}lPIe-2”ib.c1p

(41)

GO), one reaches Hosemann’s I<-factor, With Hpoo(b) + 0 (for p where for the sake of simplicity HI will be used for Hloo: ----f

+00

K ~ , I I (=~ )

+

C{HI(~)}~

=1+Re

H1( b ) 1 -H1(b)’

Hpoo(b)= 1 2Re

p=-00

The subscript I1 indicates distortions of the second kind. By further transformations and extension with 1 - H;(b) one obtains: Ki,II(b) =

1

+ Hl(b) -

1 - G2(b)

+

1 - Hl(b) - 1 - 2G(b) C O S ( ~ T ~ ~ C G2(b) ~ )

(43)

In the planes b l = h/cl { c o s ( ~ T ~ ~=c ~ 1)) with equidistant spacings l / c l which are vertical to c1, this equation is simplified to K1,11 = (1 G)/(1 - G). By analogy with the equidistant, in the l-direction, 5like plane functions in Eq. (32), discs appear here, which are practically &shaped for G(b) M 1 but at G(b) + 0 they broaden gradually and become more diffuse. In analogy to Eq. (34), it is possible to define a generalized reciprocal lattice for paracrystals in which the three paracrystalline K-factors (Eq. (43)) are multiplied by each other and their discs are perpendicular to

+

X-ray diffraction by quasiperiodic polymer structures

133

Figure 23. Schematic two-dimensional presentation of the ideal paracrystalline lattice factor in the reciprocal 1-3-plane as a product of the K-factors Kl,II(b) and K ~ , I I with ( ~ ) three vertical and five horizontal sections. Reflections appear in the area of penetration of every two sections, their width depending on the section profile at the observation points of the corresponding reflection c1, cz and c3. In this way one gets the lattice factor of Hosemann’s ideal paracrystal

ZHosernann ( b ) =

1<1,I1 ( b )I<2 ,I1 ( b )K 3 , I I ( b )

(44)

The cross-sections of any three discs result in more or less broadened reciprocal lattice maxima, their widths depending on the distortion parameter (Figure 10). As an illustration, Figure 23 shows the behaviour of the lattice factor in the 1-3-plane as a product of three vertical discs K i (from K1,11(b)) and five horizontal discs (from K3,11(b)).It is important to t o note here that the qualitative fit of the dislocation parameters the reflection broadening observed in the fibre pattern basically does not depend on the model of the ideal paracrystal, i.e. it has a general validity. The same holds for “discs” which are overlapping or becoming diffuse in the b-space on which the above-mentioned fit is based and which helps in an at least qualitative interpretation of the findings shown in Figure 13. 5.4. Inhomogeneous coordination statistics

The considered paracrystalline I<-factor is derived on the basis of coordination statistics of Gaussian type (Eq. (35)). As can be shown by folding operations, this result is, however, generally valid and does not depend on the type of coordination statistics [24]. Therefore its application to an inhomogeneous coordination statistics is also possible when chain parts can take

R. Bonart

134 I:

CI

c,

CI

c,

C)

i.

*:

mmmmr mlmmmmlml~~l~inmmIm

lmnim m

r L 2

.... CI

c1

c:

c,

c,

0-0-0

..

a 0

.

.

b

z

Figure 24. Bimodal coordination distances C A and c g in A-B copolymers or as a result of molecular inhomogeneous extension of fibrils. The distances C A and C B can be accordingly more probably statistically irregular rather than block-like ones or alternatingly distributed

alternatively only one, another and maybe a third position or orientation, etc. [35-381. In the case of chains which have shortened conformations in the unloaded state and stretch non-uniformly after loading, an inhomogegeous extension of fibrils can result, as shown in Figure 24. From the molecular point of view, one deals in this case with two discrete extension modes, A and B , with relative fractions X A and X B = 1- X A , respectively, and for the one-dimensional situation the coordination statistics is:

h(z)

XAS(z - C A )

+ (1 - X A ) S ( z - CB) = g(z - c)

(45)

For the Fourier transform one obtains:

H ( b ) = X A e - 2 " i b c A + (1 - XA)e-2"ibcB

(46)

With 1- IH(b)I2 = ~ X A ( ~ - X COS(~~~{CA-CB}) A) the I(-faCtOr (Eq. (43)) will take the following form: 2 x A ' (1 - X A ) cos(2rb{cA - C B } ) K ( b ) = 1 - lH(b)I2 1 1 - XAe-2ribca - (1 - X A ) e - 2 * i b c s 1 2 11 - H(b)12

(47)

In the case X A = (1 - X A ) = 0.5 the relations are rather simple g(z)

= 0 . 5 { S ( ~- a) + S(Z

+ a)

where a is the deviation of the monomer length from the average period c. The transform:

G(b)= cos(2~bd)

(48)

oscillates between $ 1 and -1. For a positive G(b),maxima at b = h / c appear in the usual way and they become more broad and diffuse for decreasing G(b),as for the K-factor (Eq. (43)). Figure 25 shows the straindependent reflection positions calculated by means of Eq. (47) in the case of

135

X-ray diffraction by quasiperiodic polymer structures

1 1 1

1 L

I

t

#

I

Figure 25. Reflection positions in the case of a special bimodal extension. The assumed deformation modes behave as 1 to 1.14. With an increase in the mole fraction from 20 to 80% of the extended fibrils, the macroscopic extension increases from 3% to 11%. The third order reflection shifts inward, as expected. On the contrary, the seventh order reflection remains unaffected

=1 (when non-extended) and CB = 1.14 (when extended). With an increase in mole fraction of the extended components from 20% to 80%, the total extension increases from 3% up to 11%.As expected, the first and second order maxima shift to the centre. Their initial position makes it possible to determine the total extension using Bragg’s law. On the other hand, the weak fifth-order maximum shifts outward and gives a misleading lower value of the coordination distance when Bragg’s law is used unproperly, a molecularly inhomogeneous extension. The monomer lengths are C A

136

R. Bonart

since one has to account for the newly appearing reflection (between the maxima of 3. and 4. order). The mole fractions X A = 1 and Xg = 1 lead t o an ideal periodic lattice. This analysis is performed by the tacit assumption that the coordination distances C A and C B are distributed in a statistically irregular way. In reality one deals with the formation of blocks or alternating sequences both in the case of liquid-crystalline copolyesters and molecularly inhomogeneous extensions, which cannot be accounted for by the K-factor (Eq. (47)). The replacement of the mole parts XA and XB by the linking probabilities P A A, PBB and PAB =PBA allows one to obtain the generalized K-factor:

where Q is a meaningless constant in the present case. In the statistically irregular case, ~ A +A ~ B B= 1, so that the third term in the denominator disappears. However, when blocks are formed with predominant homorather than hetero-linkages, ~ A +A~ B B> 1, and with alternating sequences A P B B < 1. in the chains, ~ A + Further, it should be noted that the complete scattering equation takes into account the molecular structure of the A- and B-units as well: this was not the case in the above considerations. Dealing with statistically irregular sequences of A- and B-units, one obtains for box-like “molecular structures” the well-known scattering equation of J . J . Hermans for the ideal lamellar stacks. Using the interference function for block copolymers, it is possible to derive, in addition, scattering equations for lamellar stacks with more or less differentiated lamellar thicknesses. Eq. (49) covers both the wide-angle and the small-angle regions. In the case of irregular comonomer sequences, one finds in the small-angle scattering a monotonically increasing background. When block formation starts, one observes a maximum at 6 = 0 which is related to the scattering effect of blocks. With an increase in the alternation of the comonomer sequences, a maximum appears at 1 / ( c ~ CB), corresponding to the newly formed periodicity C A + C B . The discussion of experimental results is beyond the frame of this presentation.

+

References 1. “International Tables for X-Ray Crystallography”, The Kynoch Press, Birm-

ingham, England 2. K. Sagel, “ Tabellen zur Roentgenstrukturanalysd, Springer, Berlin, Goettingen, Heidelberg 1958 3. J. Brandrup, E. H. Immergut, “Polymer Handbook”, John Wiley & Sons, New York, London, Sydney, Toronto

X-ray diffraction by quasiperiodic polymer structures

137

4. R. Bonart, K . Hoffmann, Colloid Polym. SCC.262, 1 (1984) 5. R. Bonart, F. Boetzl, J. Schmid, Makrornol. Chern. 188, 907 (1987) 6. C. S. Fuller, C. J. Frosch, J. Am. Chern. SOC. 61, 2575 (1939) 7. J. R. Katz, Naturwissenschaften 13, 410 (1925) 8. W. Ruhland, Acta Crystallogr. 14, 1180 (1961) 9. W. Ruhland, Pure Appl. Chern. 18, 489 (1969) 10. W. Ruhland, H. Tompa, Kolloid 2. 2. Polyrn. 250, 471 (1972) 11. (a) R. Bonart, Makromol. Chem. 92, 149 (1966) (b) R. Bonart, Kolloid 2. 2. Polyrn. 213, 1 (1966) 12. A. I. Kitaigorodskii, “Organic Chemical Crystallography“, Consultants Bureau, New York 13. R. Bonart, in: Synthesejasern, edited by B. v. Falkai, Verl. Chemie, Weinheim, Deerfield Beach, Base1 1981 14. R. P. Daubeny, C. W. Bun, C. J. Brown, Proc. Roy. SOC. 226A, 531 (1954) 15. U. Alter, R. Bonart, Colloid Polym. Sci. 254, 348 (1976); 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36.

ibid. 258, 332 (1980) J. Dulmage, L. E. Contois, J. Polym. Sci. 28, 275 (1958) D. A. Zaukelis, J. Appl. Phys. 33, 2797 (1962); Angew. Chem. 74, 569 (1962) A. Reichle, A. Prietschk, Angew. Chern. 74, 562 (1962) R. Bonart, Angew. Makromol. Chem. 22, 41 (1972) Z. W. Wilchinsky, “Advances in X-Ray Analysis”, Plenum Press, New York, vol. 6 R. S. Stein, F. H. Norris, J. Polyrn. Sci. 21, 381 (1956) H. M. Morgan, Ted. Res. J. 32, 866 (1962) W. W. Moseley, J . Appl. Polyrn. Sci. 3, 266 (1960) R. Hosemann, S. N. Bagchi, “Direct Analysis of Difiraction by Matter”, North-Holland Publ. Co., Amsterdam 1962 F. Rinne, Z. Kristallogr. 82, 379 (1932); Trans. Faraday SOC. 29, 1032 (1933) M. Friedel, G. Friedel, 2. Kristallogr. 79, 1 (1931) G. Bloechl, R. Bonart, Makrornol. Chern. 187, 1525, 1534 (1986) W. 0. Statton, Ann. N.Y. Acad. Sci. 83, 27 (1959) K. Hess, H. Kiessig, Naturwissenschaften31, 171 (1943); 2. Phys. Chem. (A) 194, 196 (1944) R. Bonart, R. Hosemann, 2. Elektrochern. 64, 314 (1960) R. Bonart, R. Hosemann, Kolloid 2. 2. Polym. 186, 16 (1962) (a) R. Bonart, Kolloid Z. Z. Polyrn. 194, 97 (1964) (b) ibid. 199, 136 (1964) W. 0. Statton, J. Polyrn. Sca. 41, 143 (1959) R. Bonart, J. Macromol. Sci., Phys. 111, 115 (1968) R. Bonart, Progr. Colloid Polyrn. Sci. 58, 38 (1975) R. Bonart, J. Blackwell, A. Biswas, Makromol. Chem., Rapid Commun. 6,

353 (1985) 37. J . Blackwell, A. Biswas, R. Bonart, Macromolecules 18, 2126 (1985) 38. (a) R. Bonart, G. Mulzer, J. Dietrich, Makromol. Chem. 188, 637 (1987); R. Bonart, Makrornol. Chem. 188, 1187 (1987) (b) R. Bonart, J. Dietrich, H. Zott, Makrornol. Chem. 189, 227 (1988)

Oriented Polymer Material> Stoyko Fakirov Copyright 0 2002 Wiley-VCH Verlag GmbH & Co. KGaP

Chapter 4

Characterization of polymer deformation by vibrational spectroscopy

H. W. Siesler

1. Introduction Apart from the chemical structure and thermal pretreatment, the mechanical properties of a polymer and its engineering applications depend primarily on the anisotropy induced by deformation and relaxation processes. Thus, the understanding of these processes is an important topic in polymer materials science. The characterization of the oriented polymer by suitable techniques provides a basis for the description of both, the processes whereby the anisotropic material is formed as well as the accompanying modification of its physical properties. Among other methods such as X-ray diffraction, birefringence, NMR spectroscopy and polarized fluorescence, vibrational spectroscopy has become one of the most frequently applied tools for the analysis of the structural effects induced by polymer deformation (see also Chapters 3 and 8). In principle, such measurements can be performed statically on a deformed polymer sample. For the elucidation of a deformation mechanism, however, the information from many test samples at different orientational states had t o be pieced together. Thus, the increased need for more detailed data has led t o the search for new experimental techniques t o monitor the structural changes on-line to the deformation process. With the advent of rapid-scanning FT-IR spectroscopy, simultaneous mechanical and IRspectroscopic - so-called rheo-optical - measurements have emerged as

Characterization of polymer deformation by vibrational spectroscopy

139

a very informative probe in the late seventies and have since then been applied to obtain data on the orientation, conformation and crystallization during mechanical treatment of a wide variety of polymers [l-51. Furthermore, with the recent availability of FT-Raman spectroscopy [6-91 and the more efficient exploitation of the near-infrared (NIR) region alongside the application of light-fibre optics [lo], rheo-optical measurements have become less restrictive with respect to sample geometry and location. This chapter is intended to demonstrate the potential of vibrational spectroscopy for the characterization of orientation phenomena in polymeric materials. Apart from the characterization of segmental mobility in liquid-cryst alline side-chain polymers, variable-temperature rheo-optical data on the bidirectional drawing of poly(ethy1ene terephthalate) film and the strain-induced conformational changes of poly(viny1idene fluoride) will be presented. 2. Experimental and instrumentation

The principles, theory and instrumentation of the FT-technique applied to infrared spectroscopy have been covered in detail in several books and reviews and the reader is referred to the pertinent literature [ll-141. Since the introduction of laser sources during the 1960s, a vast amount of work has been undertaken, using Raman spectroscopy to probe a wide range of polymeric structures [14-211. Conventional Raman spectrometers which have been used to carry out this work consisted, generally, of a visible laser source, an efficient double or triple monochromator, and a photomultiplier detection system. However, there were a number of problems inherent in the application of conventional laser Raman spectroscopy t o polymer systems. For a large proportion of samples, irradiation with visible light caused strong fluorescence of additives and impurities which were superimposed on the weak Raman signal. A number of - partly very time-consuming approaches have been tried to overcome this problem, including prior purification, burning out the fluorescence, shifting the excitation line or using pulsed lasers. These approaches have at best been only partially successful. Further problems with conventional Raman spectroscopy are that highly coloured samples or polymers containing fillers may absorb the Raman photons thereby preventing them from reaching the detector and leading to thermal degradation of the investigated polymer. Spectroscopists had to live with these difficulties for many years and they are some of the reasons why the Raman technique has not become as familiar as infrared, despite the fact that, in certain circumstances, Raman spectroscopy has a number of advantages over infrared. With the recent development of FTRaman spectroscopy [6-8, 22-24], however, it seems that this technique will also become a standard instrumentation in spectroscopic laboratories. Typically, the main features of an FT-Raman instrument are:

140

H. W . Siesler

- a neodymium-yttrium aluminium garnet (Nd-YAG) laser, operating at 1064 nm with a power output range of 0-2 W, - an efficient dielectric filter system to remove the Rayleigh component of the scattered radiation, - a FT-IR spectrometer, equipped with a quartz or calcium fluoride beamsplitter for operation in the near-infrared, - a photoelectric detector; this is usually a cooled germanium unit (at 77 K) or an indium-gallium-arsenide (InGaAs) detector operating at ambient temperature, and - a Raman sampling compartment with 180" or 90" lens-based optics. The use of near-infrared excitation confers a number of advantages on a FT-Raman system. Both fluorescence and self-absorption of the Raman signal are very much reduced and due to the lower energy of the exciting light, thermal degradation is also less of a problem. However, compared t o conventional Raman, FT-Raman also has some disadvantages and limitations. It is less sensitive because due to the proportionality of the Raman scattering cross-section to the fourth power of the exciting frequency, the shift from the visible to the near-infrared region reduces the intensity of Raman scattering. Thus, a shift of the excitation line from 488 nm to 1064 nm reduces the scattering intensity within the relative Raman region from 0 to 4000 cm-' for factors between 23 and 87 [25]. Furthermore, as a consequence of detector and filter limitations, the Raman shift can presently

11

ND-YAG LASER

Figure 1. Optical scheme of a FT-Raman module interfaced t o trometer

a

FT-IR spec-

Characterization of polymer deformation by vibrational spectroscopy

IR-DETECTOR

H

\\

..

141

..

b

Figure 2. (a) Principle of rheo-optical FT-IR spectroscopy of polymer films; (b) variable-temperature stretching machine for rheo-optical FT-IR spectroscopic measurements (A - stretching machine; B - sample transfer mechanism, 1 stress transducer, 2 - strain transducer, 3 - film sample, 4 - sample clamps)

I42

H . W . Siesler

be measured only between about 3500 cm-' and 100 cm-'. This shortwavenumber cut-off, for example, makes it impossible to investigate the longitudinal acoustic modes in lamellar polymer structures [14,19]. However, these problems will doubtlessly be reduces as a result of further research in this area, and it is evident that these disadvantages detract only slightly from the large advantages offered by the advent of the FT-Raman technique. The spectra presented here were carried out using a Bruker FRA 106 FT-Raman module which was interfaced t o a Bruker IFS 88 FT-IR unit. The basic optical scheme of such a system is shown in Figure 1. The experimental principle of rheo-optical vibrational spectroscopy is based on the simultaneous acquisition of spectra and stress-strain diagrams during deformation, recovery or stress relaxation of the polymer sample under investigation [ 1-51, Rheo-optical FT-IR experiments are restricted to thin films (Figure2(a)) and the specimen to be tested can be uniaxially drawn and recovered in a miniaturized stretching machine which fits into the sample compartment of the spectrometer. During the mechanical treatment interferograms are acquired in short time intervals (between about 0.5-5 s) with radiation polarized alternately parallel and perpendicular t o the stretching direction and upon completion of the experiment the interferograms are transformed into the corresponding spectra for further processing of the conventional data. In the final analysis, the spectroscopic and mechanical data then allow a correlation of the microscopic and macroscopic changes of the sample during the mechanical treatment. The electromechanical apparatus constructed for rheo-optical measurements is shown in Figure2(b). The implementation of a heating cell as a closed, nitrogen-purged system offers the possibility to study deformation and stress relaxation under controlled temperature conditions (&0.5') up t o 250°C. The separation of the stretching machine from the spectrometer in a rheo-optical FT-IR light-fibre experiment is shown schematically in Figure3. For orientation measurements, the polarizer has t o be mounted directly in front of the polymer sample in order t o avoid scrambling of the preferential polarization of the NIR radiation in the light fibre. Due t o the low attenuation of the quartz fibre (core diameter 600 pm) and the larger sample thickness accessible by NIR spectroscopy, this separation can be extended over large distances (> 50 m) and the mechanical measurements can be performed with common test samples on conventional tensile testers, respectively [lo]. Recently, we have also reported the first application of FT-Raman spectroscopy to rheo-optical experiments [5,9]. For this purpose, the stretching machine shown in Figure 2(b) was utilized in back-scattering geometry by rotating the clamp mechanism by 90' with the Raman beam impinging onto the sample through the front window of the stretching machine. In

Characterization of polymer deformation by vibrational spectroscopy Detector

I

143

Interferometer

Lens ( f i t 0 mm)

Sample in Stretching Machine

Source

Figure 3. Optical scheme of rheo-optical FT-NIR light-fibre spectroscopy (- - - beam without light-fibre, __ beam with light-fibre) order to improve the scattering efficiency, a mirror was mounted behind the sample. Here also, the sample geometry is no longer restricted t o a thin film, but conventional polymer tensile test samples with a thickness of up to several millimeters or polymer cables and fibres can be investigated. However, in order to obtain an acceptable signal-to-noise ratio for the Raman spectra taken during the mechanical tests, up to 100 scans had to be accumulated. Thus, for a Raman spectral data density comparable to rheo-optical FT-IR and FT-NIR investigations, the elongation rate had to be reduced to a factor of 100. Nevertheless] the results available so far indicate that this technique is very valuable for the characterization of phase transitions and strain-induced crystallization in thermoplastics and polymer networks, respectively [5,9]. 3. O r i e n t a t i o n a l m e a s u r e m e n t s by i n f r a r e d dichroism

When an oriented polymer is investigated with linearly polarized radiation the effect of anisotropy on a particular absorption band in the IR spectrum is characterized by the dichroic ratio

R = -,All Al where All and A 1 are the absorbances measured with radiation polarized parallel and perpendicular to the draw direction] respectively. The determination of the dichroic ratio is of significant importance for three aspects: - assignment of absorption bands; - determination of the molecular geometry;

H . W . Siesler

144

characterization of the relative polymer chain orientation. It should be emphasized, however, that orientational measurements by IR spectroscopy require a knowledge of the respective transition moment direction relative to the chain axis. Owing t o the small mass of the hydrogen atom, for example, the transition moment directions of X-H stretching vibrations such as C-H or N-H will be localized along the respective chemical bond. Because of the large force constants involved, transition moments of stretching modes belonging to multiple bonded atoms will also closely coincide with the bond direction (e. g. v(C=O), v(C-N)) as long as no significant delocalization of the bonding electrons occurs. Thus, strong mechanical and electrical coupling of the C=O and C-N stretching vibrations in the planar amide group -CONH- cause an appreciable deviation (approximately 20') of the v(C=O) transition moment from the corresponding bond direction [14,26]. One of the advantages of IR spectroscopy with respect to the characterization of the relative polymer chain orientation is that under certain conditions the complex process of polymer deformation may be resolved into individual components. Hence, in general, the crystalline and amorphous phase of a semicrystalline polymer or the components of a polymer blend can be characterized separately by evaluating the dichroic effects of absorption bands which are characteristic of these regions or components. For the practical analysis of orientation phenomena in polymers, mathematical relations between the parameters of distribution function models of the polymer chain axes and the dichroic ratio have been derived and can be evaluated in terms of the experimentally measured values. Although this approach is restricted to relatively simple models, it has been extensively applied to establish the basic concepts of orientation mechanisms in a great variety of polymeric systems. Thus, the presented FT-IR data have been evaluated in terms of an orientation function f [14,26,27] -

where R is the measured dichroic ratio of the investigated absorption band and Ro is given by

Ro = 2 cot2 $

(3)

II, being the angle between the polymer chain axis and the transition moment of the absorption under consideration (Figure 4). For an absorption band having its transition moment parallel ($ = 0') or perpendicular ($ = 90') to the chain axis f reads

Characterization of polymer deformation by vibrational spectroscopy

145

draw direction

Figure 4. Distribution of the transition moments o- a particu-,r vibration in a uniaxially oriented polymer with respect to the draw direction (see text)

and

A further analysis of these equations reveals that f can be expressed in terms of the more generally applicable Herrman’s orientation function [14,26,281

f=

(3(cos2 6) - 1) 2

where 6 represents the average angle of inclination of the polymer chains with respect to the draw direction (Figure 4). If the intensity of an absorption band exclusive of contributions due to orientation of a highly elongated polymer is required for quantitative analysis, the so-called structural absorbance A0 has to be evaluated from polarization measurements [14,26]:

For a more detailed discussion of the characterization of anisotropy in polymers by dichroic measurements, the reader is referred to the special literature [14,26,29](see also Chapters 3 and 8). 4. Segmental mobility in liquid crystalline side-chain polymers

With their applications in the display technology, liquid crystals have gained wide-spread scientific and technical importance within the last two

146

H. W . Siesler

MESOGENIC GROUP

Figure 5. Structure of the investigated LCSC polyester decades [30]. The proof of liquid-crystalline properties in polymers with mesogens in the main chain has led to the development of new materials with exceptional mechanical and thermal properties [31]. In the case of liquid crystalline side-chain (LCSC) polymers novel applications for optical information storage and nonlinear optics have recently been opened up [32-351. Thus, the study of segmental mobility in liquid crystals and liquid-crystalline polymers as a function of external (e. g. electrical, electromagnetic or mechanical) forces is of fundamental importance for the understanding of the dynamics of such molecular mechanisms as they play an important role in the process of information storage, for example. FTIR spectroscopy with polarized radiation is a powerful technique in this respect, since it allows the independent characterization of the orientation of specific functional groups in the mesogen, spacer or main chain of a liquid-crystalline polymer, respectively [36,37].

Figure 6. FT-IR polarization spectra of the LCSC polyester after Ar laser irradiation

Characterization of polymer deformation by vibrational spectroscopy

147

It has been demonstrated that the photo-induced orientation and reorientation of dye-containing LCSC polymers can be used for reversible optical data storage [38,39]. The orientational properties of the main chain and the mesogenic side chains are of critical importance in these storage processes. FT-IR polarization spectroscopy enables the qualitative characterization of this orientational behaviour as well as its quantitative determination by an order parameter [4,36,37,40,41]. The structure of the investigated LCSC polyester is shown in Figure5. In an unoriented polyester film, holograms with a resolution of 5000 lines/mm can be recorded by the interference of an argon ion laser beam [42]. Erasing and rewriting of the laser-induced alignment in the polyester is the basis for reversible optical data storage. To study this behaviour, the laser-induced orientation has been erased by heating the polymer above its clearing temperature. Thin, isotropic films of the polyester were obtained by solution casting (2 mg polymer in 200 pl chloroform) onto KBr plates. The film thickness obtained by this preparation procedure is approximately 5 pm. FT-IR polarization spectra were recorded with a KRS-5 wire-grid polarizer a t

0

t z

0.150

3 W

0

z

2

0.075

CT

0

2a

0.0

0)

0.150

t z 3 W

0

z

0.075

2! I 0

2

a

0.0

2300

2250

2200

2150

WAVENUMBER (cm-’) Figure 7. Temperature-dependent erasure of t h e argon laser-induced orientation of the mesogen in the investigated LCSC polyester as demonstrated by the v(C=N) absorption band

H. W. Siesler

148

I

"O

a S

0

0.4 0

8

0.2

8

0 30

I

I

35

40

1

I

I

45 50 55 TEMPERATURE ("C)

8,,,,r,,,, 60

65

9

70

Figure 8. Order parameters vs. temperature plot for the temperature-dependent erasure of the argon laser-induced orientation of the mesogen (v(C=N) absorption band) in the investigated LCSC polyester a resolution of 4 cm-' by accumulating 20 scans. For the laser irradiation experiments the Ar 488 nm line was used. The orientational effect of the argon laser irradiation on the LCSC polyester is demonstrated by the FT-IR polarization spectra shown in Figure 6. Significant dichroic effects are observable for specific absorption bands which can be assigned to the mesogenic group (v(C_N), 2229 cm-' ) and the main chain (aromatic ring modes at 1601/1583 and 1501 cm-' ). The order parameter S, which is equivalent to the orientation function f given in Eqs. (2) and (6) and which has been introduced for low molar-mass liquid crystals by Maier and Saupe [43], provides a measure of their long-range orientational order. For the v(C=N) absorption of the investigated polymer S attained a value of 0.8 after argon laser irradiation. The erasure of this laser-induced alignment during heating is demonstrated by the stack-plot of the v(C=N) absorption in Figure7 and the corresponding order parameter vs. temperature plot shown in Figure 8. For more systematic discussions of these effects as a function of the chemical structure (mesogen, side- and main-chain spacer length) of the LCSC and the conditions of laser irradiation the reader is referred to the recent literature [36,37,42]. 5. Rheo-optical FT-IR studies of the poly(ethy1eneterephthalate)

film forming process Polymeric films are used extensively in the packaging, magnetic media and graphics industry [44]. The advantages these films offer rely heavily on

Characterization of polymer deformation by vibrational spectroscopy EXTRUSION OF MOLTEN W L M l E R

I

SIDEWAYS DRAWING 1lO 'C

J

bitrvitn

OVEN

Figure 9. PET film forming process (A - drawing in the transverse direction)

-

ANNEAUNG OVEN

149

ANNEAUNG 220 *C

I

W

drawing in the machine direction; B

their physical properties. Thus, the mechanical strength of bidirectionally drawn poly(ethy1ene terephthalate) (PET) film, for example, makes it suitable for video and computer tape applications. In the film forming process, an amorphous sheet is cast from the melt onto a cooled drum, followed by sequential forward and sideways drawing at different temperatures and heat setting in ovens (Figure9). The ability to monitor and model these drawing and relaxation processes would enhance greatly the product quality and web efficiency. Thus, rheo-optical FT-IR spectroscopy appeared to be the method of choice t o elucidate the structural changes occurring during the key mechanical processes (A and B in Figure9) by combining miniaturized mechanical tests with FT-IR polarization spectroscopy. Poly(ethy1ene terephthalate) is a fortunate case for such investigations, because its conformation (gauche/trans of the ethylene glycol units) and state of order (crystalline and amorphous regions) can be correlated with specific absorption bands in the infrared spectrum of this polymer (Figure 10) [14,26,45-501. Upon annealing or drawing a plain cast film sample, an increase of the crystalline relative to the amorphous regions and of the trans versus gauche conformers can be observed. Information concerning the changes in anisotropy induced by the mechanical treatment can be derived from the dichroism in the polarization spectra monitored during the mechanical process (Figure 11). Thus, series of spectra taken on-line t o the different drawing processes of PET films have been evaluated in terms of the following structural details: - the transient changes of the amount and anisotropy of the crystalline

150

H. W . Siesler

a I

b

TEMPERATURE STRESS

-gy-fyy%1*

TRANS

GAUCHE

LZOO WAVENUMBER

1100

lo00

OOQ

/I C m T

Figure 10. Structure-spectra correlation for PET: (a) - chemical structure of the repeating unit; (b) - preferential conformations of the aliphatic segments; (c) - IR spectrum of a partially crystalline PET film (G - gauche; T - trans; A - amorphous; C - crystalline; REF - thickness reference band)) (see text) and amorphous regions were derived from the structural absorbances of the 972 cm-' v(C-0-C) (crystalline) and 1577 cm-' v ~ A ( A ~ (amorphous) ) [26,45,48] absorption bands, respectively, assuming transition moment directions parallel to the polymer chain axis; - to eliminate the influence of changing film thickness during the meZ~) whose intensity is indechanical treatment, the 1504 V ~ ~ A ( Babsorption pendent of the state of order has been utilized as thickness reference band [45,481; - changes of the trans/gauche conformation ratio of the ethylene glycol segments were monitored by the structural absorbances of the 1340 cm-' (trans) and 1371 cm-' (gauche) y,,,(CHz) absorption bands [26,45]. The starting material for the drawing in the machine direction was an isotropic, amorphous, plain cast film of 15 pm thickness with a crystallinity of only 12% (w/w) and a glass transition point T, of about 81OC as determined by differential scanning calorimetry (DSC). The samples utilized t o study the structural changes occurring during drawing in the transverse direction were semicrystalline PET films (crystallinity by DSC of about 35% (w/w)) which had been predrawn to 300% at 90" under manufacturing conditions. In the rheo-optical experiments these specimens were then elongated perpendicular to the original machine direction. The samples were stretched with variable length to width ratios (from

Characterization of polymer deformation by vibrational spectroscopy 1.50 L-

1.25 -

II

a

151

I -

1

w

y

1.00 -

$m

0.75

s a

-

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0.50 -

2Ooo

1800

1600

1400

1200

lo00

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600

lo00

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1.00

s

0.75

z

d

m

0.50 0.25

0.00 2ooo

1800

1600

1400

1200

WAVENUMBER (cm-')

Figure 11. Polarization spectra of a 400% uniaxially drawn PET film ( G gauche; T - trans; A - amorphous; C - crystalline)

1:0.7 to 1:4) at different temperatures (78OC to llO°C) and an elongation rate of 100% strain/minute, and simultaneously to the recording of the stress-strain curves 20-scan spectra were taken at a resolution of 5 cm-' in 2.6-second intervals with radiation polarized alternately parallel and perpendicular to the draw direction (Figure 12). Only selected data, however, will be presented here to demonstrate the most important phenomena observed during these drawing processes.

II

$1 II

Figure 12. FT-IR polarization spectra monitored during elongation of a P E T film in the transverse direction (process B in Figure 9) a t llO°C

!I

Characterization of polymer deformation by vibrational spectroscopy

153

5.1. Drawing of P E T in the machine direction

Figure 13 shows the stress-strain diagrams monitored during uniaxial drawing of the amorphous PET film at 78OC and 95OC. The temperature rise above T, is accompanied by a drastic decrease of the stress level and the disappearance of a distinct necking procedure. The corresponding changes in the orientation of the amorphous and crystalline regions are shown in Figure 14. Starting with a randomly oriented sample (orientation function f = 0) a significant increase in the orientation of the amorphous and crystalline regions can be observed during the drawing procedure at 78OC. The induced degree of orientation is much larger for the crystalline domains as compared to the amorphous ones and the increase is most pronounced in the strain region between about 50 and 100% strain where the neck moves past the sampling area of the IR beam. At 95OC no more amorphous orientation 20

15

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0 50

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200

250

300

350

400

250

300

350

400

STRAIN (%)

5 4 -

b

3 2 -

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100

150

200

STRAIN (%)

Figure 13. Stress-strain diagrams monitored during drawing of a plain cast PET film at 78OC (a) and 95OC (b)

H . W. Siesler

154 1.00I

1

P

Q I-

2!

0.75

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MORPHOUS (1577 cm-')

0

0.00 50

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STRAIN (%) 1.oo

b

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Figure 14. Orientational changes of the crystalline and amorphous regions observed during drawing of a plain cast PET film: (a) - 78OC; (b) - 95OC (see text)

is induced during the drawing process and the orientation of the crystalline regions upon elongation is less that at 78OC. An analogous behaviour is observed for the changes in the trans/gauche ratio during uniaxial drawing of amorphous PET at 78°C and 95OC (Figure 15). The spectra series for Figures 14(b) and 15(b) have been recorded with a lower time resolution (20 scans in 14-second intervals) on a Nicolet 7000 FT-IR spectrometer under otherwise identical conditions. 5 .2 . Drawing of PE T i n the transverse direction For the characterization of the drawing process in the transverse direction (process B in Figureg), specimens which had been taken from the film process between A and B were elongated perpendicular to the previous

Characterization of polymer deformation by vibrational spectroscopy

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L

Figure 15. Changes in the trans/gauche ratio monitored during uniaxial drawing of a plain cast PET film: (a) - 78OC; (b) - 95OC (see text) machine direction at different temperatures (8OOC and 110°C) and investigated simultaneously by FT-IR spectroscopy. For the sake of comparison with the results discussed in the previous section, here too, the orientation data derived from the polarization spectra have been evaluated in terms of a uniaxial model, although this is no longer strictly applicable. In order t o operate with positive orientation function values only, the reference direction for the evaluation of the orientation function has been changed from the machine direction into the transverse direction, as soon as the orientation function reached values of zero for the different absorption bands. Figure 16 reflects the reorientation of the amorphous and crystalline regions from the machine into the transverse direction by the inversion of the orientation function value. For the same starting material, the inversion point on the strain scale depends on the drawing temperature (Figure 16). At higher temperatures the process of realignment occurs slower

H. W. Siesler

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Figure 16. Reorientation of the amrphous and crystalline regions of PET during drawing at 80 O C and 110 OC in the transverse direction corresponding to process B in Figure9 (see text) and the inversion point is shifted t o higher strain values. In the course of this realignment the crystalline regions show again a higher reorientation tendency as compared t o the amorphous regions, i. e. the initially larger positive orientation function value of the crystalline regions reverses also into a more positive value upon realignment in the transverse direction. A comparison of the changes in crystallinity during drawing in the machine and in the transverse direction as represented by the structural absorbance ratios of the 972 cm-' crystallinity band and the 1504 cm-' thickness reference band are shown in Figures 17(a) and 17(b). These data demonstrate that by drawing a plain cast PET film at 78OC, a relatively higher crystallinity is induced as compared to the subsequent drawing process in the transverse direction at 110°C. Despite numerous publications on the deformation process of P E T [51591 and although only selected data are presented here, it becomes evident, that the technique of rheo-optical FT-IR spectroscopy offers a lot of details

Characterization of polymer deformation by vibrational spectroscopy

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Figure 17. Changes in crystallinity of PET during drawing at 78 OC in the machine direction (a) and at 110 "C in the transverse direction (b) (see text)

which are not accessible by other techniques and which yield a detailed picture of the structural changes of PET during the film forming process. It was therefore a logical consequence that we started to develop the experimental basis for a process-control method by performing rheo-optical spectroscopy in the near-infrared region and applying light fibres t o separate the mechanical measurements from the sample compartment of the spectrometer. The first results of these investigations are briefly described in the following section. 5.3. Rheo-optical F T - N I R spectroscopic light-fibre investigations of the PET film process

The scheme of a FT-NIR spectrometric light-fibre experiment for rheooptical investigations is outlined in Figure 3. Although NIR spectra are

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generally less informative than their mid-infrared analogs due to the overlap of absorption bands in this wavelength region, the details of the changes in crystallinity, conformation and orientation of PET are also contained in the overtone and combination vibrations [10,60,61]. The development of dichroic effects in the polarization spectra of an isotropic, amorphous, plain cast film of 600 p m thickness during drawing at 8OoC to 400% is shown in Figure 18. In a further step, the reorientation of the polymer chains upon stretching a predrawn film in the transverse direction is also reflected in

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Figure 18. FT-NIR light-fibre polarization spectra of a plain cast isotropic PET film (600 pm thickness) before (a) and after 400% drawing at 8OoC (200 pm thickness) (b)

159

Characterization of polymer deformation by vibrational spectroscopy

the reversal of these dichroic effects which had been induced by drawing in the machine direction (Figure 19). Thus, the effects observed with midinfrared spectra can be reproduced in the NIR spectra with the advantage that the investigations can be extended to a film thickness in the range from about 80 pm t o 600 pm [lo]. Further investigations have shown that the evaluation of these NIR data can be performed in the conventional approach by focussing on individual absorption bands or by applying multivariate, chemometric techniques such as partial least squares (PLS) [62] using the I

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Figure 19. FT-NIR light-fibre polarization spectra of (a) 250 % predrawn PET film (250 pm thickness) and (b) after 400 % drawing in the transverse direction (108 pm thickness)

H.W . Siesler

160 complete NIR spectra [63,64] (see also Chapters 2, 11-14).

6. Rheo-optical FT-Raman spectroscopy of the stress-induced

conformational changes in poly (vinylidene fluoride) In an attempt to demonstrate the potential of FT-Raman spectroscopy for rheo-optical measurements, we have also studied the conformational changes induced in poly(viny1idene fluoride) under the application of stress. Poly(viny1idene fluoride) (PVF2) is a polymer with exceptional technological and scientific properties and depending on the thermal, mechanical and electrical pretreatment, it can exist in four different modifications denoted I(@, II(a), III(7) and IV,(S) or IVp(ap). The crystal structure of the forms I(p) and II(a) is orthorhombic and their molecular conformations are tt and t g t i j , respectively. Form III(y) belongs to the monoclinic system with a t 3 g t 3 g conformation. Form IV,(S) is obtained by poling the II(a) form at high electric fields. The two polymorphs have the same chain conformation and unit cell dimensions and differ only in the interchain packing. The crystal structures of the different forms, the conditions of their formation and mutual transformation by tensile force, high pressure, heat treatment or electrical fields have been reported in detail [65-741. Although the interconversion of the various phases of PVF2 has been the topic of several infrared and Raman studies [70-751, except for our previous rheo-optical FT-IR investigations [76], no data on dynamic measurements are so far available. In view of the well-established band assignments [72751 and the significant differences also observable in the Raman spectra of

1

stress

repeat unit

repeat unit

L

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c 140°C

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Figure 20. Conformational changes of the stress-induced II(a) - I(/?) crystal transformation in poly(viny1idene fluoride) [72]

Characterization of polymer deformation by vibrational spectroscopy

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the Il(cr) and I(@) modifications [5], rheo-optical FT-Raman spectroscopy proved particularly suitable to study the stress-induced change from a crumpled t g t g conformation of the II(a) form to the all-trans conformation of the I(p) modification (Figure 20). Such rheo-optical FT-Raman measurements on-line to the drawing procedure as a function of temperature have the advantage that they can be performed on conventional polymer test samples with a thickness in the range of millimeters. In the mechanical treatment, PVFz film specimens in the unoriented II(a) phase were subjected to uniaxial elongation up to 40% strain with an elongation rate of 0.6% per minute at 75OC, 90°C, 105OC, 120°C and 15OoC, and 100-scan FT-Raman spectra were taken at a resolution of 4 4 m - l in 164-second intervals. The original polymer test samples had a thickness of 1.3 m m and gauge dimensions of 21 mm length and about 6 m m width. The stress-strain diagrams of the individual experiments at the different temperatures are shown in Figure 21. Apart from the substantial reduction of the stress level with increasing temperature, the most obvious feature is the almost complete disappearance of the stress-decreasing region beyond the yield point. Nevertheless, neck formation was observed throughout the investigated temperature interval. Previous rheo-optical wide-angle X-ray measurements [68] had revealed that this II(a) - I(p) crystal transformation occurred below 14OOC with the sample deforming by formation of a neck, whereas above this temperature no changes in crystal modification were observed. The FT-Raman spectra taken during drawing at 75OC and 15OOC are shown for the wavenumber region between 750 cm-' and 950 cm-' in Figures22(a) and 22(b), respectively. At 75OC with increasing

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Figure 21. Stress-strain diagrams of poly(viny1idene fluoride) taken during uniaxial elongation at different temperatures (see text)

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elongation, the spectra are characterized by an intensity reversal of t h e 800 cm-' and 840 cm-' absorption bands which have been assigned to v(C-F) and v(C-C) stretching vibrations of t h e t g t s and all-trans confor-

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Figure 22. RT-Raman spectra of poly(viny1idene fluoride) taken during uniaxial elongation at 75OC and 150°C (normalized to constant intensity of the 800cm-' absorption band)

Characterization of polymer deformation by vibrational spectroscopy 2.5

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Figure 23. Plot of the Raman band intensity ratios I ~ ~ o / Iversus ~ o o strain representing the modificational changes during elongation as a function of temperature (see text) mation of the II(a ) and I(p) modifications, respectively [73-751. At 15OoC, on the other hand, no significant intensity changes can be observed throughout the stretching procedure. For the detailed representation of the modificational changes during uniaxial elongation at the different temperatures, the intensity ratios 1840/1800have been plotted as a function of strain in Figure 23. Thus, with increasing temperature the transformation from the II(a) into the I(p) form becomes less significant and no conformational changes can be observed at 150OC. These findings are in agreement with previous rheo-optical wide-angle X-ray [68] and FT-IR investigations [76]. The significant changes of the 1840/1800intensity ratio only beyond 20% strain are a consequence of the propagation of the neck past the sampling area of the laser beam. Hence, the initiation of the crystal phase transformation is primarily based on a heterogeneous stress distribution during neck formation. With increasing temperature, the role of the neck as a location for the onset of orientational changes of the II(a) phase predominates over its function as a location for the II(a) - I(p) crystal phase transformation. 7. Conclusions

In contrast to the common use of vibrational spectroscopy as an analytical tool in polymer research, the present chapter emphasizes the potential of this technique for the characterization of deformation phenomena in polymers. With the advent of FT-Raman spectroscopy and the more efficient

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utilization of the FT-NIR light-fibre technique, rheo-optical measurements have been recently launched into a new era of polymer physical and processcontrol applications. Although only selected examples have been presented here, it is hoped that they illustrate the versatility of such studies for the characterization of transient order phenomena during deformation of thermoplastics and elastomers and encourage their application on a broader scale. 8. Acknowledgements

The author gratefully acknowledges the experimental assistance of U. Hoffmann, Ch. Kulinna, S. Okretic, F. Pfeifer, N. Volkl, M. Zahedi (University of Essen, Germany), J . C. Rodriguez-Cabello and J . M. Pastor (University of Valladolid, Spain) and S. Hvilsted and P. Ramanujam (Riso National Laboratory, Denmark). For the instrumental and financial support the author thanks the Deutsche Forschungsgemeinschaft, Fonds der Chemischen Industrie and the Research Pool of the University of Essen, Germany, and ICI Films, Wilton Research Centre, England. References 1 . H. W . Siesler, Adv. Polym. Sci. 65, 1 (1984) 2. H. W. Siesler, in: Advances in Applied FTIR Spectroscopyedited by M. W. Mackenzie, John WiLley, Chichester, England 1988, p. 189 3. H. W. Siesler, Makromol. Chem., Macromol. Symp. 53, 89 (1992) 4. H. W. Siesler, in: Structure-Property Relations in Polymers: Spectroscopy a n d Performance, Advances in Chemistry Series No 236, edited by M. W. Urban, C. D. Craver, Am. Chem. SOC. Books Department, Washington D. C. 1993, p. 31 5 . U. Hoffman, F. Pfeifer, S. Okretoc, N. Volkl, M. Zahedi, H. W. Siesler, Appl. Spectrosc. 47, 1531 (1993) 6. T. Hirschfeld, B. Chase, Appl. Spectrosc. 40, 133 (1986) 7. C. G. Zimba, V. M. Hallmark, J. D. Swalen, J. F. Rabolt, Appl. Spectrosc. 41, 721 (1987) 8. P. Hendra, G. Jones, G. Warnes, “Fourier Transform Raman Spectroscopy, Instrumentation and Chemical Applications”, Ellis Horwood Ltd., Chichester, England 1991 9. H. W. Siesler, Revue de l’lnstitut Francais du Petrole 48, 223 (1993) 10. H. W . Siesler, Makromol. Chem., Macromol. Symp. 52, 113 (1991) 11. R. J. Bell, “Introductory Fourier Transform Spectroscopy”, Academic Press, New York 1972 12. R. Geick, Fresenius Z. Anal. Chem. 288, 1 (1977) 13. P. R. Griffiths, J . A. deHaseth, “Fourier Transform Infrared Spectroscopy” in: Chemical Analysis Series 83, John Wiley, New York 1986 14. H. W. Siesler, K. Holland-Moritz, “Infrared and Raman Spectroscopy of Polymers”, Marcel Dekker, New York 1980

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15. T. R. Gilson, P. J . Hendra, “Laser Raman Spectrscopy”, Wiley, New York 1970 16. J . L. Koenig, Appl. Spectrosc. Revs. 4,233 (1971) 17. D. L. Gerrard, W . F. Maddams, Appl. Spectrosc. Revs. 22,251 (1976) 18. H . Tadoroko, “Structure of Crystlline Polymers”, Wiley-Interscience, New York 1979 19. D. J. Cutler, P. J. Hendra, G. Fraser, “Laser Raman Spectroscopy on Synthetic Polymers”, in: Developments in Polymer Characterization, edited by J. V. Dawkins, Applied Science Publ., London 1980, vol. 2, p. 71 20. P. C. Painter, M. M. Coleman, J. L. Koenig, “The Theory of Vibrational Spectroscopy a n d its Applications to Polymeric Materials”, Wiley-Interscience, New York 1982 21. D. I. Bower, W. F. Maddams, “The Vibrational Spectroscopy of Polymers”, in: Cambridge Solid State Science Series, Cambridge University Press, Cambridge 1989 22. P. J. Hendra, Spectrochim. Acta 46A, 121 (1990) 23. F. J . Bergin, H. F. Shurvell, Appl. Spectrosc. 43,516 (1989) 24. B. Schader, S. Keller, in: Proceedings of the 8th International Conference on Fourier Transform Spectroscopy, edited by H. M. Heise, E. H. Korte, H. W . Siesler, SPIE 1575,30 (1992) 25. A. Hoffmann, PhD Thesis, University of Essen, Germany (1991) 26. J . Dechant, ‘‘ Ultrarotspectroskopische Untersuchungen a n Polymeren”, Akademie Verlag, Berlin 1972 27. R. D. B. Fraser, J . Chem. Phys. 21, 1511 (1953) 28. P. H. Hermans, P. Platzek, Kolloid Z. 88,68 (1939) 29. R. Zbinden, “Infrared Spectroscopy of High Polymers”, Academic Press, New York 1964 30. G . Vertogen, W. H. de Jeu, “Thermotropic Liquid Crystals, Fundamentals”, Springer Verlag, Berlin 1987 31. A . M. Donald, A. H. Windle, “Liquid Crystalline Polymers”, Cambridge University Press, Cambridge 1992 32. H. Finkelmann, in: Liquid Crystallinity in Polymers: Principles a n d Fundamental Properties, edited by A. Ciferri, VCH Verlagsgesellschaft, Weinheim 1991, p. 315 33. C. B. McArdle, in: Side Chain Liquid Crystal Polymers, edited by C. B. McArdle, Blackie & Son Ltd., Glasgow 1989, p. 357 34. J. H. Wendorff, M. Erich, Mol. Cryst. Lip. Cryst. 169,133 (1989) 35. T. Nakamura, T. Ueno, C. Tani, Mol. Cryst. Liq. Cryst. 169, 167 (1989) 36. P. S. Ramanujam, S. Hvilsted, F. Andruzzi, Ch. Kulinna, H. W. Siesler, in: Organic Thzn Films for Photonic Applications, 1993, Technical Digest Series Vol. 17 (Optical Society of America, Washington D. C., USA), 244 (1993) 37. Ch. Kulinna, I. Zebger, S. Hvilsted, P. S. Ramanujam, H. W . Siesler, J . Res. Nat. Bur. Std. A68; Makromol. Chem., Macromol. Symp. (1993) (in press) 38. M . Eich, J . H. Wendorff, Makromol. Chem., Rapid. Commun. 8,59 and 467 (1987) 39. U . Wiesner, M. Antonietti, C. Boeffel, H. W. Spiess, MacromoleculesS, 2133 (1990)

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40. U . Wiesner, N . Reynolds, C. Boeffel, H . W. Spiess, Makrornol. Chern., Rapad. Cornrnun. 12, 457 (1991) 41. U. Wiesner, N. Reynolds, C. Boeffel, H. W. Spiess, Liquid Crystals 11,251 (1992) 42. P. S. Ramanujam, S. Hvilsted, F. Andruzzi, Appl. Phys. Lett. 62, 1041 (1993) 43. W. Maier, A. Saupe, Z. Naturforsch. 14A, 882 (1959); 16A, 816 (1961) 44. W. Seifried, Kunststoffe 75, 773 (1985) 45. S. Krimm, Adu. Polyrn. Sci. 2, 51 (1960) 46. A. Miyake, J. Polyrn. Sci. 38, 479 (1959) 47. C. J. Heffelfinger, P. G. Schmidt, J. Appl. Polyrn. Sci. 9, 2661 (1965) 48. M. V. S. Rao, N. E. Dweltz, J. Appl. Polyrn. Sci. 31 1239 (1986) 49. B. B. Gupta, C. Ramesh, H. W. Siesler, J. Polyrn. Sci., Polyrn. Phys. Ed. 23, 405 (1985) 50. B. Jasse, J. L. Koenig, J. Macromol. Sci. Rev. Macrornol. Chem. C 1 7 , 61 (1979) 51. U. Goschel, Polymer 33, 1881 (1992) 52. S. Rober, H. G. Zachmann, Polymer 33,2061 (1992) 53. D. R. Salem, Polymer 33, 3182, 3189, 3193 (1992) 54. T. Kawai, M. Muta, H. Sasano, N. Okui, Polyrner33, 2567 (1992) 55. P. Lapersonne, D. I. Bower, I. M. Ward, Polymer 33, 1266, 1277 (1992) 56. G. Le Bourvellec, J. Beautemps, J. P. Parry, J. Appl. Polyrn. Sci. 39, 319 (1990) 57. F. Bouquerel, P. Bourgin, J. Perez, Polymer 33, 516 (1992) 58. J. Y. Guan, L.-H. Wang, R. S. Porter, J. Polym. Sci., Polym. Phys. Ed. 30, 687 (1992) 59. D. J. Walls, J. C. Coburn, J . Polym. Sci., Polym. Phys. Ed. 3 0 , 887 (1992) 60. C. E. Miller, Appl. Spectrosc. Revs. 26, 277 (1991) 61. C. E. Miller, B. E. Eichinger, Appl. Spectrosc. 44, 496 (1990) 62. H. Martens, T. Naes, “Multivariate Calibration”, John Wiley & Sons, Chichester 1989 63. U. Hoffmann, PhD Thesis, University of Essen, Germany (1994) 64. N. Volkl, PhD Thesis, University of Essen, Germany (1994) 65. E. L. Galperin, L. V. Strogalin, M. P. Mlenik, Vysokomol. Soedin. 7, 933 (1965) 66. W. W. Doll, J. B. Lando, J. Macromol. Sci. Phys. B4,309, 889, 897 (1970) 67. S. Osaki, J. Ishida, J. Polym. Sci., Polym. Phys. Ed. 13 1071 (1975) 68. K. Matsushige, K. Nagata, S. Imada, T. Takemura, Polymer 21, 1391 (1980) 69. A. J. Lovinger, in: Developments in Crystalline Polymers, edited by D. C. Bassett, Applied Science Publ., London 1982, ch. 5. p. 195 70. K. Tashiro, K. Takano, M. Kobayashi, Y. Chatani, H. Tadokoro, Polym. Bull. 10, 464 (1983) 71. F. J. Lu, $f L. Hsu, Polymer25, 1247 (1984) 72. M. A. Bachmann, J. L. Koenig, J. Chem. Phys. 74, 5896 (1981) 73. M. Kobayashi, K. Tashiro, H. Tadokoro, Macromolecules 8, 158 (1975) 74. F. J. Boerio, J. L. Koenig, J . Polyrn. Sci. P a r t A-29, 1517 (1971) 75. F. J. Lu, D. A. Waldmann, S. L. Hsu, J. Polyrn. Sci., Polym. Phys. Ed. 1 2 , 827 (1984) 76. H. W. Siesler, J. Polyrn. Sci., Polym. Phys. Ed. 23, 2413 (1985)

Oriented Polymer Material> Stoyko Fakirov Copyright 0 2002 Wiley-VCH Verlag GmbH & Co. KGaP

Chapter 5

Morphology in oriented semicrystalline polymers

J. Petermann

1. General considerations It is widely established that the properties of polymeric materials strongly depend on the orientation of the macromolecules and it is one of the main advantages of these materials that the orientation of the macromolecules can be manipulated during processing. Under specific processing conditions, the same polymer can result in a soft and flexible, or a strong and stiff product. Orientations can be determined by a variety of experimental methods, for example optical birefringence (see Chapter 8), X-ray scattering (see Chapter 3), infrared dichroism (see Chapter 4), etc. Almost all these methods have in common that their results are averages of the molecular orientations from volume elements larger than l pm3. Since morphological entities in semicrystalline polymers are in general much smaller than 1 p m , it is evident that even with exactly the same molecular orientation, polymeric materials can exhibit very different properties: a highly oriented polyethylene having stacked lamellar crystals will have much less strength than a sample containing needle shaped (shish) crystals. Consequently, in addition to the overall orientation of the macromolecules, the morphology (supermolecular structure) influences to a great extent the properties of the material (see Chapter 2). Other parameters influencing the properties of a polymeric material with the same orientation

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and morphology are the thermal and mechanical conditions under which the orientations and morphologies are obtained. An oriented polyethylene sample having stacked lamellar morphology can be obtained by crystallization from an extended melt or by cold drawing and subsequent annealing. Both materials exhibit very different mechanical properties despite their same morphology. The reason for these differences originates from the conformations of the macromolecules in the amorphous phase (entanglements] tie molecules, chain folds, etc). In order to correlate the morphologies in oriented polymers with their properties] the conditions under which the orientations were obtained are of major importance. In this chapter mainly uniaxially oriented polymers will be considered. The experimental techniques for the investigations are transmission electron microscopy (TEM) and light microscopy. 2. Morphologies in oriented polymers Three different basic morphologies can be observed in oriented thermoplastic semicrystalline polymers: - parallel stacked lamellae; - needle crystals (shishs); -

oriented fringed micelles.

Figure l(a) is a TEM-micrograph of a parallel stacked lamellar structure in polyethylene [l].A schematic sketch of the morphology is inserted. Figure l(b) shows a molecular lattice plane resolution of single lamellae in isotactic polystyrene ( i p s ) [a]. Lamellar crystals are characterized by small dimensions in the chain direction (being much less than the length of a single molecule) and by comparatively large dimensions perpendicular t o the molecular direction.

Figure l ( a ) . TEM micrograph of a stacked lamellar morphology in HDPE (phase contrast )

Morphology in oriented semicrystalline polymers

169

Figure l(b). TEM micrograph of single lamellae in IPS (high resolution). T h e distance of the parallel lines correspond t o (300) lattice planes [2]

Figure 2(a) shows a needle crystal morphology of poly(butene-1) (PB-1) with a schematic sketch [3]. Figure 2(b) shows the molecular lattice plane resolution in a single needle crystal in isotactic polystyrene [a]. The needle crystals have a much larger dimension in the chain direction as compared t o the lamellar crystals but very small dimensions perpendicular to the chain direction. In some cases the needle crystals can reveal periodically spaced lattice disturbances in the long axis direction of the needles (Figure 2(b)). The third morphology consists of oriented fringed micelles. Micellar crystals have almost the same dimensions parallel and perpendicular t o the chain direction. In Figure 3 a dark-field TEM micrograph of such a morphology in poly(ethy1ene terephthalate) (PET) is shown. The sizes of

Figure 2(a). TEM micrograph of a needle crystal morphology in PB-1 (phase contrast)

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Figure 2(b). TEM micrograph of a single needle crystal in iPS (high resolution). The distance between parallel lines corresponds to (110) lattice planes [2]. The periodic disturbance of these lines along the needle axis are due to defect agglomerations (see Section 4) [2]

Figure 3. Dark-field TEM micrograph of an oriented fringed micellar morphology in PET. The white dots are the micellar crystals

Morphology in oriented semicrystalline polymers

171

the crystals (white spots) are of the order of 10 nm [4]. A schematic sketch is also inserted. Again, the physical properties of oriented micellar morphologies differ considerably from those of the lamellar or needle crystal morphologies. 3. Formation of morphologies in oriented polymers

Orientations can be achieved by different methods and the corresponding morphologies may reflect these methods. Flow fields in the molten state during crystallization, crystallization in thermal gradients and on interfaces, plastic deformation in the solid state, and the polymerization process itself are the main approaches to oriented polymers. In practice some of these “orientational forces” can act simultaneously (see also Chapters 2, 11 and 12). 3.1. Morphologies obtained b y crystallization of oriented melts Melt flow is involved in the processing of thermoplastic polymers. Extensional and shear flow fields are able to orient the macromolecules, whereby extensional flow is more effective [5]. Depending on the magnitude of the melt flow gradient, the macromolecules having a random coil conformation in the relaxed melt can be deformed into ellipsoids or can even be extended. Deformation occurs when the flow gradient .

dv, dx

& = - < -

1 r

(vz = flow velocity in z-direction) is smaller than the inverse relaxation time 7 . Parallel stacked lamellae (Figure 1) are the resulting morphologies under these conditions. The higher the deformation, the more parallel the lamellae are stacked. The relaxation time 7 increases with increasing molecular weight M , of the macromolecules and with decreasing temperature. Consequently, low-temperature processing and/or high M , result in higher perfecrion of the stacking. Additionally, the nucleation probability of the lamellar crystals increases with increasing melt orientation [6,7], resulting in more lamellar crystals per unit volume and hence in lamellar crystals with smaller lateral dimensions. Complete extension of a macromolecule occurs when b > l / r and needle crystal morphologies are obtained under these conditions (Figure 2). In practice, polymeric materials contain macromolecules with a rather broad distribution of molecular weight M , and the criterion for their extension is fulfilled only for the longer molecules. The resulting morphology is the “shish-kebab” structure, containing needle crystals (shish) with overgrown lamellar crystals (kebab). Figure 4 shows such a morphology in polyethylene

[31.

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Figure 4. TEM micrograph of a shish-kebab structure in PE (phase contrast) 3.2. Orientation at interfaces

Preferred orientations can also be obtained when a relaxed polymer melt crystallizes at a solid interface. The preferred orientation may extend in some cases only over a few nanometers and in other cases over several micrometers away from the interface. The orientations can be due t o two very different reasons: In the case of the transcrystallization [8], the nucleation density at the interface is higher by orders of magnitude than in the surrounding melt and consequently crystal growth can only proceed in directions perpendicular to the interface. A stacked lamellar structure with the lateral dimensions perpendicular t o the interface develops. Transcrystallization may play an important role in fibre reinforced thermoplastics [9]. Figure 5 is a light micrograph (crossed polarizers) of carbon fibres in polypropylene, where transcrystallization has oriented the polymer around the fibres. In the case of p o l y m e r e p i t a z y [lo], specific atomic arrangements at the solid surface absorb the macromolecules in such a way that adhesion of the macromolecules is preferred along distinct crystallographic directions of the solid surface. When crystallizing the polymer, these directions become the molecular direction in the polymer crystals. Epitaxial crystallization occurs on the surfaces of needle crystals leading also t o shish-kebab morphologies [ll].More spectacular is the epitaxial crystallization of polyethylene on the surface of uniaxially oriented polypropylene [lo]. The polyethylene macromolecules adhere best to the polypropylene surfaces when their

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Figure 5. Light micrograph (crossed polarizers) of transcrystallization of PP on carbon fibres

Figure 6. TEM micrograph of epitaxially crystallized PE on uniaxially oriented PP (phase contrast). T h e orientations of the PP and PE macromolecules (sketch) can be calculated from the electron diffraction patterns (insert)

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J . Petermann

molecular direction is inclined at f50° with respect to the molecular direction of polypropylene. Upon crystallization, a cross-hatched lamellar morphology of the polyethylene lamellae develops (Figure 6). Similar orientations and morphologies have been observed on several non-compatible polymer/polymer interfaces. Also, strong orientational effects have been observed when crystallizing oligomers epitaxially on polymer surfaces [12] or when crystallizing polymers on surfaces of ionic crystals. 3.3. Orientation in thermal gradients The growth rates of lamellar crystals growing perpendicular t o their molecular direction depend on temperature. This leads t o a preferred growth of the lamellae into a temperature gradient [13,14]. If a temperature gradient (T,,, > T,, Tmin< T,) is moved along a polymer sample with a sufficiently slow velocity, all lamellae are oriented with their lateral dimensions in the direction of the temperature gradient. Almost perfect uniaxial orientations have been obtained by this method (Figure 7).

Figure 7. Light micrograph (crossed polarizers) of oriented PB-1 in a thermal gradient. The orientation of two spherulites can also be seen. T h e temperature gradient is horizontal 3.4. Orientation b y plastic deformation

Large plastic tensile deformations (A tensile direction.

> 2) orient the macromolecules

in the

Morphology in oriented semicrystalline polymers

175

The morphologies which develop during this drawing depend on the drawing rate, drawing temperature and on the ultimate draw ratio. The morphologies which occur after drawing can be best understood, if one considers the molecular processes at large deformations as a complete destruction of the initial morphology by “pulling out” of the single macromolecules from the initial morphological entities and by subsequent rearrangemelit into a completely new morphology [15].

Figure 8. Dark-field TEM micrograph of needle crystals in ultradrawn PE. Draw direction was horizontal

At sufficiently low deformation temperatures, when crystallization events are suppressed, oriented amorphous structures can be obtained [16]. At deformation temperatures somewhat below or close to the glass transition temperature T’ , oriented fringed micellar morphologies (Figure 3) occur and at higher deformation temperatures (close t o the melting temperature) needle-like morphologies may develop (Figure 8). The length of the needle-like crystals and their perfection depends also on the drawing rate. 3.5. Polymerization induced orientations

The polymerization process from monomers to linear macromolecules implies orientation. However, under “normal conditions” the orientation i s lost by the entropy-driven relaxation of the macromolecules. The relaxation can be avoided either by a simultaneous crystallization process leading t o fibrillar (needle-like) morphologies during polymerization [18] or by polymer-

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J. Petermann

Figure 9. TEM micrograph (bright field) of a (SN), crystal containing a kink defect

Figure 10. TEM micrograph of a poly(4-hydroxybenzoate) crystal (bright field)

Morphology in oriented semicrystalline polymers

177

izing stiff molecules. Solid state polymerization of monomer crystals is one example [19]. Figure 9 shows a perfectly oriented polysulfurnitride (SN), crystal [20]. The morphology is almost the same as that of the monomer crystal. Whisker-like crystals may be obtained by condensation polymerization of poly(4-hydroxybenzoate) in Marlotherm-S solution [21]. The macromolecules have a perfectly extended conformation (Figure 10).

4. Morphological changes during thermal treatments The stability of a morphology depends on its free energy F = U-TS, where U is the internal energy, S the entropy and T the temperature. The entropic part T S reflects mostly the chain conformation in the amorphous regions of a morphology. Since under equilibrium conditions the free energy F takes its minimum value, the chain conformation in the amorphous regions is driven to randomize. The main factors influencing the internal energy are the specific surface areas, their surface free energies and the lattice disturbances of the crystalline parts (see also Chapters 11-14). Morphologies are supermolecular arrangements, which are metastable (not in thermodynamic equilibrium) in most cases and their changes are controlled by the kinetics of the molecular processes. Two types of processes have been observed to change the morphologies during thermal treatments: a solid state type, in which crystal defects (lattice disturbances) rearrange to lower the strain energy of the crystal, and a melting and crystallization type, where completely new morphologies can be created. The second one is predominant in polymers. The first type can be observed with highly oriented amorphous polymers, which can crystallize via a “spinodale type” of crystallization process [22,23] into an oriented fringed micellar morphology at crystallization temperature close t o Tg. In needle crystal morphologies, in which the needle crystals contain a large number of defects, an agglomeration of the defects during annealing is observed. After annealing, the needle crystals consist of periodic arrangements of defect-free and highly defective zones along the needle direction (see Figure 2(b)) [23]. With further annealing at elevated temperatures, an additional transformation from a needle crystal morphology into a stacked lamellar morphology may occur in some polymers, as depicted in Figure 11 [24]. The molecular processes responsible for these morphological changes are the diffusion of jogs, kinks and chain ends along the chain direction and do not involve complete melting of the crystalline units. For the second type of transformation of the morphologies, the melting behaviour of the crystals has to be considered. The thermal stability of polymer crystals to the melting process is predominantly governed by the crystal dimensions d i n the chain direction (Thomson melting). The melting point depression 6Tm depends mainly on this dimension and on the spe-

J . Petermann

178

Figure 11. TEM micrographs of needle crystals in PP and the transformed stacked lamellar morphology (phase contrast)

Figure 12. Dark-field TEM micrographs of shish-kebab morphologies in IPS before and after annealing at 220 OC

-

cific free surface energy, ce with 6Tm a e / d . Due to their larger dimension in the chain direction, needle crystals are more stable to the melting process than lamellar crystals. In shish-kebab morphologies, annealing close t o the thermodynamic melting point can cause the melting of the lamel-

Morphology in oriented semicrystalline polymers

179

Figure 13. TEM micrograph of a stacked lamellar morphology of HDPE, annealed a t 128 'C. The bright spots are molten parts of the lamellae (phase contrast)

lar overgrowth, and the shish crystals remain unaffected (Figure 12). In stacked lamellar morphologies, the thinner parts of the crystals will melt first (Figure 13). With further annealing the molten parts can recrystallize into thicker lamellar crystals [25]. The micellar crystal morphology is very strongly affected during heat treatments. In this case small dimensions and the high end surface free energy [26] can result in melting point depressions 6T, of more than 100 "C. At these high undercoolings 6T, melting of the oriented fringed micelles and recrystallization into a stacked lamellar type of morphology occur simultaneously and hence cannot be detected by common DSC measurements. Figure 14 shows PET having an oriented fringed micellar morphology before annealing and the transformed stacked lamellar morphology after annealing at 200 "C [4]. Since in general the oriented fringed micellar crystals are connected by an oriented amorphous matrix, the melting behaviour and consequently the morphological changes depend also on the constrains: annealing the sample with or without fixed ends. As seen from the thermodynamic melting point equation, T, = 6 H / b S (SH = melting enthalpy, 6s = melting entropy), T, is higher in the surrounding of an oriented amorphous matrix and consequently melting at higher temperatures occurs under "fixed ends" annealing conditions, rather than under unconstrained conditions.

J. Petermann

180

Figure 14. TEM micrographs of PET morphology before and after annealing at 200 "C

4

p"

z

--

-needle crystals

--._

0

stacked lamellae

20

40

60

Strain [YO]

Figure 15. Stress-strain curves of HDPE with oriented stacked lamellar and needle crystal morphologies

Morphology in oriented semicrystalline polymers

181

5 . O u t l o o k to m o r p h o l o g y - p r o p e r t y relationships

In this chapter the morphologies in oriented semicrystalline polymers were described. Different morphologies result in different mechanical (and other physical) properties. The deformation behaviour of an oriented stacked lamellar morphology and a needle crystal morphology differ considerably (Figure 15). These stress-strain curves can be interpreted from the standpoint of morphological knowledge. In the stacked lamellar morphology, as depicted in Figure 1, non-oriented amorphous regions are alternating with “hard” lamellar crystals. By straining this material in the stacking direction, craze formation in the amorphous areas will be the dominating plastic process (Figure 16). The needle crystal morphology resembles uniaxial short discontinuous fibres reinforced materials and its mechanical behaviour can be described using fibre reinforcement theories [27,28] (Figure 17). Micellar morphologies are adequate to hard particle filled polymers and, indeed, the stress-strain curves have similar shapes. The Mullin’s effect explains the stress-strain behaviour of both morphologies [29,30]. In conclusion, the morphologies of oriented polymers are composed of components with dimensions in the nanometer range, but their mechanical properties can be modelled by morphologies of conventional composite materials (fibre and other particle filled polymers). The knowledge of the

Figure 16. TEM micrograph of a deformed stacked lamellar morphology of HDPE. All lamellae are separated but connected by thin fibrils (deformation direction is horizontal)

J . Petermann

182

16 -

,T 14E

\

z

5 12w

4 k = 1200 A

ui

3 100

-

YI

m

2 4> 2-

I

1000

2000

3000

1

LOO0

5000

6a D

Needle length, A

Figure 17. Dependence of Young’s modulus ( E ) on the needle crystal length

formation of morphology and its response to external stresses allows us to obtain polymers with distinct mechanical properties. References 1. M. Miles, J. Petermann, H. Gleiter, J. Macromol. Sci., Phys. B4, 523 (1976) 2. M. Tsuji, A. Kemura, M. Ohara, A. Kawaguchi, K. Katayama, J. Petermann, Seni-Gakkaishi 42, T-580 (1986) 3. J. Petermann, R. M. Gohil, J. Mater. Sci.,Letters 1 4 , 2260 (1979) 4. J. Petermann, U. Neck: J. Polym. Sci., Polym. Phys. Ed. 25, 279 (1987) 5. M. R. Mackley, A. Keller, Phil. Trans. Royal SOC.London A278,29 (1975) 6. I. L. Hay, M. Jaffe, K. F. Wissburn, J. Macromol. Sci., Phys. B 1 2 , 4 2 3 (1976) 7. K. Kabayashi, T. Nagasawa, J. Macromol. Sci., Phys. 4, 331 (1970) 8. E. G. Lovinger, J . Polym. Sci. 8A-2, 1697 (1970) 9. J. L. Thomason, A. A. van Rooyen, Paper presented a t the 3rd Int. Conf. on Composite Interfaces (ICCI), Cleveland (1990) 10. J. Petermann, G. Broza, U. Riek, A. Kawaguchi, J. Mater. Sci. 22, 1477 (1987) 11. A. J. Pennings, A. M. Kiel, Kolloid 2. 2. Polym. 205, 160 (1965) 12. T. Okihara, A. Kawaguchi, M. Ohara, K. Katayama, J . Cryst. Growth 106, 318 (1990) 13. Y. Fujiwara, Kolloid 2. 2. Polym. 226, 135 (1968) 14. A. J. Lovinger, J.O. Chua, C. C. Gryte, J. Polym. Sci., Polym. Phys. Ed. 15, 641 (1977)

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15. 16. 17. 18. 19. 20. 21.

A . Karbach, H. Krug, J . Petermann, Polymer 25, 1687 (1984) T. Pakula, E. W. Fischer, J. Polym. Sci., Polym. Phys. Ed. 19,1705 (1981) J. Petermann, R. M. Gohil, J. Polym. Sci., Polym. Phys. Ed. 17, 525 (1979) M. Mucha, B. Wunderlich, J . Polym. Sci., Polym. Phys. Ed. 12,1993 (1974) G. Wegner, Makromol. Chem. 154,35 (1972) J. Petermann, J. M. Schultz, J. Mater. Sci. 14,891 (1979) G. Lieser, G. Schwartz, H. R. Kricheldorf, J. Polym. Sci., Polym Phys. Ed.

22. 23. 24. 25. 26. 27. 28. 29. 30.

21,1599 (1983) R. Guenther, Dissertation, 1981, University Mainz, Germany J. Petermann, Makromol. Chem. 182, 613 (1981) J. M. Schultz, J. Petermann, Colloid Polym. Sci. 262, 294 (1984) J. Petermann, M. Miles, H. Gleiter, J. Macromol. Sci., Phys. B12,393 (1976) H. G. Zachmann, Kolloid Z. Z. Polym. 231,504 (1969) J. Petermann, U. Rieck, J . Mater. Sci. 22, 1120 (1987) R.M. Gohil, J. Petermann, J. Moter. Sci. 18,1719 (1983) L. Millins, N . R. Robin, Rubber Chem. Technol. 30, 444 (1957) F. Bueche, J . Appl. Polym. Sci. 4,107 (1960)

Oriented Polymer Material> Stoyko Fakirov Copyright 0 2002 Wiley-VCH Verlag GmbH & Co. KGaP

Chapter 6

Deformation calorimetry of oriented polymers

Y. K. Godovsky

1. Introduction Conventionally, the deformation of solids is treated within the framework of elasticity theory in terms of stresses and strains, i.e. in purely mechanical terms. Although the experimental determination of stress-strain relationships provides important information concerning the deformation process, it is quite obvious that this conjugated variable pair is only one of several pairs which can be used to describe the response of a material on deformation. The necessity of using the thermodynamic instead of mechanical approach became evident when investigators began to consider deformation in terms of thermodynamic potentials, such as internal energy, free energy, etc., rather than in terms of potential energy. The first law of thermodynamics shows that energy is conserved in all deformation processess, both reversible and irreversible. Therefore, the mechanical response of any material reflects exactly that amount of energy which accompanied the deformation process as heat and/or changes of internal energy. What this means to an experimentalist is that the temperature or thermal variations brought about by adiabatic or isothermal processes have to be measured simultaneously with stresses and strains. The thermal effects and temperature variations accompanying deformation of solids are usually rather small and it is their correct measurement which constitutes the major difficulty in shifting from a mechanical to a thermodynamic approach. Thermal effects in condensed materials carry profound information about the molecular

Deformation calorimetry of oriented polymers

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changes occurring due to deformation. Physically, therefore, the thermodynamic approach must be preferred. A brilliant example of applying the thermodynamic approach to molecular processes in deformation is the thermodynamic analysis of rubber elasticity [l]. Experimental investigations of the thermodynamics of reversible deformations of glassy and crystalline polymers has attracted much less attention compared to rubberlike materials. Deformation calorimetry is now used in order to study the thermomechanical behaviour of solid glassy and crystalline polymers [2,3]. In this chapter an overview of the thermomechanical behaviour of oriented polymers is presented with a special focus on the elucidation of molecular mechanisms of macroscopic deformation and structural changes accompanying the reversible deformation of oriented polymers. 2. Deformation calorimetry The method of deformation calorimetry was first developed and applied t o polymers by Mueller in 1957 [4], who also reported the results of numerous thermomechanical studies of rubberlike and solid polymers and drew attention to this thermomechanical approach. In his early investigations, Mueller used a gas calorimeter based on the principle of a gas thermometer which measures the change in pressure of a gas in which the sample is deformed. The pressure changes in the gas were caused by temperature changes in the sample during deformation. The heat transport also occurs between the sample and the chamber wall which is maintained at constant temperature. The heat flux resulting from the deformation of the sample changed the pressure in the working chamber. This activated an electric feedback mechanism attached to the differencial manometer producing the same heating effect in the reference chamber as is produced by the sample during the deformation. The pressure difference in the working and reference chambers is maintained at zero. This instrument can be used for the simultaneous recording of the stress-strain dependence at simple elongation and thermal effects accompanying the elongation or contraction of the sample.

2.1. G a s calorimeters The most perfect version of such an instrument was developed by Lyon and Farris [5]. A schematic drawing of the deformation calorimeter is shown in Figure 1.The instrument consists of two hermetic cylindrical chambers with 1.9 cm diameter and 12 cm length in one of which the sample is fixed. The sample can be stretched by means of a thin Invar pull wire which passes through an air-tight mercury seal. The reference cell is identical t o the measuring cell including the pull wire, so that there is no change in volume due to motion of the wire during deformation. Changes in sample volume

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Figure 1. The Mueller's gas deformation calorimeter. 1 - sample; 2 - measuring chamber; 3 - reference chamber; 4 - thermostate; 5 - differencial pressure transducer; 6 - pulling wires; 7 - stretching unit, including load cell 8; 9 - recorder

due to the Poisson effect turned out to be very small compared to the total volume of the sample cell and, therefore, do not contribute to the pressure change. Any differential pressure which occurs is a result of heating or cooling of the gas surrounding the sample. The differential pressure between the two chambers is monitored during deformation. To avoid convective streams into the measuring chamber there are polyester film partitions placed horizontally every 4 cm. These partitions make pressure changes independent of the axial positioning of the sample or heater. The calorimeter also contains a load cell and displacement transducer. The load cell contains a dynamometer up to 5 kg. The mechanical system can perform the deformation with rates in the range from 0.027 to 27 cm/min. The analog outputs from the load cell, pressure transducer, and displacement transducer are connected to an analog-to-digital converter. The work of deformation is calculated from the force-displacement data and the heat of deformation is calculated from the pressure-time data. Lyon and Farris [5] performed a more complete analysis of this gas calorimeter than the analysis given by Mueller. They demonstrated that the differential pressure is connected with the heat flux through the following linear integral equation

where one

< is time dependent. This equation can be transformed into a new

Deformation calorimetry of oriented polymers

Q(t)= C

I87

f AP(()d( + C r A P ( t ) 0

which is identical to the Tian-Calvet equation (see below) and in which temperature is replaced by the gas pressure. In this equation C is a constant independent of the position of the source of heat and its properties for the construction of the calorimeter described above, K and r are constants of the calorimeter. Thus, the relationship between gas pressure and heating history is described by a convolution integral, the solution of which yields equations for calculating the rate of change of heat d Q ( t ) / d t and the total heat Q(t) at any time during the deformation process. The time constant of the calorimetric cells is 7-8 s, the limited thermal 0.42 mJ. The accuracy of the flux 84 pw, the minimal amount of heat heat measurements in the interval of 10-500 mJ is f3%.

-

2.2. Heat-conducted deformation calorimeters

Heat effects resulting from the deformation of solid and rubberlike materials are as a rule very small. For determining small thermal effects the most suitable calorimetric principle is the Tian-Calvet one [6]. For thermomechanical studies of polymers this principle was used for the first time by Godovsky [7,8], who developed a fully automatic deformation microcalorimeter for the simultaneous recording of the thermomechanical behaviour of rubbers and glassy and crystalline polymers in the form of films, fibres and strips with uniaxial deformation. A schematic diagram of the deformation calorimeter is demonstrated in Figure 2. The instrument consists of two parts: microcalorimeter and mechanical loading system with a dynamometric assembly. The calorimeter consists of two cells, the working dimensions of the calorimetric cells being as follows: diameter - 10 mm, length - 125 mm. The temperature difference between measuring and reference cells is measured by means of two thermobatteries, each of them including 810 copper-constantan thermocouples made electrochemically. The thermobatteries cover the whole surface of the cells. A sensitive amplifier and electronic recorder are used for automatically detecting heat fluxes. The microcalorimeter is placed in a thermostat with a working temperature range of 20-80OC. The dynamometric assembly which includes an automatic bridge-type dynamometer with a sensitivity of 0.5 g/mm allows one to record force and deformation which can be used for determining the work of deformation. The loading device allows the use of 8 linear rates of deformation in the range from 0.0146 to 1.865 mm/s. According to the theory of the method, the relation between the power of a relatively slow thermal process taking place in the calorimeter measur-

Y . K . Godovsky

I88

(31

Figure 2. Block scheme of Calvet-type deformation calorimeter. 1, 2 - recorders; 3 - loading device; 4 - force transducer; 5, 6 - thermostating system; 7 microcalorimeter with measuring and reference cells; 8 - sample ing cell, and the temperature difference between the measuring and reference cells is as follows (Tian equation):

+

dQ/dT = K [AT(t) d A T ( t ) / d t ],

(3)

where I< and r are the constant of the heat flux and time constant, respectively, which can be determined experimentally. The total heat resulting from the heat process for time t can be determined using the integral equation

Q ( t )= l t ( d Q / d T ) d t = K 0

I'

+

( A T t ) r(dAT(t)/dt)dt= K S ( t ) , (4)

where S ( t )is the area under the temperature-time experimental curve. The calorimeter can be calibrated by Joule heat by the procedure suggested by Calvet. The maximum sensitivity of the first instrument at room temperature was 3 x lov6 J/s. Later the sensitivity was improved, by using a more sensitive amplifier, to 2 x J/s. The time constant of the empty calorimetric cells is about 30 s. This value is lower by about one order of magnitude than in standard Calvet-type calorimeters. The total time constant of the cell with the sample and sample holders placed into the cell is somewhat higher than for the empty cell. Its value can be determined experimentally by embedding tiny electrical heaters into the samples of various dimensions. The error for both heat and work measurement is estimated to be f3% . The calorimeter is capable of working not only in the normal mode described, but in the ballistic mode, and allows the detection of thermal effects of deformation of less than 1 s duration. Many thermal measurements in deforming polymers can be carried out in the ballistic mode. According to the theory of the method, if the thermal process lasts for a time

Deformation calorimetry of oriented polymers

189

t < 0 . 2 (T,H ~ ~is ~the effective time constant of the cell with a specimen), then AT/Q = const to an accuracy of 1% and is time-independent (AT is the maximum of the ballistic curve peak, Q is amount of heat). The experimental ballistic curve corresponds to a very sharp peak. The minimum heat pulse that can be detected in a deformed polymer is about 4 x J. In the case of when the measurements are carried out in the ballistic mode, it is important to estimate the characteristic time in which the equilibrium temperature distribution across a specimen becomes established. It can be estimated from the ratio 6’/a, where 6 is the specimen thickness and Q is the thermal diffusivity (for solid polymers and elastomers a m/s). For 6 = 0.01 cm this time is about 0.1 s, and for 6 = 0.03 cm it is about 1 s. The use of ballistic conditions in measurements allows one to analyze, although roughly, two consecutive processes, one of which is a ballistic process, for example, rapid tension of elastic material to a constant elongation followed by stress relaxation Q = Qel + Qrel. In this case the integral thermal effect can be determined as the area under the thermal effect curve and the thermal effect of elastic tension Qel according to the peak maximum. Using this approach, one can estimate the heat effect resulting from the stress relaxation. Experiments show that the delay in the peak maximum after the supply of ballistic thermal power has stopped is about 5 s. Therefore, in the first approximation, the contribution of the relaxation heat to the thermal effect of elastic deformation can be ignored. The calorimetric experiments with the deformation calorimeter can be performed in various deformation modes, first of all in the elongationcontraction mode either in a nonstop regime or with the intermediate interruption.

-

3. Thermodynamics of the stretching of oriented polymers The linear thermomechanical analysis of various deformational modes is given in [2,3,9]. According to this analysis the following simple relations for the mechanical work W ,the heat effect Q, the change in the internal energy U and the heat t o work ratio are valid for uniaxial stretching of rods, films and fibres (as a first approximation)

W= EE’/~ Q = PTEE q = 2PT/& In these equations E is the elasticity modulus, p is the linear thermal expansion coefficient, E is strain, T is the absolute temperature. It is assumed that E and ,B are temperature independent. The relationships between the heat, work and internal energy change at constant temperature are shown in Figure 3. It is seen that the thermal and temperature effects resulting

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a

Figure 3. Mechanical work (I), elastic heat (2), internal energy (3), and heat to work ratio (4) as a function of strain E according to Eqs. (5)-(10). (a) - with positive 8; (b) - with negative from the reversible uniaxial stretching are determined by the coefficient of thermal expansion. As it is shown below, the negative thermal expansivity is very characteristic of oriented crystalline polymers. Therefore, the thermomechanical inversion of the internal energy during stretching of these polymers should be a remarkable phenomenon. The characteristics of the internal energy inversion are the following:

Above Tg most drawn crystalline polymers often exhibit a shrinkage on heating, i.e. a negative thermal expansion along the orientation axis [2,3]. One can suggest that this shrinkage is a consequence of the fact that Pel is negative. However, comparison of PI, for drawn crystalline polymers anA Pel,indicates that macroscopic PI, may considerably exceed PeI . Therefore, a t least two negative contributions to PI, must exist. One of t i e m is really determined by the value of Pel,for crystallites oriented along the orientation axis. The second contribution may be due to shrinkage of oriented chains in the amorphous regions above Tg. Thus, the shrinkage of oriented

191

Deformation calorimetry of oriented polymers

crystalline polymers on heating seems to include two molecular mechanisms: the conformational elasticity of oriented amorphous chains and the shrinkage of oriented crystallites. In contrast to the isotropic state, in the well-drawn state all crystallites are oriented along the drawing axis and therefore crystallite axes are parallel to the draw direction. On heating they become shorter. This contribution seems to be negative both below and above Tg.The contribution of the amorphous regions is determined by the degree of crystallinity, the portion of the tie chains and the degree of their orientation. Negative coefficients of thermal expansion along the axes of macromolecules in crystalline lattices were found for many polymers (Table 1). Hence, the contraction of the crystalline macromolecules along their axes can be considered as a rather general behaviour, independent of their chemical structure. Normally, the contraction along the macromolecules is sometimes less than the expansion perpendicular to the chains, suggesting that the volume thermal expansion coefficient has a positive value. It is very interesting that the negative thermal expansivity along the chains occurs not only at low temperatures, but at room temperatures as well. Another very important feature which can be seen in Table 1, is that the negative thermal expansivity is a rather weak function of the chemical structure of polymers. Dilatometric studies have demonstrated negative thermal expansion for many drawn crystalline polymers [2,3,10-161. The results of these experimental studies can be summarized as follows: Cold drawing of PE below T, and solid-state extrusion under elevated pressure lead to a monotonous decrease of the positive thermal expansion coefficient with increasing draw ratio. At a certain degree of drawing, dependent on temperature, PI becomes negative with PI, < pel,.For less crystalline polymers such as LbPE Table 1. Thermal expansion coeficients of polymeric lattices [2,3] Polymer PE

PC,, x105 K-'

PET

-1.2 -1.8 -(1.1-1.3) -2.2

PA-6

-4.5

Cellulose

-4.5

PCP NR

-4.1 -8.4

PC,

x105

Pa = 14.7 = 6.0 -130 60 Pa = 17.1 P b = 12.7 Pa = 6.0 P b = 23.4 pa = 6.0 Pc = 2.8 pa = 13.1 Pa = 12.5 P b = 20.5 Pb

+

K-'

Temperature interval, O C 20-60 20-120 22 -196 20

+ -196 + 20 -196 + 20 -196 + 20 -196 + 20

192

Y. K . Godovsky

with degree of crystallinity w, = 42%, one gets PI, = -5 x lo-' K-' at X = 2 and PI, = -20 x K-l at X = 4.2. The temperature dependence of PI, shown in Figure 4, typical of oriented crystalline polymers, reveals a very large increase of negative values of p,, with temperature. In a rather narrow temperature range (50-60 K) PI, increases several times. The temperature coefficient dpll/ d T does not depend much on the polymer type, although the absolute value of p of LDPE is approximately ten times larger than that of other polymers. %he following fact is also worth mentioning: for many oriented polymers such as POM with X = 6.5, HDPE with X = 4.2, PP with X = 5.5, PA with X = 2.5, increases in the the thermal expansion coefficient pll is positive below Tg, region of glass transition, decreases monotonously on further heating and becomes negative at a temperature characteristic of the polymer and its thermomechanical history. Such behaviour is consistent with the idea that the intermolecular interaction in amorphous regions is the factor controlling the expansivity and thermomechanical properties of oriented crystalline polymers. Summarizing the consideration of the thermal expansivity of oriented crystalline polymers, one may conclude that in two-phase polymers the behaviour of their amorphous regions above Tgis controlled by conformational changes strongly restricted by interchain interaction.

- -40 260

300

340

TI K

Figure 4. Temperature dependence of PI, for drawn crystalline polymers. 1 HDPE = 70%, X = 8 - 15); 2 - LDPE ( w C = 43%, X = 4.2); 3 - POM (wC (wC

= 63%, X = 6.5)

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Deformation calorimetry of oriented polymers

4. T h e r m o p h y s i c a l b e h a v i o u r of oriented p o l y m e r s during defor-

mation

4.1. Oriented amorphous polymers The most thorough deformation calorimetric investigation of drawn glassy polymers was carried out by Bonart et al. [17] on P E T films. The effect of the degree of cold drawing of P E T films on the value and sign of thermal effects at small and fully reversible stretching was studied. Typical results are shown in Figure 5. When the degree of cold drawing increases the endo-effect Q resulting from the stretching to the same strain decreases. With degrees of cold drawing larger than X = 4 the heat effect changes its sign and stretching of the film is accompanied by heat release, i.e. due to cold drawing, the linear thermal expansion coefficient changes its sign from positive t o negative. Despite this change, the dependence of heat to work ratio r] on strain is hyperbolic as predicted by the theory (Figure 3). It is worth mentioning that the samples of a degree of cold drawing higher than 4 possess some crystallinity, because the cold drawing occurred near the glass transition. However, cold drawing of P E T films at room temperature, which leads only to the appearence of the so-called amorphous c-texture

t

-

0.4

20

0.3

15

0.2

10

M 1

d

0.1

55 \

0’

-0.1

-5

Figure 5. Dependence of elastic heat (1-5) and heat to work ratio Q/W (1‘-5’) on strain for PET of various degrees of drawing. Degree of drawing: 1, 1’ undrawn; 2, 2‘ - X = 2; 3, 3’ - X = 3; 4, 4‘ - X = 4; 5, 5’ - X = 5; 6, 6’ X=6

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Y. K. Godovsky

without any crystallization, also causes a change in sign [9]. Hence, although stretching of well oriented PET films at room temperature (which is well below glass transition) is accompanied by heat release, the strain dependence of 77 as well as the elastic inversion of the internal energy correspond to the thermomechanical behaviour of the solid with a negative thermal expansion along the stretching axis, and is not characteristic of elastomers. The parameters of internal energy inversion and the values of p obtained with the aid of Eqs. (8) and (10) using values of are listed in Table 2. 4.2. Oriented crystalline polymers

Drawn crystalline polymers turned out to be extremely interesting thermomechanical materials. In an early study [4], it was found that cold drawing of PA-6 leads to a change in sign of the thermal effect accompanying reversible stretching of a cold-drawn sample, i.e. absorbtion of heat of an undrawn sample changes into heat release on stretching of a cold-drawn 0.8

15

0.6 10 0.4

0.2 M 1 h

d -0.2

5

5

1

0’ -5

-0.4

-10

-0.6 -0.8

-15

Figure 6. Heat (1,2) and heat to work ratio (3,4) of elastic deformation of LDPE at 2 O O C . 1,3 - isotropic sample; 2,4 - cold-drawn sample (A = 4, deformation along orientation direction)

Deformation calorimetry of oriented polymers

195

sample. Further comprehensive studies [2,3,9]showed that the change in sign is observed in many crystalline polymers. Typical results are shown in Figure 6 . The origin of the sign change is determined by the nature of the negative thermal expansion of drawn crystalline polymers. It should be stressed that after orientation, only the sign of the thermal effect changes while the general behaviour is similar for both samples. Such thermodynamic behaviour is observed with many polymers after orientation. Thus, in spite of the fact that there are amorphous regions in crystalline polymers, the thermophysical behaviour of such polymers above the glass transition of such amorphous regions is described fairly well by the formulas that are valid for solid materials rather than for elastomeric ones. The inversion of the internal energy on elastic extension is a very important feature of the thermomechanical behaviour for drawn Crystalline polymers. Such a behaviour is predicted by Eqs. (8) and (10) for solids having negative thermal expansivity. This inversion of the internal energy is actually observed in drawn crystalline polymers. Figure 7 illustrates the inversion behaviour for various drawn polymers, and in Table 2 the main inversion parameters are given. Although a similar inversion of the internal energy may also occur upon extension in elastomers [2], the sign of the inversion and its molecular origin are quite different. Indeed, for drawn crystalline polymers, AU at first decreases and only then begins to increase. In elastomers, such a change of AU cannot be observed in principle. It is important to point out that the inversion of the internal energy in crystalline polymers is determined only by the value of PI,, while the intrachain conformational energy changes do not play any role in this case. Numerous studies of the structure and properties of drawn crystalline polymers have led to the microfibrillar models of fibrous morphology [18-201.

-0.5

I

Figure 7. Internal energy changes ( A U )vs. strain ( E ) for drawn crystalline poly- LDPE ( A = 4); 2 - HDPE ( A = 10); 3 - HDPE ( A = 20); 4 - P P (A = 8); 5 - P P (A = 30); 6 - PA-6 (commercial film); 7 - PET (A = 5.4)

mers. 1

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Y. K . Godovsky

Table 2. Parameters of internal energy inversion on stretching drawn polymers

PI Polymer

Characteristics of sampleso) Extension of drawn polymers LDPE X=4 Tdr = 2 O o c HDPE X = 10 Tdr =95OC HDPE X = 20 Tdr = 95OC PP = 8 Tdr = 2O0c PI? = 30 Tdr = 140°C PA-6 Commercial film PET X = 5.4 Tdr = 20°C p = 1.338 g/cm3 PET [34] X = 6.0 Tdr = 85OC p = 1.380 g/cm3 ")wC- degree of crystallinity; b)&

AU

einv ni,€

%

%

J/crn3

p,, x lo5 E K-'

GPa

10.5 5.3 -0.43 4.5 2.2 -0.40 2.2 1.0 -0.45 3.4 1.8 -0.39 2.2 1.0 -0.22 5.0 2.4 -0.15 0.5 0.2 -0.012

-19.40 0.27

0.27 0.13 -0.015

-0.50b) 14.0

Poisson's ratio -

-7.50 1.70 0.56-0.63 -3.65 8.0 0.55 -6.30 2.35 -3.70 3.8 -

-8.20 0.55 0.50-0.55 0.58 -0.80 5.0 -

- drawing temperature

According t o these models the long and thin microfibrils are the basic elements of the fibrous structure. The microfibrils consist of alternating crystallites and amorphous regions. The axial connection between the crystallites is accomplished by intrafibrillar tie molecules inside each microfibril. The adjacent microfibrils may be interconnected by interfibrillar tie molecules (see also Chapters 2, 5, 11 and 12). The detailed thermomechanical analysis of various models of oriented crystalline polymers is given in [2,3]. It demonstrated that the PeterlinPrevorsek model is most suitable for analyzing the thermomechanical behaviour of oriented crystalline polymers. The correlation of the thermomechanical behaviour with molecular parameters (MW, MWD and degree of branching) and orientation parameters (temperature and draw ratio) has been established for P E [2,3]. The study included a calorimetric investigation of thermomechanics combined with an X-ray analysis and the analysis of molecular mobility with the aid of a molecular probe. This complex study showed that the sign and values of the thermal effects on stretching do really depend on the molecular weight and strain as shown in Figure 8. Combined analysis of the thermomechanical behaviour and structural changes showed that the heat evolution seems to be due to a compression of the interfibrillar amorphous molecules and the heat absorption to expansion of the intrafibrillar regions containing a small number of tie molecules. The resultant thermal effect depends on the relative ratio of the compressed and expanded amorphous regions. Based on the thermal effect and long-period variations in deformation as shown in Figure 8, a method was proposed for the quantitative evaluation of the volume fraction occupied in P E by interfibrillar tie molecules. The method involves

197

Deformation calorimetry of oriented polymers

Table 3 . Structure and thermophysical characteristics of drawn P E [2,9] 1 L XAI 1 - (wc -XAI) E p,, x l o 5 Thermal % nm nm % % GPa K-' effect of

Specimens and their thermal history

wc

PE1

72

initial elongation 21 26

0

28 4.4

1.1

endo

63 23 28

12

25 1.43

-0.5

exo

79 35 40 78 32 38 98 100 -

10 8 6

11 1.43 14 0.63 0 0.38

-

endo endo endo

68 25 28 81 27 28 81 39 41 44 19 29

23 17 15 27

9 2 4 29

-1.1

exo ex0 endo-exo exo

M,,=-4.2 x 10'; M,,/M,, = 3.0; 0.1 CH3/100 c X=6 PE-2 3' x lo5; M,/M, = 1.95; 0.1 CH3/100 c X=6 Isometric annealing Free annealing Annealing under pressure of 0.7 GPA at 264'C X = 15 Isometric annealing Free annealing PE-3 7' x 106 M,JM, = 2.5; 0.1 CH3/100 X = 5.5

gv

g,

5.00 4.90 3.40 0.70

-

-10.0

c

Symbols: X - draw ratio; I - longitudinal dimension of crystals according to WAXS; L - long period according to SAXS; X A I - volume fraction of interfibrillar amorphous regions; 1- (wc+ X A I )- volume fraction of intrafibrillar amorphous regions. The degree of crystallinity of a specimen was determined from calorimetric measurements of fusion heat. In all cases the cold-drawing temperature was 108'C. Annealing temperature was 132'C under atmospheric pressure; annealing time 30 min

summing up the contributions of the thermal effects of intra- and interfibrillar amorphous regions. The structural and thermomechanical characteristics of PE analyzed with this method are given in Table 3. As can be seen from the results, low-molecular-weight specimens are practically free of interfibrillar amorphous regions. An increase in molecular weight causes a monotonous increase of the fraction of interfibrillar regions for comparable temperatures and degrees of drawing. Furthermore, their fraction increases with the degree of drawing at a given temperature and with decreasing draw temperature. These experimental findings are quite consistent with theoretical estimates and X-ray structural measurements [21,22].

Y . K. Godovsky

198 0.2

a

0.61

0

a

3

0.4

0.2

a

M

\

-

0

6 -0.2

--0.2

-0.4

M

\ h

-0.6

6 -0.4

-0.8

b

6 4

-0.6

2 0

2

4

6

8c.%

Figure 8. Heat of elastic elongation (a) and deformation of long period (b) versus macroscopic deformation of PE-1 (l), PE-2 (2) and PE-3 (3). Characteristics of the samples are shown in Table 3. The form of corresponding heat effects is also shown

Figure 9. Effect of annealing of HDPE ( A = 15) on the heat of elastic extension. 1 - initial unannealed sample; 2 - after isometric annealing at 132'C for 30 min; 3 - after free annealing at 132'C for 30 min

Annealing of free or fixed drawn crystalline polymers is accompanied by considerable changes in their supermolecular structure and, as a consequence, in their mechanical properties [18,19,23]. The changes are most radical in highly stretched interfibrillar chains and tie chains in the intrafibrillar amorphous interlayers. Such abrupt changes can affect the thermomechanical behaviour. The data presented in Figure 9 show that the changes are most tangible in highly drawn specimens after annealing in the free state, which causes a change of the sign of the extension heat. The variations observed under all annealing conditions may be explained with disorientation and loosening of highly stretched interfibrillar molecules. As a result of these changes, the contribution of the endothermal effect may become predominant during the initial stretching. However, with increasing deformation the endo-effect turns to exo-effect. Free state annealing considerably reduces the elasticity modulus. Although, after isometric annealing the elasticity modulus remains practically unchanged, the thermal effect of stretching and respectively p,, vary considerably and in some cases sign inversion may follow. Hence, the thermomechanical phenomena occurring

D e f o r m a t i o n c a l o r i m e t r y of oriented polymers

199

during deformation of annealed samples reflect closely the changes caused by annealing. High pressure annealing of drawn PE results in the formation of the so-called extended-chain crystals [24,25]. The crystallite dimension along the extension axis is over 100 nm and the density is 0.996-0.997 g/cm3, the heat of fusion &f = 285 J/ g corresponding to a crystallinity of 96-98%. Such specimens usually have a laminar structure in which the crystalline layers of large longitudinal and transverse dimensions alternate with disordered layers where only a few chains are tie chains. As seen in Table 3, such specimens are characterized by a small elasticity modulus and endothermal effect on stretching. These results show that large crystallites and a high degree of crystallinity are not sufficient for attaining high mechanical properties of drawn crystalline polymers. The thermomechanical reason for this is the fact that the work of deformation is mostly spent for overcoming the weak intermolecular interactions in the disordered regions whereas the deformation of valence angles and bonds of the transconformers of crystallites remains largely unrealized . 4.3. Superoriented crystalline p o l y m e r s

Let us consider briefly the thermomechanical properties of superdrawn polymers. Articles of this kind have been obtained in recent years from PE, PP and POM polymers by cold drawing, hydrostatic extrusion in the solid state and by controlled crystallization of a flow of polymer melt or solution. From the standpoint of thermomechanics, two characteristics of such superdrawn polymers have great importance: the very high elasticity modulus which may be as high as E,, > 0.5 E,, at -150OC and (0.3-0.35) E,, at 2OoC and the negative coefficient PI,. At the same time the superdrawn polymers are characterized by morphological and structural features typical of standard well-drawn polymers [26], viz. the clearly outlined fibrillar structure and high concentration of lamellar crystallites. A morphological feature of superdrawn polymers which is most essential is that they contain crystalline regions whose length is much greater than the long period (see also Chapter 15). The data concerning the thermomechanical behaviour of superdrawn polymers are shown in Figure 10. Despite the absence in superdrawn crystalline polymers of extended chain crystals, their properties are quite comparable to those of crystal lattices. One can suggest that the ultimate properties are a result of the existence of perfectly oriented chains in intraand interfibrillar amorphous regions, which are a kind of “shunt” allowing transmission of stress through the chain skeleton rather than via a weak intermolecular interaction. If the intercrystalline intra- and interfibrillar bridges are really crystalline in the conventional sense of the word, the superdrawn polymers must be expected to have an excellent dimensional stability up to the melting point due to the small value of p,,. This

Y.

200

K.Godovsky

x = 200

201

//

E = 180 GPa A=20

E=8GPa

/3

10.

-10. -20.

QjJlgl

Figure 10. Elastic work ( W )and heat (Q) vs. strain E . 1 - crystalline transPE (calculated according to Q = PTEE with E,, = 240 GPa, p = -1.3 x deg-I); 2 - HDPE (A = 200, E = 180 GPa); 3 - HDPE (A = 20, E = 8 GPa)

is actually observed with superdrawn PE in a temperature range from -150 to +5OoC, but above 50’C the negative coefficient begins to rise rapidly. This has been attributed to high-temperature annealing (120’C). However, this fact may be explained in a different way if one assumes that the inter-crystallite bridges are not truly crystalline but consist of ultimately oriented chain portions. In contrast t o the dimensional variations within the temperature range from -150’ to +5OoC, those occurring above 50’C must be irreversible - and this is actually the case [27]. Similar effects are also observed with high-modulus P P fibres [28,29]. Quite recently the deformation calorimetry was applied for studying small reversible deformations of single crystal mats of ultra-high-molecular weight P E oriented to various extension ratios (up to 200) [30]. The results of deformation calorimetry, coupled with X-ray data, allowed to resolve the elastic and viscoelastic components of the reversible deformation. It was established that the internal energy change is irreversible in the loadingunloading cycles. The decrease of the internal energy seems to be due to the “curing” of conformational defects and the increase in the internal energy with the deformation is determined by the process of the accumulation of defects in crystalline regions and by loss of continuity of the material. 5. Anisotropy of thermophysical behaviour of oriented polymers

Polymer crystallites exhibit a striking anisotropy of thermal expansion. A strong anisotropy of this property is also typical of solid drawn polymers and stretched elastomers. The linear thermal expansion decreases along the orientation axis (pll) and increases in the direction perpendicular to the

20 1

Deformation calorimetry of oriented polymers 0

a

4

2 h F)

0 r(

X

0’

-2 -4

T Figure 11. Dependence of the linear coefficient of thermal expansion of LDPE on the angle to the drawing direction. Values of &, were obtained from the heat of elastic stretching

Figure 12. Elastic heat as a function of elastic force f for LDPE. 1 - isotropic; 2 - drawn; 3 - redrawn; 4 - at the angle 45’ to the draw direction; 5 - at 90’ to the draw direction; 6 - at 15’ to the draw direction

draw direction (p, ) both for crystalline and glassy polymers. However, the anisotropy of oriented crystalline and glassy polymers may be considerably different at comparable draw ratios. The p,/P,, ratio is strongly dependent on the type of polymer. For glassy PS and PMMA at a draw ratio of X = 4, the ratio is equal to 1.1 and 2.5, respectively, and for PVC which has a low degree of crystallinity, it is equal t o 4.5 at a draw ratio of X = 3 [31]. The anisotropy of thermal expansion of oriented crystalline polymers is considerably higher, due t o of a very high anisotropy of crystallites along the orientation axis and a higher degree of orientation of tie molecules. A typical dependence of the linear thermal expansion of an oriented crystalline polymer is shown in Figure 11. Figure 12 shows that the dependences of the elastic heat on elastic force follow Eq. (6) in any direction. A similar behaviour has been observed with drawn P E T and PA-6. Dependences of heat to work ratios upon strain with all these drawn polymers support the idea that in any direction to the draw axis the thermomechanical behaviour is controlled by the intermolecular interaction.

202

Y . K . Godovsky

6. Mechanisms of d e f o r m a t i o n of oriented p o l y m e r s as revealed

by d e f o r m a t i o n calorimetry and their relation to morphology Above Tg, moderately drawn crystalline polymers have an elasticity modulus of the order of a few GPa and are capable of being reversibly deformed by 15 to 25%. Since this deformation is concentrated in the amorphous regions, the true strain in these regions at typical values of crystallinity (30 to 70%) may be several times higher than these values. These reversible deformations of amorphous regions with the relatively small elasticity modulus must, of course, be due t o stretching of the otherwise coiled conformations. Such transitions in drawn crystalline polymers (HDPE, PP, PA-6) have been registered by IR spectroscopy [18,32]. However, in contrast to elastomers, these gauche-trans transitions in amorphous regions of microfibrils occur simultaneously with variations of volume and intermolecular energy, which determine the elasticity modulus since the cis-trans transitions alone cannot result in rather high values of elasticity modulus if the intermolecular interactions remain practically constant. The available data on the thermomechanical behaviour of two-phase crystalline polymers prompt the conclusion that, in contrast to classical elastomers, in crystalline polymers it is the intermolecular interaction which controls the thermomechanics of deformation both below and above the glass transition temperature of the amorphous regions. This peculiar thermomechanical behaviour of crystalline polymers led to the conclusion [2,3] that, despite the localization of reversible deformations in amorphous regions, the submicroscopic size of crystallites and amorphous regions, as well as the molecular bonding of the amorphous and crystalline regions by means of tie molecules create, during deformation of this microheterogeneous system, the conditions, under which it is, in principle, impossible for the amorphous regions to deform on the account of shape variation (conformational elasticity) only and they undergo complex deformations involving volume variations. The latter are typical of solid polymers rather than of elastomers and, what is even more essential, the free energy of deformation is related t o these volume variations. In other words, the work of deformation is spent to overcome the volume elasticity of the amorphous regions. Although conformational changes (the cis-trans transitions) also occur in this case, making considerable reversible deformations geometrically possible, the thermodymanics of such deformations is controlled by the intermolecular interactions between chains in the amorphous regions. These complex volume deformations of amorphous regions including elements of both conformational and volume elasticity are responsible for the unique thermomechanical properties of crystalline polymers. The question of the elasticity modulus and other properties of amorphous regions of crystalline polymers at temperatures above Tgis one of the most complex ones in the analysis of crystalline polymers. So far there has been no reliable method for calculating the elasticity modulus of amor-

Deformation calorimetry of oriented polymers

203

Figure 13. Heat of elastic elongation (1,3) and contraction (2,4) as a function of strain for HDPE (1,2) with degree of cold-drawing X = 20 and for PP (3,4) with degree of cold-drawing X = 8 phous regions and all estimates have been, to a larger or lesser extent, based on comparison with elastomers. It becomes obvious that the conventional approach t o the analysis of elasticity modulus of crystalline polymers based on treating them as crystallite-reinforced elastomers is oversimplified. The fact that macrodeformation does not coincide with deformation of the long period in specimens with a large content of interfibrillar amorphous regions seems to be due to reversible slip of microfibrils relative to each other and, therefore, must bring about an interesting thermomechanical effect. The slip of microfibrils must result in an additional heat release, since the work of internal friction must, at least partly, be converted into heat. On contraction, the microfibrils must return to their original position, i.e. slip back, which must again involve heat release. One may assume, therefore, that when such polymers are stretched, the beginning of slipping must be manifested by a sharp increase of the exo-effect and, further, the sign of the thermal effect of contraction may be reversed from endo to exo. Analysis of stretching and contraction heat shows (Figure 13) their variations t o be consistent with the slippage of microfibrils with interfibrillar amorphous regions as discussed above. These results may be regarded as an indirect indication of the presence of interfibrillar amorphous regions in drawn P E and PP. The abruptness of the change in sign of contraction heat is strongly dependent on the draw ratio and this is not unexpected if one takes into account that length differences among interfibrillar chains are smaller when drawing is greater (see also Chapter 2 ) . Recently a mechanism of flow during tensile deformation of high modulus P E fibres is proposed [33] in which, at first, tie molecules or intercrystalline bridges are pulled reversibly out of crystalline blocks, and this is consistent with our proposed mechanism.

204

Y . K . Codovsky

7. T h er m o physi c a l be ha viour of oriented polymers under f r a c t u r e

Even in early considerations, it was recognized that a macromolecule or its adequately large part stressed to its load-bearing capacity is an extremely powerful source of elastically stored energy [34]. Loading of any macromolecule by an external force results in the storage of elastic energy in each of its chemical bonds. The stored energy is higher, the closer the tensile stress to the limit of bond strength. When none of the stressed bonds are broken, the macromolecule is in equilibrium and is capable of producing external work. If, however, only one stressed bond is broken, the equilibrium is disturbed immediately and all the energy stored in both parts of the broken macromolecule must be dissipated as heat. The mechanical work spent on the dissociation of one molecular bond and formation of two radicals is only a small part of the whole elastically stored energy. If the broken parts are localized in a very small volume which seems to be a rule in crystalline polymers, the dissipation of the stored energy may look like a microexplosion (see Chapter 1). A detailed analysis of the energetics of chain rupture in stressed oriented crystalline polymers showed that such “microexplosions” really take place [2,35,36]. In such polymers the tie molecules connecting adjacent crystallites may be overstressed considerably during elastic deformation. The length of the overstressed tie molecules, the rupture of which is accompanied by dissipation of the stored elastic energy, depends upon the intermolecular interaction, morphology and rigidity of macromolecules. Because the intermolecular forces in polymers are considerably weaker than the intramolecular ones, the overstressed segments must be rather long, which is a necessary condition for exothermic fracture. The micromechanics of the deformational behaviour and scission of the tie macromolecules in highly drawn crystalline polymers was considered for the first time by Chevychelov [37,38], and a further extension of the treatment was made by Kausch [39]. The following problems were considered theoretically: (i) what are the maximum stresses which can transfer a completely extended tie chain before the parts of the macromolecule embedded in two different crystalline layers can begin to pull out from the crystallites; (ii) at what distance in the periodic intermolecular potential of the crystallites is the stress in the tie molecule affected; (iii) in what manner are these stresses dependent upon the intermolecular interaction in crystallites. Without going into too many details concerning the calculations, let us consider only some results necessary for the following estimates. For typical values of the dimensions of the crystallites and the amorphous regions in P E and PA-6, the following estimates have been made: The stress limits which can be applied to the extended tie molecule in the amorphous region through the ideal crystallites are 7.5 GPa for P E and 22.4 GP a for PA-6. The higher values of the static strength of the PA-6 crystallites are due t o the presence of strong hydrogen bonding. Because of this difference

205

Deformation calorimetry of oriented polymers

the stresses in PA-6 crystallites disappear at a distance of about 3.5 nm, while for PE at a distance of about 5 nm. The value of the limit stress for PE is about 30% of the molecular strength, while for PA-6 it is close t o the molecular strength. The typical contour length of the macromolecule embedded in two adjacent crystallites including the amorphous region consists of 200 C-C bonds. The length of the tie part of the molecule consists of some dozens of C-C bonds. Suggesting that the stresses disappear close t o the centers of the crystallites, one can arrive at a length of the overstressed segments consisting of about one hundred C-C bonds. According to calculations, the rupture of such a segment is an exothermal process. It is especially applicable to PA-6 crystallites which are more rigid. It is a well-established experimental fact that major differences in subsequent loading-unloading cycles are observed between the first and the second loading, whereas only minor differences occur between the second loading curve and those obtained for subsequent deformation cycles. The conclusions based on these data are that the drastic changes in the sample structure and properties occur namely during the first loading. From the energetic point of view this means that in the energy balance of the first loading the contribution resulting from chain scissions should exist, while during the second and subsequent loadings the energy balance should be governed only by the elastic response of strained segments. It should be kept in mind, however, that such an energy balance should be characteristic not only of the purely elastic stretching and scission of macromolecules. If chain scissions during the first loading are accompanied by the appear-

4

40

M

\

h

s; 22

M

I

\ h

6 20

II

1

5

‘Q

a

u . ~ O - ~(MPa)

b

8’

0.10-~ (MPa)

Figure 14. Mechanical hysteresis 6W = We,- W , (a) and heat Q dissipated (b) as a function of stress u for highly drawn PA-6 fibres. 1 - first cycle; 2 - second and subsequent cycles

Y. K.Godovsky

206

ance of irreversible (plastic) deformation, the latter also may contribute to the energy balance. Therefore, this approach needs very careful control of the appearance of the irreversible deformation during the first loading and the corresponding separate estimation of the contributions resulting from plastic deformation and from chain scissions. The only experimental study of such energetical effects was carried out by calorimetric measurements of highly drawn PA-6 fibres [2,40]. These PA-6 fibres, drawn t o 5.5 times their original length at 21OoC,were repeatedly stretched in the Calvet-type calorimeter at room temperature. The specimen was stretched to some definite deformation, then the load was removed, after which it was reloaded to the same deformation in the same manner. In both cases the work spent in the extension-contraction cycle (mechanical hysteresis) and the total thermal effect during the cycle were measured. The energy characteristics for the first and the second cycles are equal only when the stress is below about 400 MPa. On further deformation the situation changed drastically: both the mechanical work and the thermal effect upon the first loading, when molecular ruptures occurred, turned out to be a few times higher than those upon the second and subsequent loadings when molecular ruptures were not involved in the energy effects. It is very important t o emphasize that the difference occurred only at the stage of loading, because the unloading stages for all cycles were en-

~ . 1 0 -(MPa) ~

Figure 15. Energy effects due to molecular rupture upon loading of the PA-6 fibres

Deformation calorimetry o f oriented polymers

207

ergetically equivalent. The energy characteristics above 400 MPa resulting from the irreversible events occurring during the first loading are shown in Figure 15. Two very important features are seen. First of all both mechanical work and heat release grow exponentially with increasing tensile stress. This is seen when the data are replotted in semilogarithmic coordinates. As an example, Figure 15 shows the plot log AQ = p(a) from which it follows that AQ = AQ exp(pu), where u is the applied tensile stress, Furthermore, the mechanical work always exceeds the heat release, so that some energy AU remains in the polymer. The growth of AU is also exponential with the stress. It should be noted that the concentration of free radicals also increases exponentially under extension of these PA-6 fibres above 400 MPa during the first loading. Therefore, the stress dependence of the energy parameters measured correlates qualitatively with the corresponding dependence of the number of bonds ruptured in the polymer during the first loading. Using these data, various estimations have been made: the role of the plastic deformation in energy characteristics, the number of broken chains, the length of the segments where the rupture of one bond is accompanied by the dissipation of the total energy stored [2,40]. Thus, from all these estimations one can conclude that the mechanical destruction process has a chain character when free radicals resulting from the rupture of the first molecule lead t o the fast rupture of tens to hundreds of adjacent stressed molecules. Due to this “group” dissipation process, a very high local heat release can occur. The latter is localized in the weak amorphous interlayers and, therefore, the local overheating resulting from heat release can be classified as peculiar thermal microexplosions. The latter will accelerate the formation of submicroscopic cracks, which can be detected by small angle X-ray results. According to such X-ray analysis, the number of submicrocracks in similar samples of PA-6 in the prerupture state is about 5 x 10l6 ~ m - their ~ , diameter being close t o 15 nm [36]. Therefore, it is now possible to estimate the local temperature rise resulting from the “microexplosions” . Assuming the microadiabatic character of the microexplosions one can arrive at the following result:

where N,, and V,, are the number of cracks and their volume, respectively. Hence, this estimation shows that the local overheating reaches a very high level. Nevertheless, it is in good agreement with IR-measurements of the local temperature rise accompanying the propagation of fast-moving cracks in solid polymers.

208

Y. K . Godovsky

References 1. L. R. G. Treloar, “The Physics of Rubber Elasticity”, Clarendon Press, 3rd edition, 1975 2. Yu. K. Godovsky, “Thermophysical Properties of Polymers”, Springer-Verlag, Berlin, Heidelberg, New York 1992 3. Yu. K. Godovsky, Adv. Polymer Sci. 76,30 (1986) 4. F. H. Mueller, “Thermodynamics of deformation. Calorimetric investigation of deformational processes”, in: Rheology, Academic Press, New York 1969, vo1.5, p.417 5. R. E. Lyon, R.J. Farris, Rev. Sci. Instr. 57, 1640 (1986) 6. E. Calvet, H. Prat, “Microcalorimetry”, Masson, Paris 1956 7. Yu. K. Godovsky, G.L. Slonimsky, V.F. Alekseev, Vysokomol. Soedin. All, 1181 (1969) 8. Yu. K. Godovsky, “Thermophysical methods of polymer characterization”, Khimija, Moscow 1972 (in Russian) 9. Yu. K. Godovsky, Colloid Polym. Sci. 260,461 (1982) 10. W. T. Mead, C. R. Desper, R. S. Porter, J . Polym. Sci., Polym. Phys. Ed. 17,859 (1979) 11. N. J. Capiati, R. S. Porter, J. Polym. Sci., Polym. Phys. Ed. 15,1427 (1977) 12. C. L. Choy, F. C. Frank, K. Young, J. Polym. Sci., Polym. Phys. Ed. 19, 395 (1981) 13. C. L. Choy, M. Ito, R. S.Porter, J. Polym. Sci., Polym. Phys. Ed. 21,1427 (1983) 14. F. P. Wolf, V. H. Karl, Angew. Makromol. Chem. 92,89 (1980) 15. F. P. Wolf, V. H. Karl, Colloid Polym. Sci. 259,29 (1981) 16. F. P. Wolf, V. H. Karl, Makromol. Chem. 182, 1787 (1981) 17. L. Morbitzer, G. Hentze, R. Bonart, Kolloid 2. 2. Polym. 216/217, 137 (1967) 18. V. A. Marikhin, L. P. Myasnikova, “Supermolecular structure of polymers”, Khimija, Leningrad 1977 (in Russian) 19. A. Peterlin, Colloid Polym. Sci. 265,357 (1987) 20. D. C. Prevorsek, G.A. Tirpak, P.J. Heged, J. Macromol. Sci., Phys. B9, 733 (1974) 21. “Ultra-high modulus polymers”, edited by A. Ciferri, I. M. Ward, Applied Science Publishers, London 1979 22. V. A. Marikhin, L. P. Myasnikova, N. L. Victorova, Vysokomol. Soedin. A18, 1302 (1976) 23. “Structure and properties of orientedpolymers”, edited by I. M. Ward, Wiley, New York 1975 24. Yu. A. Zubov, V. I. Selikhova, M. B. Konstantinopolskaya, Vysokomol. Soedin. A14,2090 (1972) 25. Yu. A. Zubov, A. N. Ozerin, N. F. Bakeev, Dokl. Akad. Nauk USSR 221, 121 (1975) 26. G. Capaccio, Colloid Polym. Sci. 259,23 (1981) 27. W. T. Mead, R. S. Porter, J . Appl. Phys. 47,4278 (1976)

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28. Yu. K . Godovsky et al, III Internat. Symp. Man-Made Fibers, Kalinin, Prepr., vol. 1 (suppl.), p. 66 11Internat. Symp. Man29. Yu. A. Zubov, N. F. Bakeev, V. A. Kabanov et al, 1 Made Fibers, Kalinin, Prepr., vol. 1 (suppl.), p. 53 30. S. N. Chvalun, Yu. A. Zubov, N. F. Bakeev, Polymer Science USSR 35, 1 (1993) 31. K. H. Hellwege, J. Hannig, W. Knappe, Kolloid. Z. Z. Polym., 188, 121 (1963) 32. P. M. Pakhomov, M. Shermatov, V. E. Korsukov et al., Vysokomol. Soedin. A18, 132 (1976) 33. H. van der Werff, A. J. Pennings, Colloid Polym. Sci. 269,747 (1991) 34. G. A. Patrikeev, Dokl. Akad. Nauk SSSR 120, 339 (1958) 35. E. E. Tomashevskii, Solid State Phys. (FTT) 12, 3202 (1970) 36. V. R. Regel, A. I. Slutsker, E. E. Tomashevskii, “Kinetic nature of the strength of solids”, Nauka, Moscow 1974 (in Russian) 37. A. D. Chevychelov, Vysokomol. Soedin. 8,49 (1966) 38. A. D. Chevychelov, Mekhanika Polym. No 5, 664 (1966); N o 1, 8 (1967) 39. H. H. Kausch, “Polymer Fracture”, 2nd ed., Springer-Verlag, Berlin, Heidelberg, New York 1986 40. Yu. K. Godovsky, V. S. Papkov, A. I. Slutsker, E. E. Tomashevskii, G. L. Slonimskii, Solid State Phys. ( F T T ) 13, 2289 (1971)

Oriented Polymer Material> Stoyko Fakirov Copyright 0 2002 Wiley-VCH Verlag GmbH & Co. KGaP

Chapter 7

Scanning force microscopy on the orientation of gel-crystallized ultrahigh molecular weight polyethylene

S. S. Sheiko, M. Moller

1. Introduction Uniaxial orientation and chain extension of the macromolecules are basic requirements for the preparation of strong polymer fibres. Fibres with properties which approach the theoretical limits in strength and modulus can be obtained by principally different technologies. These are spinning lyotropic liquid crystalline solutions of “stiff rod” polymers, e.g. polyaramides [1,2] and the so-called gel-spinning/drawing technology which was developed for flexible polymers like linear polyethylene [3,4]. Reversible UHMW P E gels are the precursors for the preparation of P E fibres with excellent mechanical properties [5]. In recent years, the drawing process and the resulting properties of solution crystallized UHMW P E have been studied extensively [6-91. Our knowledge of the structure is mainly based on studies by spectroscopic and diffraction methods [lo-151. Direct visualization of the fibre morphology was possible by scanning and transmission electron microscopy [16-211. As an important alternative t o diffraction techniques, microscopy allows direct observation of the structure and can also monitor the microscopic mass transfer. The latter is beyond

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the possibilities offered by X-ray diffraction and spectroscopy which usually give only an averaged information on the complex and heterogeneous deformation process. Additional details can be visualized by the rather newly developed scanning probe microscopy techniques, i.e. in particular Scanning Force Microscopy (SFM). SFM is based on the detection of force profiles between a probing needle and the investigated surface [22]. The method does not require any surface treatment, and it allows to monitor the three-dimensional surface structure at ambient conditions approaching an atomic resolution. SFM can be applied almost t o all kinds of materials because of the universal character of the employed interaction and it has been used successfully for studies on polymer materials [23-301. Complementary to other methods, interfacial interactions and micromechanical properties of a surface can be evaluated using this method [31-341. First SFM studies on gel-drawn UHMW P E will be reviewed in this chapter. As it will be shown, SFM can reveal morphological details which are at the limit of or even beyond the possibilities of conventional electron microscopy, and thus help to document the structural changes which occur during the drawing process and which control the properties of the final product. 2. O n the structure of dried and solvent containing gels

Reversible UHMW PE gels are formed by cooling semi-dilute solutions of UHMW P E in decaline or xylene from a temperature above the dissolution temperature of polyethylene to room temperature [35]. A large number of investigations have been performed on the films which are obtained after drying of the gels [36-401. In most cases, the solvent had to be removed for these experiments and the original structure collapsed. An alternative preparation that allows to investigate microtomed thin sections of the gels by TEM is based on the polymerization of the solvent. For TEM investigations of biological samples consisting of water containing “jelly” cells, different techniques have been developed to arrest the structure in the most original state and harden it so that samples can be microtomed [41-431. Correspondingly, xylene in the PE gel can be replaced by a mixture of methacrylate monomers which than can be polymerized by UV initiation [42]. The low viscosity and the hydrophobicity of the monomer mixture allow rapid penetration into the gel. Miscibility with the original solvent facilitates the substitution. N o swelling or shrinkage of the jelly sample is observed during this procedure. In general, the micrographs of the PE gels show a network structure of randomly distributed chain folded single crystals (Figure l(a)). Actually, the crystals form curved, dome-like structures. Only lamellae which are oriented at an angle close to 90’ with respect to the plane of the section

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Figure 1. Electron micrographs of a polymethacrylate embedded polyethylene gel prepared by cooling a solution in xylene (3% by wt.) from 135OC t o room temperature: (a) network of curved (dome-like) single crystals; (b) high magnification of an edge on view of a crystal-crystal junction [16]

are clearly visible in the two-dimensional projection. The crystals appear as thin, bright stripes with dark borders, embedded in a light matrix. The dark borders are due to the preferential reaction of the folded, constrained chains on the crystal surfaces with the staining agent, i.e., Ru04 [44]. The highly crosslinked methacrylate is only slightly stained and shows a pepper and salt structure. The gel (network) is formed by alignment of short lamellasegments with dark interlayers of amorphous material as the actual connection (Figure l(b)). Branching points, where the lamellae themselves ramify have not been detected. Therefore, the gel topology is described by bridges of isolated (or a few stacked) lamellae which are locally interconnected by adhesion of the crystal surfaces. Figure 2(a) gives an example of a ridged structure. The formation of the creases can be regarded as crystal twinning. A schematic drawing of the ridged crystal is shown in Figure 2(b) including the relevant angles. The zigzag structures form an angle of about 120' which is consistent with the formation of ridged crystals and sectorized, hollow pyramids as well as

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b

Figure 2. A ridged PE crystal: (a) TEM edge on view of the crystal; (b) schematic drawing of a ridged crystal with relevant angles [16]

tent- and chair-like crystals [45-471. The chains in these ridged crystals are not oriented normal to the crystal surface but inclined at an angle of 58”

PI.

Upon evaporation of the solvent, the sheet-like crystals orient themselves parallel to each other and form stacks of lamellae. Removing half of the solvent resultes in a structure where the network has not been formed from single lamellae but from bundles or stacks of lamellae (Figure 3). This may be the explanation for the observation of the diffuse clover-leaf small angle light scattering patterns indicating rod-like structures or bundles [36,40]. Electron micrographs of the finally dried gel film show stacked lamellae which are oriented parallel to the film surface (Figure 4). The fibre pattern of the wide angle electron diffraction demonstrates that the chain axis is mainly oriented normal to the lamella surface. From the small angle electron diffraction pattern the long period could be calculated t o be 7.1 nm, which is in good agreement with the value obtained by measurements on the micrographs. A scanning force micrograph of the surface of the dried gel film which has been recorded with a “super tip”’ is shown in Figure 5(a). Small convex grains with diameters in the range of 100-400 nm and average variations *The “super tip” was prepared according to Keller [48], it has a peculiar high aspect (length/diameter) ratio.

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Figure 3. Electron micrograph of an embedded polyethylene gel after removing half of the solvent [16]

Figure 4. T E M micrograph of the cross-section perpendicular to the surface of a film after complete drying at 5OoC. The inset on the left shows the WAED pattern and inset on the right the LAED pattern of the same sample area [16]

in height of about 100 nm have been observed to be characteristic of the surface of the gel. However, in the case of a relatively rough surface, convolution of the surface profile with the tip shape can result in “tip image” artifacts [49-511. In order t o verify the surface topology shown in Figure 5(a), scanning electron microscopy experiments have been performed. Comparison of the SEM micrograph in Figure 5(b) with the SFM image in Figure 5(a) demonstrates that both techniques give similar surface mor-

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Figure 5. Scanning force (a) and scanning electron ( b ) micrographs of the surface of dried, gel-crystallized polyethylene. T h e sample for SEM measurements was coated with a thin carbon film and for SFM study a “super tip” was employed. Scale bars = 500 nm [51]

phology in the flat areas. Thus, the grains can be assigned t o the surfaces of polyethylene lamellae crystals. 3. Gel necking

Upon drawing, the original chain folded lamellar structure is transformed into a chain extended fibrillar morphology. Different approaches were used to explain the transition from a lamellar to a fibrillar structure [52-561. A widely accepted model to describe the formation of a fibrillar structure has been proposed by Peterlin [52]. Mainly based on wide and small angle X-ray scattering data, the deformation of solution-crystallized UHMW P E was considered to comprise fragmentation of the lamellae via shear and tilting combined with subsequent unfolding of the chains [8,10] (see Chapter 2). The most significant morphological changes occur in a narrow necking region which separates the original lamellar material from the drawn fibrous sample. In order to monitor different stages of the deformation and the conversion from lamellar to fibrillar crystallites, the bulk structure of the necking region can be studied by TEM and the surface structure scanned by SFM. In addition, also surface replicas can be used to verify SFM images. Figure 6 indicates the different locations where TEM and SFM pictures have been taken. A TEM micrograph which has been taken directly a t the edge of the necking transition is shown in Figure 7(a). The structure is similar t o that of the undrawn gel (Figure 4). When a sample was taken from a location slightly more inward the necking zone where the deformation had proceeded

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Figure 6. Locations of the necking region from which TEM (1,Z) and SFM (3,4,5,6)images were recorded

Figure 7. TEM micrographs and corresponding electron diffraction patterns taken from different locations in the necking region; (a) location 1; (b) location 2 according to Figure 6 [16] further, a herringbone type pattern was observed as i t is shown in Figure 7(b). T h e axis of this pattern is aligned parallel to the draw direction while

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Figure 8. Force (a,c,e) and height ( b , d , f ) scanning force micrographs as recorded in different locations in the necking region; (a) and (b) location 3; (c) and (d) location 4; (e) and ( f ) location 5 as indicated in Figure 6 . Scale bar = 40 /I [64]

the constituting lamellae are inclined towards the backbone. The lateral width of the lamellae and the size of the stacks indicate that lamellae were sheared against each other without breaking the crystallites into small blocks. A series of SFM measurements were performed within the 0.5 mm wide

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necking region between the neck and the undrawn material. Figure 8 shows the height and force micrographs which were taken at different distances from the necking front. They demonstrate a fibrillar structure which is well oriented in the draw direction. More clearly seen in the force micrographs, the fibrils themselves are structurized. A series of micrographs which correspond to those of Figure 8 but with a higher magnification are shown in Figure 9. In the close vicinity of the necking front, Figure 9(a) depicts lamellae which are yet not destroyed but are sheared relatively t o each other. The stacked and sheared crystallites form "ribbons " with their long axes

Figure 9. Enlargements of the scanning force micrographs of Figure 8; (a) location (b) location 4; (d) location 5; (e) location 6. Scale bars = 1 p . The twodimensional profile was taken from (a) along the A-A line [64] 3;

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oriented parallel to the draw direction. This orientation is seen even more clearly in Figure 9(b). The a-axes reorientation was described by Keller as a process which occurs in the intermediate stages of the stretching of wet gels [5]. Similarly, WAXS patterns from the necking region show that the b-axis of the crystallites aligns almost immediately perpendicular to the draw direction [lo]. Sliding of the lamellae is in agreement with a simple geometrical observation upon comparison of two samples of identical size and shape from which one has been prepared from gel crystallized and the other from melt crystallized UHMW PE. After drawing t o a draw ratio just above necking, the width of the gel film does not change while the lateral size of the melt film is altered significantly as it is shown in Figure 10. In contrast to melt films, the strongly anisotropic gel films are formed from parallel thin sheet lamellae with 8-10 nm thickness and 300-700 nm width, whose constituent chain folded molecules are little entangled and which are linked mostly only by rather weak adhesion forces. A thickness reduction without significant contraction in width results when the sheets slide over each other.

Figure 10. Photograpic image of a neck drawn melt crystallized (a) and solution crystallized (b) UHMW PE film; the elonagtion in the neck is X = 9

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Figure 11. Transmission electron micrographs of polyethylene lamella crystallites which have been picked up with a cellulose acetate replica a t the surface of the necking region [64]

Figure 9(c) shows a profile along one of the ribbons depicted in Figure 9(a) which demonstrates that the height of the inclined steps of about 812 n m corresponds well to the thickness of PE lamellae as measured by TEM. The inclined lamellae at the beginning of the necking are consistent with the herringbone structure in Figure 7(b) and with the 4-point SAXS diagrams reported by van Aerle and Braam [lo].

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Figure 12. Different levels of fibrillar structure as monitored with threedimensional scanning force micrographs: (a) bundles of microfibrils; (b) microfibrils constituted of nanofibrils; (c) polyethylene chains on the surface of two nanofi brils

T h i n cellulose acetate films which were cast a n t h e surface and then pealed off can be used as an “adhesive tape” in order to pick u p surface

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entities like single lamella and fibrillar crystallites which have been linked to the tape structure rather loosely. These can be observed then by TEM as shown in Figure 11. Everywhere on the surface of the necking region, isolated and aggregated lamellae were found which could be identified as polyethylene single crystals by means of their electron diffraction pattern. The transition from chain folded lamellae to fibrils became evident further away from the necking front. Figure 9(d) shows remnants of the lamellae which coexist with just formed fibrils. As the lateral size of the lamellae decreased, fibrils with a diameter of 100-200 nm were drawn out of them. In some cases splitting of the fibrils is visible, yielding the smallest fibrillar elements with a diameter of about 50 nm. Further from the necking front, these nanofibrils became even smaller in diameter (20-50 nm). This is shown in Figure 9(e) where small blocks of the lamellae remnants still exist in addition to fully developed nanofibrils which finally become the dominant structural units as shown in Figure 13(a). Clearly, the SFM observations are in agreement with experimental data on the bulk deformation as obtained by TEM and SAXS and the surface picture reflects the bulk deformation rather directly. Basically, three steps of the deformation process have been discriminated. In the first step, extended ribbons of sheared stacks of lamellae are formed by coherent sliding of the rather loosely attached sheet-like lamellae. Apparently, the stacks of lamellae are formed during gel preparation (Figure 3) and they constitute a basis for the ribbon structure. During sliding, the lamellae tend to orient with their short axes perpendicular to the draw direction while they get tilted relatively to the draw direction. This process will ultimately lead to a shear deformation of the lamellae whereby the c-axis gets inclined towards

Figure 1 3 . Nanofibrils at the surface of drawn gel films do not show significant changes in diameter as the draw ratio increases: (a) X = 10; (b) X = 70. A single nanofibril is seen as lying over the surface of the X = 70 film. Scale bars = 250 nm [51]

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the lamella surface (see also [lo]). Before shearing to cause a fragmentation of the lamellae, it already contributes substantially to the macroscopic strain. Formation of the ribbon structure might be important as it yields small structural units for which the yield stress can be attained easily before breakage of the material occurs. In the second step fibrils are drawn out of the stacks of lamellae. With increasing draw ratio, the heterogeneous and gradual transformation of lamellae into fibrils leads to the coexistence of lamellar remnants and new fibrils. Splitting of the microfibrils having a diameter of about 100 nm results in formation of the smallest fibrillar elements, i.e. the nanofibrils. At further drawing the transition to nanofibrils gets complete and the diameter of the nanofibrils is reduced to 20-50 nm. 4. Fibrillar structure

The three-dimensional surface structure measured by SFM makes it possible to distinguish geometrically different levels of organisation in the fibrillar structure (Figure 12): (i) bundles of microfibrils, (ii) microfibrils, (iii) nanofibrils, and (iv) macromolecules. While bundling of microfibrils to fibrils (Figure 12(a)) is well described [8,9,57,58],it is a controversial observation that microfibrils are constructed from apparently well defined smaller nanofibrils which represent the constituent thread of the microfibrils (Figure 12(b)). Observations at a higher magnification allow to visualize the molecular surface structure of the nanofibrils as it is shown in Figure 12(c). Surface images of tapes which had been drawn to different draw ratios are compared in Figure 13. Within the limits of draw ratios between X = 10 to X = 70, the microfibrils were always found to be formed from smaller strings of a diameter between 20-50 nm. An improvement of the alignment of these nanofibrils becomes evident as the draw ratio increases. The nanofibrils get packed more densely, while defects like twisting and interlacements are removed. It is a peculiar observation that the smallest fibrillar elements, i.e. the nanofibrils, were formed in the initial deformation steps during necking and did not change their width significantly upon further drawing. In agreement with the SFM observations, TEM micrographs 50 nm on surface replicas in Figure 14 show nanofibrils with a diameter which actually does not depend on the draw ratio. Although the bulk structure is certainly related to the details in the surface structure, which could be observed by SFM, conclusions on the bulk structure are not always unambiguous. A possibility to observe the bulk structure rather directly by SFM, is based on fracture techniques. Cryomilled gel drawn UHMW P E fibres were examined by SFM and showed similar nanofibrils with diameter of 50 nm [60]. Apparently, Figure l2(c) represents the regular arrangement of polyethylene chains at the surface of the nanofibrils. As no intermediate

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texture could be observed and taking into account the rather uniform and constant diameter of the nanofibrils, it can be concluded that the observed nanofibrils represent an elementary building unit of the fibrillar structure in gel drawn UHMW PE. Such a minimal diameter is in agreement with many observations on the deformation and fracture of polymers and it has been suggested that smaller entities cannot form because of the unfavourable surface energy [17,19,20,59]. The molecular resolution which was already demonstrated in Figure 12(c) allows the comparison of the packing of the

Figure 14. TEM micrographs of replicas of the surface of drawn U H M W PE films. At higher draw ratio X = 70 (b) the replicating cellulose acetate film acted as an adhesive tape picking up the nanofibrils which were not bonded strong enough to the bulk, while the replica at X = 10 (a) is a normal carbon replica. Scale bars = 50 nm [ l o l l

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chains in the surface and the bulk structure. A period between 4.8 8, and 5.2 8, was measured in Figure 15 which corresponds to the dola interchain distance of orthorhombic polyethylene. The corresponding orientation of the crystal planes is in good agreement with IR-dichroism [60] and X-ray diffraction experiments [10,61]. Upon uniaxial elongation of gel crystallized UHMW P E tapes, the b-axis of the unit cell tends t o align parallel to the tape surface. This orientation becomes more pronounced with increasing draw ratio. At high draw ratios it becomes evident that also the nanofibrils are anisometropic and get oriented with respect to their cross-section. Figure 16 shows terraces of a layered bundle of nanofibrils which are sheared relatively to each other. This picture resembles shear bands with the characteristic angle of about 55'. As SFM gives a three-dimensional surface profile, the dimension of the nanofibrils perpendicular to the surface, i.e. the height of the step, could be measured. It was determined to be about 20 nm which is smaller than the value of 40 nm of the corresponding parallel diameter. Such a peculiar anisotropy from the molecular up to the fibrillar level might be expected because the original structure of the gel cast film is highly anisotropic. Cast films are composed of thin sheet lamellae which lie almost parallel to the film surface with the c-axes perpendicular to the lamella surface. Starting from an anisotropic structure the anisotropic deformation process resulted in an anisotropic fibrillar structure. In many cases, the standard normal force SFM modes do not allow to visualize fine details in the structure of the relatively soft P E because the interaction with the probing tip can result in surface deformation [62,63]. Although normal force micrographs depict the shape of the nanofibrils rather correctly; the detailed surface structure can be smeared out. Improvements

Figure 15. Polyethylene chains at the surface of a nanofibril, X = 70 [51]

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Figure 16. Scanning force micrograph recorded at the surface of an ultradrawn film (A = 70) show shear band formed of nanofibrils. Scale bar = 250 nm [loll

are offered by the rather recently developed friction (lateral force) and tapping modes*. Figure 17 shows SFM micrographs which were recorded from the same area of a drawn tape (A = 10) by four different modes. A normal force micrograph depicts just the nanofibrils with a diameter of 50 nm, while the lateral force and tapping modes were able to visualize a regular pattern along the nanofibrils with a periodicity of 26 nm [64]. This periodicity is consistent with the long period of gel-drawn PE derived from SAXS data [lo]. The image contrast might be caused either by true variations in height or by a difference in modulus between crystalline and disordered 'In the case of the tapping mode, the surface is probed with the needle oscillating at high frequency (ca. 300 kHz) and less force (ca. lo-'' N ) . Thus, surface deformation of soft materials like polymers is reduced.

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Figure 17. Nanofibrils (A = 10) which were scanned with three SFM modes: (a) normal force (height); (b) lateral force; (c) tapping. The insert in the top of (b) shows a two-dimensional Fourie transformation pattern taken from a smaller area of (b). The pattern yields two periodicities of which one corresponds to the parallel alignment of the nanofibrils, while the 26 nm periodicity matches the long period of a gel drawn UHMW PE [lo]. Scale bar = 100 nm [loll parts of the nanofibrils. T h e structure in Figure 17(b) can be explained by the modulated lateral forces due to the surface deformation t h a t results in an exageration of the structural details. Such a n explanation would be consistent with the tapping mode images which show a less corrugated surface. T h e 2-D Fourier transformation of the friction image in Figure 17(b) shows just the periodicity perpendicular to the aligned nanofibrils. Only when t h e transformation was done for a smaller area containing not more than 3-5 nanofibrils, t h e 26 n m periodicity along t h e nanofibrils became apparent. Thus, there is a short range interfibrillar correlation of t h e periodic striped structure of the nanofibrils within a n area of 3-5 neighbouring nanofibrils. T h e striped structure of the nanofibrils does not change with increasing draw ratio but it gets less pronounced and the interfibrillar correlation vanishes as it is shown in Figure 18: the periodicity of about 26 n m can still be discriminated, however the structural details are smoothed, a n d in some cases they are observed as irregular corrugations or protrusions

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Figure 18. Lateral force micrographs of nanofibrils at the surface of drawn gel films. The periodic substructure along the nanofibrils of lower draw ratio (A = 30, (a)) film can still be recognized, while the periodicity vanishes at high draw ratio (A = 70, (b)). Scale bar = 60 nm [ l o l l

on the surface of the nanofibrils. These changes in the structure are again consistent with SAXS studies which yielded an increase in the half width of the meridional reflection [lo]. The short range correlation found at low draw ratios suggests that neighbouring nanofibrils are formed interdependently. The corresponding bundles of nanofibrils might originate from the above described stacks of lamellae. As the short range correlation between the neighboring nanofibrils is lost upon fibre drawing, one can conclude that the deformation process includes shear deformation of microfibrils due to sliding of the nanofibrils. For comparison, ultrathin sections of the drawn tapes have been studied by TEM. Because of the restricted diffusion of the staining agent into the crystallite, oxidation of the crystalline material is slow and mostly restricted to the crystallite surfaces. Thus the preferentially stained areas in the TEM micrographs in Figure 19 can be assigned to crystalline interfaces or less ordered regions of the fibrillar structure. Long dark stripes which are oriented perpendicular to the fibre axis have been observed in the case of a low draw ratio (A = 10). Upon ultradrawing (A = go), the stripes get short and distorted. TEM and SFM indicate a structural organization in which the packing of the PE chains within the nanofibrils is not uniformly crystalline. This is consistent with calorimetric experiments yielding 8590% crystallinity [9,67] the remaining fraction, however, does not appear to be rubber elastic. In agreement with dichroic IR experiments and X-ray scattering, 'HNMR spectra have indicated that an almost perfect orientation of the P E chains is already achieved after necking. However, 'H-NMR spectra reveal also a significant deviation from perfect orientation. Spectra of a tape drawn

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Figure 19. Transmission electron micrographs of thin sections from drawn UHMW PE tapes: (a) X = 15; (b) X = 90 [16]

to X = 30, could be fitted by a superposition of all-trans planar P E subspectra according to Gaussian distribution with a half width p = 3" f0.5'. This deviation appears to be independent of the draw ratio. 2H-NMR spectra for tapes with X = 15, X = 30, and X = 60 did not alter with increasing draw ratio. Because crystal domains which, as a whole, deviate in their orientation from the director axis should become further oriented upon drawing, it was supposed that a contribution of mobile gauche defects causes the variance of the C-D bond orientation. Thus, although the PE-crystals become oriented relatively perfect already in an early stage of the drawing process, a distribution in the methylene group orientation can remain due to mobile conformational defects. In order to clarify the question whether the UHMW PE tapes contain components of different mobility, differences in the relaxation times have been probed by means of several saturation pulses shortly prior to the solid echo excitation (see Figure 20) [68]. If the delay t2 between the saturation pulses and the solid echo sequence is small compared to T I ,no magnetization can be recorded and the crystalline signal can thus be suppressed. Figure 20 gives a comparsion of the 2H-NMR spectra of UHMW PE tapes (A = 30) recorded at 300 K with different delays t2. The angle between the order axis and the magnetic field was set to /3 = O", 45', and 90'. The intensities of spectra recorded with the same delay t2 have been normalized to the /3 = 0' spectrum. The spectra on the left side represent the oriented,

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crystalline component. This crystalline component is fully supressed in the spectra on the right side and a second component becomes obvious. The fraction of the noncrystalline component was estimated to be < 10%. Remarkably, one can observe two sharp resonance peaks on the outer edge of the spectrum recorded with t 2 = 70 ms and ,O = 0'. The observation

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Figure 20. 2H-NMR spectra of UHMW PE tapes (A = 30) recorded at 300 K with different delays: (a), (b), (c) 22 = 400 s (6 scans); (d), (e), (f) t 2 = 70 ms, (3000 scans) [66]

Scannig force microscopy on the orientation of U H M W P E

23 1

after a delay of only 70 ms and the splitting of 6 = 122,5 kHz indicates a highly oriented but mobile component. Comparison with the “crystalline” spectrum obtained at t 2 = 400 s for p = 0” shows, in addition to the difference in the quadrupolar splitting (Scryst = 124,5), that also the half width has been increased from 3.5 kHz to 7.5 kHz. Thus, it appears that the spectra at t 2 = 70 ms represent the overlapping resonances of a less oriented and a highly oriented mobile component. As the experimental splitting constant of the oriented component is only slightly smaller than that for the rigid crystalline modification, either the motional amplitude is small or the population of the orientational sites is strongly polarized. Because the reduced spin-echo intensity (the ratio of the solid-echo intensities at tl = t compared t o tl = 0) does not change upon raising the temperature and the fast 7’1 relaxation, fast motional processes can be assumed. The nearly perfect orientation can be explained by extended chain segments aligned to the fibre axis and containing a high fraction of trans bonds. Thus, as in the crystalline state, most C-D bonds are perpendicular to the chain backbone. Because of a small fraction of gauche-conformers there are also C-D bonds on a cone at an angle of 35.3” towards the chain direction. If fast exchange occurs, the C-D bonds jump quickly between these two different orientations which results in orientational averaging depending on the fraction of gauche bonds. Simulation of the spectra has been possible by a double-cone-6-jump-model assuming a stationary Markov process and a gauche content of 2-3% [67]. Systematic variation of t 2 demonstrated that the line width and the splitting are shifted continuously from rigid to mobile. On the other hand, the very long spin-lattice relaxation times of the rigid component indicate a very high degree of perfection of the fibrillar crystallites. Hence, it can be concluded that the oriented mobile segments are part of the crystalline structure or are at least directly linked to the crystallites. The conclusion that (conformational) defects are concentrated in small areas inside the fibrillar crystallites or are tightly attached to them is not only in agreement with the observation of striped structures in the SFM and TEM pictures, but also supported by X-ray and vibrational spectroscopy studies. While the observed SAXS periodicity does not change upon drawing, the (002) crystallite dimension becomes larger than the long period [11,52]. Based on the observation of the diffraction on the first layer line, it has been concluded that both fraction and length of unidimensionally ordered macromolecules increase upon drawing and correlate with the modulus. In IR- and Raman experiments on strained fibres and tapes, it was possible to detect different band shifts as a response to the applied load indicating two oriented and regularly packed components [65].

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S. S. Sheiko. M . Moller

5. Gel blending

Gel drawing allows t o prepare films of nearly perfect uniaxial orientation. In addition, gel technology provides a special and easy route to prepare blends of incompatible, crystalline polymers with rigourous control of the morphology [69]. Typically, crystalline polymers do not cocrystallize or form eutectic mixtures. In dilute or semidilute solutions, as employed for the gel preparation, a ternary polymer-l/polymer-2/solvent system can be homogeneous. Gel crystallization of one polymer component is little disturbed by the second polymer. The first formed crystals may even serve as nuclei for the second component. In the case of only one component forming a crystal network, single crystals of the second component will be entrapped in the cavities. In the case of subsequent crystallization of two high molecular weight polymers, the open structure of the polymeric gels allows formation of an interpenetrating network of polymer crystals. This section describes the employment of poly(di-n-alkylsily1ene)s as photoactive and photoreactive components which can be dispersed in the polyethylene gel as nanometer size crystallites and which can be cooriented upon drawing. Considerable research efforts are focused at present on the preparation and characterization of highly organized polymeric architectures [70731. Also the potential of conducting or semiconducting polymeric materials for molecular electronics, nonlinear optics, display fabrication signalprocessing and data storage is widely investigated [74-791. Polysilylenes are of particular interest because of their special properties, i.e. photoconductivity, piezochromism and thermochromism [80]. Due to the conformation dependent a-electron delocalization [81],the catenated Si-chain serves as a one-dimensional semi- and photoconductor and also as chromophore. Another important peculiarity of the symmetrically substituted poly(din-alkylsily1ene)s is that they form mesomorphic phases [82]. In the mesophase, the polymer backbone and the side chains are conformationally disordered, while the macromolecules remain extended and are packed hexagonally [83]. Solid state 13C- and 29Si-NMR experiments on similar phases of poly(di-n-alkylsi1oxane)s demonstrated that the segmental mobility and conformational order can be described by a picture where the molecules are constrained t o hexagonally packed tubes, in which, however, they can move rather freely [84-871. By the example of cyclic alkanes, it has been shown that the motion also includes diffusive translation along the chain axis [88]. As a result of the peculiar motional state and translational mobility, the materials can easily be plastically deformed in the mesomorphic state. Poly(di-n-pentylsilylene) (PDPS) and poly(di-n-hexylsilylene) (PDHS) transform at 65OC and 42OC, respectively, from a rigid crystal state into the hexagonal columnar LC-phase [80,82]. These temperatures are just below the &-transition of PE [89], above which gel crystallized UHMW P E can be drawn to ultrastrong fibres or tapes and blending of minor frac-

Scannig force microscopy on the orientation of U H M W P E

233

Figure 21. TEM micrograph of an ultrathin section of a gel crystallized 9:l blend of UHMW PE/Poly(di-n-pentylsilylene) stained with RuOa [92]; Scale bar = 160 nm tions of poly(di-n-alkylsily1ene)s with UHMW P E does not thus affect the drawability of the latter. Consequently, blends of poly( di-n-alkylsilylene) with UHMW PE can be drawn to highly oriented fibres or tapes. Figure 21 shows a transmission electron micrograph of a thin section obtained from a blend where PDPS was dispersed in a matrix of PE lamellae as nanometer size domains. FT-IR and UV spectroscopy were used to monitor the conformation and orientation of the components of the PE/PDPS blends separately during the drawing procedure. Figure 22 shows the polarized FT-IR spectra of the drawn PE/PDPS blend. Bands below 700 cm-' are due to vibrational modes of polysilylene backbone segments [go]. The band at 660 cm-' can be assigned to Si-C stretching vibrations and is highly sensitive to conformational changes of the polysilylene backbone. The PDPS backbone adopts a 7/3 helical conformation in the crystal low temperature phase [go]. However, upon drawing, the absorption around 660 cm-' became asymmetric and shifted to larger wavenumbers. The effect is due to the occurrence of a new relatively sharp band a t 670 cm-' and can be attributed to all-trans segments which are constrained in the matrix of P E fibrils [91]. The observation is in agreement with the UV-spectra, demonstrating an increasing fraction of trans-planar segments [92]. The stretching dependence of the dichroic ratio A/A of the 660 cm-' band was inverse to that of the PE band doublet at 720/730 cm-'. This observation suggests a comparable orientation for both blend components. When the temperature was raised, the polarized IR-spectra of both P E and PDPS components showed no changes up to temperatures of 125OC. This proves the constrained state of the molecules of poly(di-n-pentylsilylene) which cannot disorder at the temperature of the mesomorphic transi-

S. S. Sheiko, M. Moller

234

Wavenumbers Figure 22. FT-IR absorbance spectra of UHMW PE/PDPS blend of X = 30 recorded with a polarizer oriented perpendicular (1) and parallel (2) to draw direction [92] tion. Complementary t o polarized FT-IR spectroscopy experiments, polarized UV-experiments were also performed. Harrah and Zeigler reported a dichroic behaviour of PDHS films deposited and stretched on a polymeric substrate [93]. In the drawn PE/PDPS blends, the orientation and thus the dichroic effects can be much stronger due to the constrained state of the interfibrillarly dispersed PDPS. Figure 23 depicts the result of polarized UVspectroscopic measurements on a film with X = 20. Spectra taken with the polarization perpendicular t o the stretching direction showed practically no absorption. This suggests close to perfect orientation of both helically and all-trans ordered segments of the polysilylene chain. Gel drawing can be used for the preparation of very efficient polarizing films as it was recently also demonstrated for ultradrawn P E with dispersed dichroic low molecular weight dyes [94]. Due to UV-decomposition of polysilylenes [92] the dichroism will, however, be destroyed by high dose radiation. Such a decomposition can be directly observed by SFM measurements. In contrast t o pure UHMW P E tapes, small droplets form on the surface of the drawn and subsequently irradiated PE/PDPS blend as it is shown in Figure 24. These droplets can be assigned to the chain scission products of PDPS. The easy and near to perfect coorientation of polysilylenes raises the question about the intrinsic electrical conductivity of polysilylene. Using a pulse-radiolysis time resolved microwave conductivity (TRMC) technique, it is possible to study the conductivity by actually monitoring the charge mobilities on a molecular scale [95]. Inhomogeneous

235

Scannig force microscopy on the orientation of U H M W P E

-.-2

1.1

-

wl *

FI

1

8 9

0.55-

t 2

e

I

250

300

I

350 wavelength (nm)

4 10

Figure 23. UV-dichroism of a drawn UHMW PE/PDPS blend ( A = 2 0 ) obtained with the polarizer oriented parallel (1) and perpendicular ( 2 ) to draw direction [921

Figure 24. Scanning force micrograph recorded at the surface of a drawn (A = 70) and subsequently UV-irradiated UHMW PE/PDPS blend [92] materials can be studied without electrode contact or boundary effects which have to be considered in other drift mobility experiments. Pulseradiolysis results in close to uniform charge carrier formation throughout the sample. In addition, the TRMC technique allows to perform time re-

S. S. Sheiko,

236

51

M.Moller

1

."

n

\

b

a

lo-'

10-~ Time ( s )

10-~

10-3

Figure 25. Dose normalied radiation-induced conductivity transients obtained at room temperature on drawn (A = 30) PE/PDHS films with the film (and thus polysilane backbone) orientation parallel (All) and perpendicular ( A i ) to the microwave field. Use was made of 50 ns pulses depositing ca. 120 kJ/m3 per pulse. The signals are normalized to 100% PDHS content. The half of the pulse length is taken at time = 0 [97]

solved experiments on the decay of the mobile charge carriers within the time scale from nanoseconds to milliseconds. The dose normalized radiation induced conductivity transients of A are shown in Figure 25 with the polysilane backbone orientation either parallel (All) or perpendicular ( A l ) to the applied microwave field. The diagrams are normalized to 100% PDHS content. The experiment revealed an anisotropy of the conductivity of roughly one order of magnitude depending on whether the backbone orientation in the oriented PE/PDHS blend was perpendicular or parallel to the direction of charge transport. Charge transport took place preferentially along the highly oriented polym2V-'s-' in mer chains with charge carrier mobilities of at least 3 x the solid phase. The radiation-induced conductivity in the solid phase was also found to correlate with the backbone conformation of PDHS increasing with the fraction of the all-trans planar segments [96,97]. In summary, gel crystallization of UHMW PE results in a material with a peculiar structure and rather interesting applied properties. Simultaneous crystallization of UHMW PE and a second crystalline polymer represents a simple route t o the efficient blending of two incompatible materials. Because of their mesomorphic state, nanometer size crystallites of poly(di-nalkylsily1ene)s can be subsequently co-oriented. In addition to polysilylenes, there is a rather large groupe of polymers which exhibit a similar mesomorphic behaviour and which are suitable for gel blending/gel drawing

Scannig force microscopy on the orientation of UHMW PE

237

experiments, e.g. some polyphosphazenes, poly(di-n-alkylsiloxane)s, trans poly( 1,4-butadiene) and others [98-1001. Oriented molecular architectures can yield considerably improved properties in comparison with polycrystalline materials. Furthermore, the orientation in the isolating host material allows t o combine the photoelectric properties of polysilylene with the mechanical stability and processability of UHMW PE. References 1. M. G. Northolt, D. J. Sikkema, Adv. Polym. Sci. 8, 115 (1991) 2. “Liquid Crystalline Polymers”, edited by R. A. Weiss, C. K. Ober, ACS Symposium Series 435, Washington 1990 3. P. Smith, P. J. Lemstra, J. Mater. Sci. 15,505 (1980) 4. R. Kirschbaum, J. L. J. Dingenen, in: Integration of Polymer Science and

5. 6. 7. 8.

Technology, edited by P. J. Lemstra, L. A. Kleintjens, Elsevier Appl. Sci. Publ., London 1989, vol 2, p. 178 P. J. Barham, A. Keller, J . Mater. Sci. 20, 2281 (1985) L. H. Wang, R. S. Porter, T. Kanamoto, Polymer Commun. 31,457 (1990) H.v.d. Werff, A. J. Pennings, Colloid Polym. Sci. 269,747 (1991) P. J. Lemstra, N. A. J. M. van Aerle, C. Bastiaansen, Polymer J . 19, 85

(1987) 9 . K. Anandakumaran, S. K. Roy, St. J. R. Manley, Macromolecules 21, 1741 (1988) 10. N. A. J . M. van Aerle, A. W . M. Braam, J. Mater. Sci. 23,4429 (1988) 11. Y. A. Zubov, S. N . Chvalun, V. I. Selichova, M. B. Konstantinopolskaya N. F. Bakeev, J . Fizich. Khimii LXII, 2815 (1988) (in Russian) 12. E. Agosti, G. Zerbi, I. M. Ward, Polymer 33,4219 (1992) 13. A. Tshmel, I. A. Gorshkova, V. M. Zolotarev, J . Macromol. Sci., Phys. B 32, 1 ( 1993) 14. M. Pietralla, H.-G. Killian, J . Polym. Sci., Polym. Phys. Ed. 18,285 (1980) 15. H. W. Spiess, Colloid Polyrn. Sci. 261,193 (1983) 16. M. Kunz, Ph. D. Thesis, 1990, Freiburg 17. P. F. van Hutten, P. C. E. Koning, A. J. Pennings, Makromol. Chem., Rapid Commun. 4, 605 (1983) 18. H. D. Chanzy, P. Smith, J.-F. Revol, R. St. Manley, Polymer Commun. 28, 133 (1987) 19. J . M. Brady, E. L. Thomas, Polymer 30, 1615 (1989) 20. P. Smith, P. J. Lemstra, J. P. L. Pijpers, A. M. Kiel, Colloid Polym. Sci. 259,1070 (1981) 21. D. M. Huong, M. Drechsler, M. Moller, H.-J. Cantow, J . Microscopy 166, 317 (1992) 22. G. Binnig, C. F. Quate, Ch. Gerber, Phys. Rev. Lett. 56,930 (1986) 23. R. Patil, S.-J. Kim, E. Smith, D. Reneker, A. C. Weisenhorn, Polym. Commun. 31,455 (1990) 24. W. Stocker, G. Bar, M. Kunz, M. Moller, S.N. Magonov, H.-J. Cantow, Polym. Bull. 26, 215 (1991)

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25. B. K. Annis, D. W. Schmark, J. R. Reffner, E. L. Thomas, B. Wunderlich, Makromol. Chem. 193, 2589 (1992) 26. D. Snetivy, J. E. Guillet, G. J. Vancso, Polymer 34, 429 (1993) 27. L. M. Eng, H. Fuchs, K. D. Jandt, J. Petermann, Ultramicroscopy42-44, 989 (1992) 28. G. F. Meyers, B. M. DeKoven, J. T. Seitz, Langmuir8, 2330 (1992) 29. H. Hansma, F. Motamedi, P. Smith, P. Hansma, J. C. Wittman, Polymer 33, 647 (1992) 30. S. N . Magonov, H.-J. Cantow, J . Appl. Polym. Sci., Appl. Polym. Symp. 51, 3 (1992) 31. J. A. Harrison, C. T. White, R. J. Colton, D. W. Brenner, Surf. Sci. 271, 57 (1992) 32. U. Hartmann, Ultramicroscopy 42-44, 59 (1992) 33. M. Radmacher, R. W. Tillmann, M. Fritz, H. E. Gaub, Science 257, 1900 (1992) 34. A. L. Weisenhorn, P. H. Hansma, T. R. Albrecht, C. F. Quate, Appl. Phys. Lett. 54, 2651 (1989) 35. P. Smith, P. J. Lemstra, Makromol. Chem. 180, 2983 (1979) 36. C. Sawatari, T. Okumura, M. Matsuo, Polymer J . 18, 741 (1986) 37. T. Kyu, K. Futjita, M. H. Cho, T. Kikutani, J.-S. Lin, Macromolecules 22, 2238 (1989) 38. P. J . Barham, M. J. Hill, A. Keller, Colloid Polym. Sci. 258, 899 (1980) 39. C. W. M. Bastiaansen, P. Froehling, A. J. Pijpers, P. J. Lemstra, in: Integration of Fundamental Polymer Science and Technology I, edited by L. A. Kleintjens, P. J. Lemstra, Elsevier Appl. Sci. Publ., London 1987, p. 508 40. S. K. Roy, T. Kyu, J. R. St. Manley, Macromolecules 21, 1741 (1988) 41. E. Carlemalm, R. M. Gravito, W. Villiger, J . Microscopy 126, 123 (1982) 42. M. Drechsler, Ph. D. Thesis, 1990, Freiburg 43. J. H. Luft, J . Biophys. Biochem. Cytol. 9, 409 (1961) 44. M. Kunz, M. Moller, U.-R. Heinrich, H.-J. Cantow, Makromol. Chem, Makromol. Symp. 20/21, 147 (1988) 45. A. Keller, Kolloid Z. Z. Polym. 197, 98 (1964) 46. D. C. Bassett, in: Principles of Polymer Morphology, Cambridge University Press, New York 1981 47. P. H. Geil, “Polymer Single Crystals”, Interscience Publishers, New York 1963, p. 132 48. D. J. Keller, C. Ching-Chung, Surf. Sci. 268, 333 (1992) 49. P. Grutter, W. Zimmermann-Edling, D. Brodbeck, Appl. Phys. Lett. 60, 2741 (1992) 50. S. J. Hanley, J. Giasson, J.-F. Revol, D. G. Gray, Polymer 33, 4639 (1992) 51. S. N. Magonov, S. S. Sheiko, R. A. C. Debliek, M. Moller, Macromolecules 26, 1380 (1993) 52. A. Peterlin, Colloid Polym. Sci. 265, 357 (1987) 53. P. J. Flory, D. Y. Yoon, Nature272, 226 ( 1988) 54. W. Wu, G. D. Wignall, L. Mandelkern, Polymer 33, 4137 (1992) 55. K. Kobayashi, in: Polymer Single Crystals, edited by P. H. Geil, Interscience Publishers, New York 1963, p. 473 56. Z. Bartczak, R. E. Cohen, A. S. Argon, Macromolecules 25, 4692 (1992)

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57. C. Sawatari, M. Matsuo, Colloid Polym. Sci. 263,783 (1985) 58. D. J. Dijkstra, J. C. M. Torfs, A. J. Pennings, Colloid Polym. Sci. 267,866 (1 989) 59. B. Wunderlich, ‘Macromolecular Physics”, Academic Press, New York 1973, vol 1, p. 228 60. S. S. Sheiko, H. Frey, M. Moller, Colloid Polym. Sci. 270,440 (1992) 61. N . A. J. M. van Aerle, P. J. Lemstra, Polymer J . 20, 131 (1988) 62. A. S. Lea, A. Pungar, V. Hlady, J. D. Andrade, J. N. Herron, E. W . Voss, Longmuir 8 , 68 (1992) 63. H. G. Dickland, S. S. Sheiko, L. van der Does, M. Moller, A. Bantjes, Polymer 34,1773 (1993) 64. S. S. Sheiko, M. Kunz, M. Moller, Polym. Prepr. 34, 778 (1993) 65. B. J. Kip, M. C. P. van Eijk, R. J. Meier, J . Polym. Sci., Polym. Phys. Ed. 29,99 (1991) 66. H. Deckman, M. Moller, L. Govaert, P. J. Lemstra, in: Integration of Fundamental Polymer Science and Technology I, edited by L. A. Kleintjens, P. J. Lemstra, Elsevier Appl. Sci. Publ., London 1991, vol 5, p. 178. 67. R. Ebelhauser, H. W . Spiess, Ber. Bunsenges. Phys. Chem. 85, 1208 (1985) 68. D. Hentschel, H. Sillescu, H. W. Spiess, Polymer 25, 1078 (1984) 69. Y. Tervoort, Dissertation, 1991, Eindhoven, T h e Netherlands 70. J. C. Wittmann, P. Smith, Nature 352,414 (1991) 71. F. W. Embs, D. Funhoff, A. Laschewsky, U. Licht, H. Ohst, W . Prass, H. Ringsdorf, G. Wegner, R. Wehrmann, Adu. Mater. 1991, 3(1), Special Issue:

Organic Thin Films 72. F. W . Embs, G. Wegner, D. Neher, P. Albouy, R. D. Miller, C.G. Willson, W . Schrepp, Macromolecules 24, 5068 (1991) 73. F. Garnier, G. Horowitz, X. Peng, D. Fichou, Adv. Mater. 2,592 (1990) 74. R. D. Miller, S. A. MacDonald, J . Imaging Sci. 31,43 (1987) 75. M. A. Abkowitz, M. J. Rice, M. Stolka, Phil. Mag. B. 61,25 (1990) 76. J . Kido, K. Nagai, Y. Okamoto, T. Skotheim, Chem. Lett. 1267 (1991) 77. M. Kakui, K. Yokoyama, M. Yokoyama, Chem. Lett., 867 (1991) 78. F. Kajar, J . Messier, C. Rosilio, J . Appl. Phys. 60,3040 (1986) 79. J. C. Baumert, G. C. Bjorklund, D. H. Jundt, M. C. Jurich, H. Looser, R. D. Miller, J . Rabolt, R. Sooriyakumaran, J. D. Swalen, R. J. Twied, Appl. Phys. Lett. 53, 1147 (1989) 80. R. D. Miller, J. Michl, Chem. Rev. 89,1359 (1989) 81. A. Herman, B. Dreczewski, W . Wojnowski, Chem. Phys. 98,475 (1985) 82. P. Weber, D. Guillon, A. Skoulios, R. D. Miller, J . Phys. France 50, 793 (1989) 83. F . C. Schilling, A. J. Lovinger, J. M. Zeigler, D. D. Davis, F. A. Bovey, Macromolecules 22,3055 (1989) 84. G. Kogler, A. Hasenhindl, M. Moller, Macromolecules 22,4190 (1989) 85. G. Kogler, K. Loufakis, M. Moller, Polymer 31, 1538 (1990) 86. M. Moller, S. Siffrin, G. Kogler, D. Oelfin, Makromol. Chem., Macromol. Syrnp. 34, 171 (1990) 87. B. Wunderlich, M. Moller, J. Grebowicz, H. Baur, Adu. Polym. Sci. 87, 1 (1988)

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89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100.

talline and Mesomorphic Phases of Large Size Cycloalkanes as a Model for Polyethylene” in: Solid State NMR of Polymers, edited by L. Mathias, Plenum Press, New York 1991 K. Schmidt-Rohr, H. W. Spiess, Macromolecules 24, 5287 (1991) R. D. Miller, B. L. Farmer, W. Fleming, R. Sooriyakumaran, J. F. Rabolt, J . Am. Chem. SOC. 109,2509 (1987) J. F. Rabolt, D. Hofer, R. D. Miller, G. N. Fickes, Macromolecules 19,611 (1986) M. Moller, H. Frey, S. Sheiko, Colloid Polym. Sci, in press L. A. Harrah, J.-M. Zeigler, Macromolecules 20, 601 (1987) C. W. M. Bastiaansen, H.-W. Schmidt, L. Govaert, P. Smith, Polym. Prepr. 34, 776 (1993) J. M. Warman, M. P. de Haas, in: Pulse Radiolysis, edited by Y. Tabata Y., CRC Press 1990, p. 101-132 G. P. van der Laan, M.P. de Haas, I.M.Warman, H. Frey, M. Moller, Macromolecules 26, 89 (1993) G. P. van der Laan, M. P. de Haas, A. Hummel, H. Frey, S. Sheiko, M. Moller, submitted to: Macromolecules V. S. Papkov, Yu. K. Godovsky, V. S. Svistunov, V. M. Litvinov, A. A. Zhdanov, J. Polym. Sci., Polym. Phys. Ed. 23, 1043 (1985) J. H. Magill, J. Petermann, U. Rieck, Colloid Polym. Sci. 264, 570 (1986) F. C. Schilling, F. A. Bovey, A. J. Lovinger, J. M. Ziegler, D. D. Davis, F. A. Bovey, Macromolecules 22, 3055 (1989)

Oriented Polymer Material> Stoyko Fakirov Copyright 0 2002 Wiley-VCH Verlag GmbH & Co. KGaP

Chapter 8

Polarized light scattering from polymer textures

I. T. Moneva

1. Introduction Transmission polarized light methods, such as conventional polarized light microscopy, transmitted light intensity and birefringence measurements, and small angle light scattering (SALS) [l]have proved t o be useful experimental tools for the elucidation of morphology and orientation in optically anisotropic polymer substances and materials in the solid state and in solution, on the scale of some microns and higher (see also Chapters 3 and 4).

The polarized light techniques, similarly to other microscopic and diffraction methods, are applicable provided that a suitable contrast exists between the features of interest. The physical reason for the contrast in the case of observation between crossed polaroids is the presence of fluctuations in the optical anisotropy and orientation, causing birefringence in a specimen illuminated by polarized light. The contrast in the polarized light images of a uniaxially birefringent specimen (i.e. with n1 = 712 # 713, ni denoting its principal refractive indices) placed between crossed polaroids is determined by the well known equation for the intensity of the transmitted light 11 [2]: 11

= 10 sin2 2psin2 612.

(1)

Here 1 0 is the intensity of incident light, 'p is the orientational angle of the optic axis of the specimen with respect to the polarization direction of

242

1. T. Moneva

the polarizer, and 6 is the usual phase retardation of light after crossing a specimen of thickness h and birefringence A n = (n: - no):

6 = 2rhAn/X.

(2)

The maximum transmittance is at pmax= r / 4 , 3 ~ 1 45, ~ 1 4etc., , when, according to Eq. ( l ) ,the highest possible contrast is achieved. Extinction (zero contrast) is observed at pmin= 0, r / 2 , r, etc., when the principal directions of the refractive index indicatrix of the specimen are aligned with the polarization directions of the polaroids. Otherwise, 11 (and, in general, the image) depends on p. The complex case of a specimen comprising birefringent units of different orientation is especially noteworthy. In such a case the p-dependence of the image can be avoided and the highest contrast can be achieved by a newly proposed elegant technique [3]. It involves the record of two images of the specimen, taken at 'pi and (pi 45) superimposed on one and the same photograph. The summation of the relevant intensities in this case reduces to:

+

the available full-contrast image being thus obtained. In principle, the full-contrast polarized light imaging of oriented polymers should be more efficient, since birefringence of solid polymers is strongly enhanced by orientation and elongation of polymer molecules and orientation of crystallites [4]. Recent reviews of the polarized light methods can be found in [4-81; new considerations of the birefringence phenomenon involved may also be of interest [3,9]. The measurement of statistically averaged quantities for the structural parameters, the non-destructive operating mode, the simple sample preparation and the relatively easy performance of image registration (also in a conventional polarizing microscope) are among the reasons that SALS was and still is a wide-spread tool in the studies of spherulitic polymer materials (as produced and deformed) and of polymer films and fibres. Recently, the interest in the SALS method and its development is growing again because of its potentialities for the characterization of the morphology and director orientation in liquid crystalline substances [10,11],the latter being currently subject of extensive and most active investigations. The term polarized light scattering (PLS) is adopted here instead of the conventional one (SALS) [l]in order to put an accent on the considered specific physical distinction of this method from other related methods of electromagnetic scattering since this difference is inherently much more important in the case of oriented specimens. This chapter begins with a brief consideration of the principles governing the PLS method and its interpretation in some cases of oriented

Polarized light scattering from polymer textures

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structures (textures) in polymers. Then, examples are given of less encountered applications of PLS in orientation processes, such as zone drawing and shear crystallization, based to a great extent on own research. The potentialities of a PLS-based technique, that of double exposure speckle photography, for the determination of Poisson’s ratio of deformed polymers are also discussed. Finally, an introduction t o the analysis of textures in liquid crystalline polymers aims t o emphasize a new insight into the scattering method. 2. Polarized light scattering: theory and instrumentation

2.1. Fluctuations in density and fluctuations in optical anisotropy and orientation In 1949, Debye and Bueche proposed the use of electromagnetic scattering for the elucidation of the structure in a variety of heterogeneous solids, such as glasses, gels, liquid crystals, and amorphous polymers [12]. The theory considers in terms of the Rayleigh-Debye-Gans (RDG) approximation [13,14]) the scattering from continuously distributed fluctuations in the refractive index or density with a correlation in space given by a correlation function. An important step further w a s the idea to consider the RDG scattering by fluctuations i n the optical anisotropy and orientation [15,16], thus extending the analysis to optically anisotropic heterogeneous solids (with a direction-dependent refractive index), and in particular, t o polymer solids. The scattering function describes fluctuations in polarizability on the basis of the assumptions that: (i) the fluctuations are small enough t o satisfy the relation ni = 4mri, where ni is the refractive index of the i-th volume element and cyi is its polarizability, and (ii) local fluctuations have the symmetry of uniaxial crystals. The validity of the RDG approximation in the scattering by optically anisotropic solids is extensively discussed in [17,18]. The physical argument is the same as in the isotropic case [13]: each volume element gives Rayleigh scattering independently of the other volume elements; the waves scattered by all elements interfere because of their different positions in space. The formulas for the Mie scattering [14] get simpler in the anisotropic case due to the restrictions imposed by the approximation [17,18]:

Here Ic = 27r/X, and d, and m; are, respectively, the size of the scattering region in the i-th direction and its direction-dependent refractive index relative to the surrounding medium. Another simplification is due t o the assumed Fraunhofer model, provided that one deals with small scattering

1. T. Moneva

244

Polarizer

Analyzer

-* Light source

specimen

Fraunhofer plane

Figure 1. Principle scheme of the optical arrangement in PLS angles (< 10’ - 15’) and the far field hypothesis is valid. The approximation and the model led t o restrictions imposed on the dimensions and optical properties of the scattering regions to be analyzed, on the thickness of the specimen, etc. (for polymers, see [6,18]). The concept of the non-isotropic component of light scattered by polymers led Stein et al. [19] t o the introduction of polarizing elements into the optical system. Two polaroids, put before and after the specimen under study (Figure l), provide for the incidence of linearly polarized light and for the analysis of a definite linearly polarized component of the scattered light. As a result, the incident light affords the coherence of each pair of the resolved light components in the birefringent specimen, while the analyzer is bringing their polarization in one plane to allow interference [20]. The use of polarized light led to a further simplification of the theoretical interpretation of the scattering data and secured to a great extent the informativity and the extensive application of the light scattering analysis. 2.2. Scattering considerations

Hereafter, we refer to the case of polarized light scattering with crossed polaroids (in two geometries: H, 3 horizontal analyzer and vertical polarizer, and vice versa 3 v h , leading usually to identical results). The information thus obtained is of value for the unique revealing and characterization of optically anisotropic regions in specimens. Since the information is simplified, this case is a routine one when dealing with other scattering geometries. The basic relations in the method for the interpretation of experimental data make use of the “model” approach. According to this approach, the scattering regions are ascribed a specific geometrical form (sphere, ellipsoid or rod) and the scattering intensity is calculated as a sum of the intensity contributions of all regions. The “model” approach proved applicable in many cases of independent scattering by assemblies of spherulites or rods. Following Stein and Rhodes [l],Figure 2 illustrates the scattering geometry of a homogeneous spherulite particle, centered at 0, with radius R and optical anisotropy (a,- at),where a, and at are its polarizabilities in the radial and tangential direction. The vertical direction is along OZ, and the unit vector of the incident linearly polarized plane wave is along O Y . A unit scattering volume dv = r2sin(a)drdadQ is situated at a point

so

245

Polarized light scattering from polymer textures

Figure 2. Coordinate system related to the scattering by an optically anisotropic volume element (see text) of spherical coordinates r , a and R. The direction of the scattered ray 9 is given by the radial and azimuthal angles 0 and ,u, Then, the amplitude F, of scattered light by an optically anisotropic particle is [I]:

F, = K

f (Po')

cos[k(r'$]dv.

V

Here P' is the induced polarization in a unit volume dw at a distance r'from the centre of a specimen with volume V ,the unit vector 0' is perpendicular t o the propagation direction 9 of scattered light and lies in the plane containing the polarization direction of the analyzer [6], S = So - S', k = 27r/X and K is a proportionality constant related to the device employed. The first factor next t o the integral in Eq. ( l ) , (Po'), represents the scattering power of an anisotropic unit volume placed between two POlaroids. According to the definitions of P' and 6 , it depends on the optical anisotropy and on the polarization directions of incident and analyzed scattered light. The second factor is the interference factor accounting for the waves' interaction between all unit volumes of the spherulite. Eq. (6) has provided the formalism of relating the scattered intensity ZH, of various anisotropic particles to their structural parameters, such as size, shape and orientation of the optic axis. Recently, the subject was reviewed in [6,8], although, all the vast literature could hardly be covered. Here, it is preferred merely to put an accent on the physical origin of basic scattering patterns in relation to the optical properties of scattering units which is of primary interest for the understanding of the analysis. The well known scattering patterns of undeformed spherulites calculated by Eq. (6) for models of optically anisotropic spheres with different optical properties are in good agreement with the experimental patterns shown in Figure 3 [21]. The models include the frequent case of the optic axis P situated transverse to the spherulite radius R (optically identical -

4

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a

b

C

Figure 3. Typical H,-PLS patterns of specimens with nondeformed spherulites and scheme of their appropriate optical models when at > ar:(a) with the optic axis P transverse to the radius R; (b) with P inclined to R; (c) of a banded spherulite

t o the case P 11 R), e.g. in polyethylene, polyamide, etc., as well as the case when P is inclined to R , e.g. in poly(ethy1ene terephthalate), etc. In both cases, the patterns display the scattered light intensity in a four-leaf clover shape, of the x - or +-type, respectively, with a maximum intensity at Omax # 0, which is related to the spherulite radius R by the equation

PI : R = 4.09X/ 4~si n( 6'~ ~ , /2).

(7)

The scattering pattern in Figure 3(c) of an undeformed spherulite with order in the inner inhomogeneity as in banded spherulites is also noteworthy. An additional intensity maximum appears at larger angles 6' [l], providing a convenient measure of the periodicity da in the change of the polarizabilities along R according to: da = A/ sin(6'/2).

(8)

If the H,-patterns are recorded in a microscope, calibration is required for the evaluation of the proper values of Omax and 0, the procedure being described below. When the spherulites are deformed, the changes in their scattering patterns depend basically on the change in their shape and inner structure, and more particularly, on the manner of orientation of the crystalline lamellae therein. The calculation of the scattered intensity by deformed spherulites was performed for models of anisotropic ellipsoids of rotation, a result from the nondisruptive deformation of anisotropic spheres [22-241.

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Figure 4. Experimental H,-PLS patterns of vertically stretched specimens with deformed spherulites and scheme of their appropriate optical models when at > ar:(a) with the optic axis P transverse to the radius R; (b) with P inclined to R; (c) with reoriented crystallites

Typical scattering patterns of deformed spherulites with different optical properties are presented in Figure 4 [2l]. According to the theory, in a process of affine deformation the four-lobe shape of the pattern is preserved; however, the lobes shift with spherulite elongation, intrinsically reciprocally to its extension, i.e. toward the equator in Figure 4(a), which provides a convenient measure of the spherulite elongation; d, increases with the draw ratio [22]. Again, as in Figure 3 , the position of the deformed four-lobe pattern is governed by the position of the optic axis with respect to the polarization directions (compare Figures 4(a) and (b)). The spherulite elongation A, in affine deformation can be readily evaluated by:

where pmaxis the azimuthal angle of maximum intensity [25]. The attempt to account for the reorientation of crystallites [23], that is particularly true in cases of highly compliant materials, has led to an eight-lobe pattern shape like that shown in Figure 4(c) [21,26], where each initial spherulitic lobe is splitted into two. The fibrillar structure in fibres and films is often modelled by the use of uniaxially anisotropic rod-like entities. The study of the independent light scattering from anisotropic rods was pioneered by Rhodes and Stein [27] and generalized by van Aartsen [28]. It provided the formalism for the

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later extension t o coherent scattering by assemblies of rods through t h e introduction of correlation statistics. The calculated scattering patterns of randomly distributed anisotropic rods with t h e optic axes lying along (or perpendicular) and at 4~45' to the rod axes L are in good qualitative agreement with experiment (Figure 5 [29]). Again, a four-lobe shape is observed as in the case of randomly

a

b

Figure 5. The two general H,-PLS patterns of independent rods' scattering. The appropriate optical models are shown on top of the figure. (a) with the optic axis P oriented at wo = O o , 90' with respect to the rod axis L , (b) with P a t w = f45' inclined to L ; the lines indicate optic axes, The corresponding H,-PLS patterns for single rod scattering where the left and right quadrants indicate the contour patterns at small and large angles, respectively, [29] are shown below for comparison

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Polarized light scattering from polymer textures

distrubuted anisotropic spherulites; the intensity maximum in this case is, however, at Omax = 0. The azimuthal orientation of the lobes in Figures 5(a) and (b) is again related to the orientation of the optic axes in the rodlike aggregate [27], As expected, the &dependence of the scattered light intensity is related reciprocally to the size of the rodlike unit [29]. There are features, however, which the simple single rod theory still fails to describe ~3,291. It is also of interest to introduce the coherent light scattering from assemblies of anisotropic rods [29-321. In the case of long range correlation in the orientation of rods and their optic axes, the effects of the associated oo= 0"

oo = 45" 0"

oo =

90"

Figure 6. Effect of the orientation of rods (asdetermined by the angle () and effect of the orientation of their optic axes (as determined by the angle W O ) on the H,scattering patterns of ordered rods' assemblies [29]. Schemes of their appropriate optical models where the lines indicate optic axes are inserted. The left and right quadrants indicate the contour patterns at small and large angles, respectively. Below, a special case of the orientation of anisotropic rods and the correspondent numerical H,-PLS pattern [31] are shown

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interparticle interference lead to complex patterns. In Figure 6 [29,31],various arrangements in a one-dimensional assembly of anisotropic rods are presented showing both the effect of the orientation of the rod axes and that of the optic axes upon the calculated H,-patterns. The problem of the interparticle interference was theoretically approached in terms of a modified Zernike-Prins theory or a paracrystal theory [29]. In general, the numerical calculations indicate that interparticle interference effects are significant at small scattering angles while the scattering from the assembly at large scattering angles can be described in terms of the single rod theory. A special case of correlation in the rods orientation (and in the optic axes as well) is depicted in Figure 6 (bottom) [31]. The model is composed of rod textures which build up a peculiar network structure of a “parquett”-like type. Such a network structure has been encountered in various forming processes and in orientational draw of different polymer films (of polyethylene [29], poly(ethy1ene terephthalate) [31], amorphous polymers [31], block copolymers [31]). Below, a quantitative study of the evolution of a similar structure network in a zone draw process is presented and its physical consistency will be approached. Network structures with different optical properties were tentatively considered: (i) with the optic axes P being parallel to the rod axes L [31], and (ii) with P being arbitrarily inclined to L [32]. The scattering consideration made use of the formalism in small angle X-ray scattering [33]. In the scattering pattern of the network structure in case (i) (Figure 6(c) [31]), two systems of four-leaf reflections are evident: one being related to the independent rods’ scattering (that of the X-shape), and the other resulting from the interrod interference effect at the equator. In general, the scattering patterns in case (ii) are dependent on the interrod distance used in the calculation [32]. The interrod interference effect reported is at still smaller angles than in case (i). The calculated effects are, however, not so strong as those observed in the experiment, indicating that further elaboration of the model is required [32]. 2.3. Polarized light scattering technique

The standard photographic technique [l] is widely used in practice, with an output being qualitative or semiquantitative in nature. It is illustrated here in the case of the polarizing microscope used as a diffractometer since most of the microscopes are fitted with a Bertrand lens which allows observation of the back focal plane (BFP) of the objective, in other words, of the optical diffraction pattern [34]. The use of the microscope for acquiring scattering patterns seems convenient on specimens which one normally images by the microscope. In the case of observation of single crystals in convergent light, this imaging gives rise t o “conoscopic images” [35], which term is also used when polycrystalline solids are being

Polarized light scattering from polymer textures

25 1

examined. Obviously, in the case of Fraunhofer diffraction at a specimen, light needs not obligatory be convergent [36]. Fraunhofer diffraction can be afforded readily t o this purpose, e.g. after aligning the illumination in such a way that, in the absence of the specimen, the image of the light source is observable in the BFP [36]. The use of the Bertrand lens allows the easy characterization of any resolvable periodicity in the sample. The repeating period dp in any onedimensional periodicity can be determined from the angular position of the maximum intensity at Om and the wavelength of light in the medium X/n, according to:

dp = M X / n .sin 0, , where M is the diffraction order and n is the macroscopic refractive index of the specimen. Since incident light in the microscope is usually not parallel, calibration of the recorded micrographs is required in order to obtain the correct parameters. For instance, the correct dp value can be obtained by means Of:

where d,, is the repeating period of a one-dimensional calibration grating and up and ag, are the distances from the centre t o the points of maximum intensity in the diffraction patterns of the specimen and the grating, respectively [36]. Recent trends in the PLS techniques are based on the availability of commercial two-dimensional detectors coupled with a computer which make possible rapid and easy quantitative one- and two-dimensional scattering data acquisition in on-line studies of various processes (see [8,37,38] and references there). It may be of interest that advanced qualitative and quantitative structural analysis of polymers can be performed by the new method of digital image analysis [39], that has recently been extended t o polymers by Japanese authors to involve also computer simulation of PLS [9,40]. 3. Applications of the scattering analysis

The method of PLS can be used also in deformation studies of localized ordering or disordering, i.e. in an area of ca. 7r mm2 with a radius T = 1 m m of the cross-section of the incident laser beam, or in a partial area of the view field of the microscope. It is noteworthy that the output of the PLS method can be made available for use in process analysis and scientific computations, in integrating morphological data with polymer mechanics and engineering [41]. Examples given below illustrate the kind of data obtained by PLS in some localized deformation processes.

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3.1. Formation of shear bands during zone drawing

The proposed models of the mechanism of plastic elongation of semicrystalline polymers disagree, among others, on how microfibrils are formed. It is believed that microfibrils form first in isolated deformation zones, crazes and shear bands, producing what would appear as row-nucleated structures (as established, for example, on polyethylene [42]). Such structures, being anisotropic in nature, should inevitably give rise t o distinct interparticle interference effects, and therefore, could be characterized by P L S (see Chapters 2, 11, and 12). A study by laser light scattering (LLS) of the stress-induced structural changes in a zone-draw process of extruded polyethylene at constant strain velocity is reported [43]. The process under consideration proceeds at two different regimes, depending on the temperature of the heated zone: a) a pre-stationary (auto-oscillating) regime of nonuniform draw, when stress, velocity of neck formation and temperature of loci of formed neck are changing, and b) a stationary regime of uniform draw. It was observed that H,-PLS patterns changed progressively along the neck from spherulitic through X-shape patterns toward rod-like patterns.

a

b

Figure 7. The “parquett”-like type of network structure, as observed in zone drawn PE: (a) optical micrograph; (b) its H,-scattering pattern; vertical draw direction [43]. A relevant optical model [31] and the sketch of the H,-PLS pattern (the evaluated parameters are indicated) are shown below

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Under auto-oscillating necking, “parquett”-like structures (Figure 7(a) [43]) formed in the yield region, extending over distances of several hundred microns. These are also referred t o as “shear bands” since they seem t o be induced by shear forces [43a]. The experimental LLS X-shaped pattern in Figure 7(b) [43] and the theoretical contour in Figure 6 (bottom) are in fairly good agreement. The nature of the units in the model in Figure 7(a) can be related to the microstructure depicted in Figure 8 [44]. On this basis, the shape of shear bands in drawn tapes at various zone temperatures, the row-to-row distance and their orientation toward the draw direction can be assessed quantitatively by LLS [44]. Such data can be helpful in the analysis of the constitution of bands, complementing and quantifying on a larger scale microstructural evidence revealed by small and wide angle X-ray scattering and electron microscopy [45,46] (see Chapters 3, 5, and 7).

Figure 8. Typical interpenetrating shish-kebab morphology of zone drawn PE bands (at low strain rate). Replica prepared after etching in permanganic acid [44]. O n the left, the cores are close together so that lamellar overgrowths taper and interpenetrate, but on the right, they are apart, leading t o lamellar twisting and disorientation

3.2. Formation of macrofibrils in shear crystallization

Laser microdiffraction was applied in a study of the structure formation in thin films of high density polyethylene isothermally crystallized under

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Figure 9. Characteristic orientation zones in shear induced crystallization of high density polyethylene at shear rate v,h and crystallization temperature T,: (a) radial orientation at low v , h and T,; (b) azimuthal-dependent orientation at moderate v s h and T,; (c) mixed-type orientation at higher v&and T, [47]

the action of a steady shear gradient in a rotating plate-plate device of a viscometer-like type [47]. The polymer melt was subjected t o stationary shear deformation and subsequent crystallization proceeded from oriented melt [48]. In such a case and under ongoing relaxation, there is an orientation in the melt depending on the shear rate l&, and the relaxation time 7 when the following relation holds [49]:

Various deformation zones resulted in the shear gradient field along R (Figure 9) where different morphological types formed, varying also with crystallization temperature T,. The microdiffraction technique allows us to assess the radial (Kh-) dependence at any T, of the morphological types, their inner structure and orientation toward the direction of acting forces. Examples are given in Figure 10. The results obtained in the study of specimens produced within a wide range of K h and T, suggest that the orientation of the optically resolvable structures with increasing K h tends in the flow direction as in the case of

Figure 10. Evolution of microdiffraction patterns of shear crystallized polyethylene specimens with shear rate from spherulitic through complex patterns toward scattering from oriented fibrils; vertical shear direction [47]

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strain-induced crystallization [50,51],while the structure formation is more temperature sensitive. The mechanism of structure formation in the shear-induced crystallization and the transition from spherulitic to fibrillar structures were generally in correlation with l/sh and T,, although, at large l/sh some disorientation was often observed. The overall pattern of structure formation, emerging from systematic PLS data, will be reported in [47]. 3.3. Determination of Poisson’s ratio b y double exposure speckle photography

Double exposure speckle photography (DESP), discovered in the early 70s, is a non-contacting method with a number of applications in experimental strain analysis of low-molecular weight materials [52], but this far has found only a few applications in the field of oriented polymers. When fairly coherent light propagates through a medium with random fluctuations or, when ever an optically rough surface is illuminated, patterns displaying a random intensity distribution arise, known as speckle patterns [53,54]. Attention to polymer speckles was first drawn in [55-571. As shown there, in the case of coherent light illumination of polymer specimens, effects of interparticle interference bring about a phenomenon of fine modulation of the scattered light intensity observable in the scattering pattern as speckles [24,56]. Initial experimental studies of basic statistical properties of polymer speckles have suggested, a t least in principle, the applicability of conventional speckle methods t o polymer analysis [58]. Applications of the standard DESP analysis to measure the Poisson’s ratio of deformed polyolefins were first reported by Holoubek et al. (see [59] and references there). In principle, the DESP analysis [60] is performed in a two-step process (Figure 11). In the first step, a double exposure speckle pattern is generated on an ordinary scattering device with coherent light illumination (Figure l l ( a ) . The double exposed pattern is made up of two speckled scattering patterns of the specimen in two different stages of strain, in the initial state and after the deformation, which are superimposed on one and the same photograph. In the second step, the double exposed negative is examined in a diffractometer (Figure l l ( b ) . If both superimposed speckle patterns are correlated (i.e. the initial units have been only displaced by deformation), the Fraunhofer diffraction pattern from the negative displays a set of equidistant fringes as in Figure l l ( c ) , similar to the Young fringes. The interfringe distance is directly related to the displacement ddis of the scattering units by a Bragg-type equation, providing a measure of the deformation : ddis.sina = M.X.

(13)

I. T. Moneva

256

A

P

Laser

Stretched object

DESP pattern

b

C

Figure 11. Scheme of (a) the recording and (b) the evaluation of double exposure speckle photographs; (c) schematic explanation of the relation between parameters (see text) Here M is the diffraction order and t g a = (YFF/(Y,FF, where ~ F and F CX,FF are, respectively, the distance from the centre t o the relevant fringe (in the F F plane), and the distance between the negative and the FF plane. It should be noted that the method is applicable t o nondisruptive deformation processes when the deformed substructure is still preserved. A DESP study of the stretching of high density polyethylene films (produced by tubular extrusion) at room temperature and low strain rate is illustrated below. The DESP patterns were on-line recorded on drawing in small steps of specimens along (11) and at 90' (I) to the extrusion direction (a typical DESP pattern is shown in Figure 12 [Sl]).Then, point-by-point diffraction at the DESP patterns was applied in order t o measure the relative extension in length and the relative contraction in width. The apparent Poisson's ratio p of strained specimens at any degree of strain was deduced according t o the equation [59]:

= d d i s l /ddisll.

(14)

Polarized light scattering from polymer textures

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Figure 12. The speckled spherulitic H,-PLS pattern of tubular extruded polyethylene film, and a typical double exposure speckle photograph showing the record of the scattering patterns for two subsequent strain states of the film superimposed on one and the same photograph [61]

Anomalous local values (exceeding 0.5) were obtained with both kinds of specimens even at the early stages of stretching (4-5%) [61]. These results were ascribed to the characteristic microstructure resulting from micronecking observed also in a direct electron microscopic study.

4. Polarized light scattering from textures of liquid crystalline polymers The specific structural feature of substances in the liquid crystalline (LC) state is the preferential long range orientational order of asymmetric molecules or their parts while their positional order remains low (in one or two dimensions) [62]. Since the free energy differences between the various LC states are small, apparent insignificant perturbations such as wall boundaries or flow history, etc., can have a marked effect on producing a great variety of metastable morphologies [63] (see also Chapter 4). The morphology of films of main-chain mesogenic polymers in the nematic state a t rest is shown t o depend upon whether the films were previously subjected to orientation or not. In a film not previously oriented, the texture is usually the schlieren one (Figure 13 [64]), typical of low-molecular liquid crystals [65]. The schlieren texture formed in the nematic phase is represented in terms of a continuous director field with abrupt discontinuities at the disclinations [66]. In the case of shear oriented polymer films, for instance, the most evident feature is a system of bands arranged normal to the shear direction as shown in Figure 14(a); it has been explained in terms of a sinusoidal arrangement of the chains about the shear direction [67-691. 4.1. Polarized light scattering f r o m schlieren textures

The four-leaf clover scattering pattern with intensity maxima at azimuthal angles along the polarization directions of the polaroids as in Figure 13 [64]

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seems to be of general validity. It is reported for thermotropic both rigid and semiflexible main-chain polymers in the nematic state [70] and in the cholesteric state [71] as well as for lyotropic polymers [72,73]. This pattern is believed t o arise from the spatial arrangement of the disclinations which mark the boundaries between the domains (here referred to as correlation areas of molecular orientation). The characteristic dimension, associated with the angle of maximum intensity Omax in this pattern, has been related to the disclinations density, i.e. the size of the domains L o , through the scattering vector Qmax[70]:

where Qmax = 2 u / L ~ u, being an approximately constant scaling factor of a value close to 1 [64] or of 2.7 [74], and X is the wavelength of light employed. A few ab initio calculations have appeared which assess the scattering pattern starting from one single disclination point of different strength or from a collection of disclination points. The resulting four-leaf clover pattern has been obtained either starting from an isolated disclination point of a strength +1 or from a system of three disclinations of strength f 1 / 2 [75,76],or from a dipole of two disclination points of strength f1/2 [77]. It should be noted that so far the considerations of PLS are restricted to two dimensions and are thus basically valid for thin samples.

Figure 13. Polarized light micrograph of schlieren texture and its H,-scattering pattern [64]

Polarized light scattering from polymer textures

259

4.2. Polarized laght scattering f r o m banded and other nematic

textures Drawn fibres and shear oriented films of thermotropic LC polyesters are shown to have a banded structure (Figure 14(a) [78]), with striations lying

Figure 14. Polarized light micrographs of sheared main-chain liquid crystalline copolyesters differing in the length n of the spacer (number of CHz-groups): (a) n = 4; (b) n = 7 . T h e relevant H.-scattering patterns are inserted [78]. T h e shear axis is horizontal

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normal to the fibre axis or to the shear direction (resulted from shear at elevated temperatures and preserved by rapid cooling). This structure is highly reminiscent of related structures previously reported in high strength fibres produced by solution spinning [79,80] and in lyotropic polymers [72,73], suggesting that the supramolecular organization in the form of banded structure is a feature characteristic of oriented LC polymers in general. The lateral bands are thought [67-691 to be a consequence of a periodic variation in the orientation of the principal optical vibration directions about the fibre or shear axis; the optical situation resembles to some extent that in banded spherulites along a single radius. Hence, optically resolvable bands should have a periodic-like diffraction pattern. The insert t o Figure 14(a) [78] displays a typical diffraction pattern of a one-dimensional grating with imperfect order, the latter being apparent from the relatively broad equatorial and azimuthal spread of the reflections. One finds by Eq. (10) the interband distance, db = 1.05 pm, and then, the maximum diffraction orders to be observed, M , = 1.68 (from M , = da/X). The actual banded texture, however, can be modelled more realistically by the assumption of non-linearity of band lines (pleated structure [SO]), finite band width (here, up to 80 pm) as well as different thickness of the specimen; all these factors leading to a broadening of the reflections (see, for example [Sl]). Therefore, the breadth of the reflections cannot be used alone as a unique measure of the first kind disorder of the interband distance in the shear direction. Lateral banded textures apparently form during the relaxation process after shearing [82]. It should be noted that, during ongoing relaxation, a variety of structures can form which would display different scattering patterns [78,83,84]. The example in Figure 14(b) [78] shows another state in the relaxation process. The micrograph and the inserted PLS pattern imply that rod-like regions (probably domains) are formed, with directors having different orientations toward the shear axis. 5 . Concluding remarks

The application of polarized light scattering to liquid crystalline polymers is expected to extend further the scattering analysis, and this might have twofold significance. The approach to the scattering as due to defects interaction could find, in principle, use in the field of oriented semicrystalline polymer materials, and in particular, in the new developments of high performance materials. As much as the highly oriented matrix is incorporating defective regions, fluctuations in anisotropy and orientation should be present and they will give rise to polarized light scattering. Although related considerations of anisotropic scattering (e.g. of disorder [85,86]) were of little use this far, there is no doubt that intensive research and discussion will go on, attempting to elucidate further the nature and role of

Polarized light scattering from polymer textures

26 1

defects scattering in the overall non-isotropic scattering envelope, with new potentialities. Second, the consideration of defects scattering will provide a deeper insight into the orientation patterns of LC polymers and into their evolution with external fields. This would result in a better understanding of their structure and defects formation and will certainly help the efforts to controlled texturing and to extension of the applications of polymeric LC substances.

Acknowledgement The author acknowledges the valuable aid in the above experimental studies by Mrs. S. Alexandrova, Mrs. V. Dukova and Mr. A. Sokolov. The work was supported in part by the Bulgarian National Fund of Research (Contract

X73). References 1. R. S. Stein, M. B. Rhodes, J . Appl. Phys. 31, 1873 (1960) 2. M. Born, E. Wolf, “Principles of Optics”, Nauka, Moscow 1970, Ch. 14, p. 761 (in Russian) 3. N. Donkai, H. Hoshino, K. Kajiwara, T. Myamoto, Makromol. Chem. 194, 559 (1993) 4. H. Harding, in: Optical Properties of Polymers, edited by G. Meeten, Elsevier, London & New York 1986, Ch. 2 5. C. Viney, Polym. Eng. Sci. 26, 1021 (1986) 6. J. Haudin, in: Optical Properties of Polymers, edited by G. Meeten, Elsevier, London & New York 1986, Ch. 4 7. I. Rabec, ”Experimental Methods in Polymer Chemistrg , Wiley-Interscience, New York 1980, Part 2, Ch. 35 8. R. S. Stein, M. Srinivasarao, J. Polym. Sci., Polym. Phys. Ed. 31, 2003 (1993) 9. I. T. Moneva, J. Polym. Sci., Polym. Phys. Ed. (1994), in press; Summary in Proc. 25th Europhysics Conference, St. Petersburg 1992, pp. 204-205 10. I. Litster, Phil. Trans. Roy. SOC. London A 309, 145 (1983) 11. C. Noel, in: Side Chain Liquid Crystal Polymers, edited by C. McArdle, Blackie, Glasgow & London 1989 12. P. Debye, A. Bueche, J. Appl. Phys. 2 0 , 518 (1949) 13. H. van de Hulst, ”Light Scattering by Small Particles”, Inostrannaja Literatura, Moscow 1961, p. 104 (in Russian) 14. M. Kerker, ” The Scattering of Light and Other Electromagnetic Radiation”, Academic Press, New York 1969 15. M. Goldstein, E. Michalik, J. Appl. Phys. 26, 1450 (1955) 16. P. Horn, Thesis, 1954, Strasburg 17. S. Stoylov, M. Stoimenova, J . Colloid €4 Interface Scr. 59, 179 (1977) 18. I. T. Moneva, J . Polym. Sci., Polym. Phys. Ed. 15,1501 (1977)

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19. A. Plazza, F. Norris, R. S. Stein, J. Polyrn. Sci. 24,455 (1957) 20. N . Zhewandrov, “Polarization of Light”, Nauka, Moscow 1969, p. 104 (in

Russian) 21. I. T. Moneva, P h D Thesis, Inst. of Macromolecular Compounds, 1970,

Leningrad (in Russian) 22. S. Clough, J. van Aartsen, R. S. Stein, J. Appl. Phys. 36,3072 (1965) 23. R. S. Stein, P. Ehrhardt, J. van Aartsen, S. Clough, M. Rhodes, J . Polym. Sci. C13, l ( 1 9 6 6 ) 24. R. Samuels, J . Polym. Sci. C 13,37 (1966) 25. V. Baranov, T. Volkov, in: Advances in Research Methods, edited by S. Rogovin, V. Zubov, Mir, Moscow 1968 (in Russian) 26. B. Ginzburg, D. Rashidov, I. T. Moneva, Vysokomol. Soedin. A28, 2237 (1971) 27. M. Rhodes, R. S. Stein, J. Polym. Sci. A 2, 1539 (1969) 28. J. van Aartsen, Eur. Polyrn. J. 6, 1095 (1970) 29. T. Hashimoto, S. Ebisu, H. Kawai, J. Polym. Sci., Polym. Phys. Ed. 19,59 (1981) 30. G. Wilkes, Mol. Cryst. Lip. Cryst. 18, 165 (1972) 31. C. Sawatari, M. Iida, M. Matsuo, Macromolecules 17,1765 (1984) 32. M. Matsuo, N. Yanagida, Polymer 32,2561 (1991) 33. D. Blundell, Acta Crystallogr. A 26,472 (1970) 34. S. G. Lipson, H. Lipson, “Optical Physics”, CUP, Cambridge 1981 35. A. Shubnikov, “Optical Crystallography“, Nauka, Moscow-Leningrad 1950 (in 36. 37. 38. 39.

40. 41.

42. 43.

44.

45. 46. 47.

Russian) I. Moneva, S. Frenkel, Commun. Dept. Chem., Bulg. Acad. Sci. 4 , 1 7 3 (1971) F. Perreault, R. Prud’homme, Polyrn. Prepr. 32,661 (1991) W. Culberson, M. Tant, J. Appl. Polym. Sci. 47, 395 (1993) C. Harlow, S. Dwyer, G. Lodwick, “Digital Picture Analysis”, in: Topics of Applied Physics, edited by A. Rosenfeld, Springer Verlag, Berlin 1976, vol. 11, p. 70 H. Tanaka, T. Hayashi, T. Nishi, J. Appl. Phys. 59, 3627 (1986) D. Prevorsek, H. Oswald, in: Solid State Behavior of Linear Polyesters and Polyamides, edited by J. Shultz, S. Fakirov, Prentice Hall, Englewood Cliffs, N J 1990, Ch. 3 T. Juska, I. Harrison, Polym. Eng. Rev. 2, 13 (1982) (a) I. Moneva, V. Dukova, M. Michailov, 7th Int. Microsymp. on Polymer Morphology, Dresden 1987; (b) I. Moneva, M. Michailov, 20th Europhysics Conf., Lausanne 1988, p. 48; paper to submitted t o Compt. Rend., Acad. Bulg. Sci. I. Moneva, A. Sokolov, D. Patel, D. Bassett, Int. Conf. on Hydrodynamics of Engineering Processes for Materials Production, Sofia 1991, p. 20; paper in preparation M. Kakudo, N. Kasai, “X-ray Diflraction by Polymers”, Elsevier Publ. Co., Amsterdam & London & New York 1972, pp. 403-420 Z. Bashir, J. Odell, A. Keller, J. Mater. Sci. 19,3713 (1984) I. Moneva, A. Sokolov, J. Melior, R. Hirte, M. Michailov, Proc. of the 13th Disc. Conf. on T h e Mechanisms of Polymer Strength and Toughness, Prague 1990; paper in preparation

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48. R. Hirte, P. Melior, 8th Intern. Symp. on Morphology of Polymers, Kiev (USSR), 1989, p. 95 49. A.Peterlin, in: Flow-Induced Crystallization in Polymer Systems, edited by R. Miller, Gordon and Breach Science Publishers, 1979 50. I. Dairanieh, A. MacHugh, J . Polym. Sci., Polym. Phys. Ed. 21, 1473 (1983) 51. M. Chien, R. Weiss, Polym. Eng. Sci. 28, 6 (1988) 52. ”Speckle Metrology”, edited by R. Erf, Academic Press, New York 1979 53. J. W. Goodman, in: Laser Speckle and Related Phenomena, edited by J. Dainty, Springer Verlag, Berlin 1975, p. 42 54. J. Dainty, in: Progress in Optics, edited by E.Wolf, N.-H. Go., 1976, vol. 1 4 55. C. Picot, R. S. Stein, R. Marchessault, J. Borch, A. Sarko, Macromolecules 4, 467 (1971) 56. I. Moneva, Yu. Brestkin, B. Ginzburg, S. Frenkel, Eur. Polym. J . 8, 1033 (1972) 57. R. Prudhomme, R. S. Stein, J . Polym. Sci., Polym. Phys. Ed. 11, 1357 (1973) 58. I. Moneva, M. Michailov, Makromol. Chem., Rapid Commun. 2 , 2 6 7 (1981); I. Moneva, M. Michailov, 27th Int. Symp. on Physical Optics in Macromolecular Systems, Prague 1984, pp. 42.1-3 59. J . Holoubek, J. Ruzek, Opt. Acta, 26, 43 (1979); J. Holoubek, B. SedlaEek, Makromol. Chem. 185, 2021 (1984) 60. T. Dudderar, P. Simpkins, Opt. Eng. 21, 396 (1982) 61. I. Moneva, J. Holoubek, M. Michailov, 8th Int. Conf. on Polymers, Varna (Bulgaria) 1983, p. 128 62. P. G. de Gennes, “The Physics of Liquid Crystals”, Clarendon Press, Oxford 1974 63. S. Guido, N. Grizzuti, G. Marucci, L:q. Cryst. 7, 279 (1990) 64. R. Silvestri, L. Chapoy, Polymer 33,2891 (1992) 65. D. Demus, L. Richter, “Textures of Liquid Crystals”, Verlag Chemie, Weinheim & New York 1978 66. F. C . Frank, Disc. Faraday SOC.25, 19 (1958) 67. A. Donald, C. Viney, A. Windle, Polymer 24, 5 (1983) 68. A. Donald, A. Windle, J . Mater. Sci. 18, 1143 (1983) 69. C. Viney, A. Donald, A. Windle, J . Mater. Sci. 18, 1136 (1983) 70. S. Rojstaczer, R. S. Stein, Mol. Cryst. Liq. Cryst. 157, 29 (1988) 71. G. Wilkes, J . Polym. Sci., Polym. Lett. Ed. 10, 935 (1972) 72. G. Balbotin, T. Asada, 33rd IUPAC Int. Symposium on Macromolecules, Montreal 1990, Session 2.2.6 73. S. Rojstaczer, B. Hsiao, R. S. Stein, ACS Polym. Prepr. 29, 486 (1988) 74. G. Meeten, P. Navard, J . Polym. Sci., Polym. Phys. Ed. 26, 413 (1988) Nakai, T. Shiwaku, H. Hasegawa, S. Rojstacer, R. S. Stein, 75. T. Hashimoto, -4. Macromolecules 22, 422 (1989) 76. T. Shiwaku, A. Nakai, H. Hasegawa, T. Hashimoto, Macromolecules 3, 1590 (1989) 77. F . Greco, Macromolecules 22, 4622 (1989) 78. I. Moneva, D. Trifonova, D. Patel, G . Mitchell, D. Bassett, 9th Nat. Symp. Polymers’93, Varna (Bulgaria) 1993; paper in preparation 79. M. Dobb, D. Johnson, B. Saville, J . Polym. Sci., Polym. Phys. Ed. 15, 2201 (1977)

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Oriented Polymer Material> Stoyko Fakirov Copyright 0 2002 Wiley-VCH Verlag GmbH & Co. KGaP

Chapter 9

Deformation induced texture development in polyethylene: computer simulation and experiments

A. S. Argon, Z. Bartczak, R. E. Cohen, A. Galeski, B. J. Lee, D. M. Parks

List of symbols A skew part of Schmid tensor C R rubbery modulus of amorphous component Da plastic strain rate tensor of amorphous component DC plastic strain rate tensor of crystalline component D' plastic strain rate tensor averaged over inclusion D macroscopic average plastic strain rate tensor Fa deformation gradient tensor of amorphous component Ha back stress tensor (hardening) of amorphous component I identity tensor Lc velocity gradient tensor of crystalline component N number of rigid links between entanglements in rubbery model of amorphous component R" symmetric, traceless Schmid tensor giving orientation of slip system Q S" deviatoric Cauchy stress tensor in amorphous Component (with superscripts c and I for crystalline component and inclusion)

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Sc* contracted deviatoric Cauchy stress tensor with vanishing component in the chain direction of the crystalline component S macroscopic average deviatoric Cauchy stress tensor W ctotal crystalline spin tensor W P plastic spin tensor W* lattice spin tensor W' inclusion average spin tensor W macroscopic average spin tensor a lattice identity vector in [loo] direction a plastic resistance coefficient of amorphous component b lattice identity vector in [OlO] direction c lattice identity vector in [OOl] direction f a volume fraction of amorphous component g a reference plastic shear resistance of slip system Q n power law stress exponent in visco-plastic kinetic law (with superscript a and c for amorphous and crystalline components) nja component of unit normal vector of slip plane a n' unit vector normal to plane of amorphous layer s," component of unit tangent vector parallel to slip direction on slip system a p pressure simple shear rate on slip system a T O revolved shear stress on slip system Q T~ experimentally measured plastic shear resistance of the chain slip system (100) [OOl] -

+"

1. Introduction Plastic deformation of semicrystalline polymers, in particular polyethylene, has been experimentally studied intensively from the viewpoint of changes in morphology as well as characterization of mechanisms of deformation and their relative resistances [1-111. The principle mechanisms involved in the plastic deformation of semicrystalline polymers are crystalographic in nature, albeit very complex when considered in the context of the local morphology. The specific mechanisms involved in the plastic deformation of these polymers have been reviewed by many investigators; among those, two earlier reviews by Bowden and Young [4] and by Haudin [5] are noteworthy. Many of these investigations of the mechanisms of deformation have been concerned with high density polyethylene (HDPE) because of its relatively simple structure and its high degree of crystallinity. The plastic deformation mechanisms of highly textured HDPE prepared by plane

267

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(4

I"

Amorphous Layer Crystalline lamella Figure 1. Schematic representations of (a) spherulite and (b) composite inclusion

strain compression in a channel die as a convenient approximation in bulk to single crystalline materials were studied recently in great detail by Bartczak et al. [6]. The deformation processes of HDPE were investigated in a wide variety of loading conditions such as uniaxial tension [7], uniaxial compression [8],simple shear [9,10],and plane strain compression [ll].On the other hand, there have been relatively few studies aimed at the numerical simulation of large plastic deformation and texture evolution in semicrystalline polymers, in a mechanistically faithful manner. We take the morphology of undeformed HDPE to be spherulitic [12,13], consisting of a radial arrangement of broad thin crystalline lamellae separated by amorphous layers, shown schematically in Figure l(a). The numerous morphological studies of plastic straining of HDPE in extensional flow have now established that important morphological reorganization occurs

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as a result of the deformation, with the structure changing from spherulitic t o a highly oriented one consisting of alternating crystalline and amorphous layers. At the same time, crystallographic axes of the crystalline lamellae and macromolecular chains of the amorphous component rotate and tend t o align preferentially with respect t o principlal axes of macroscopic deformation. Thus, it has been established that, when plastically deformed, HDPE develops three important types of texture: 1. crystallographic tezture, due t o preferential orientation of crystallographic axes in the crystalline lamellae; 2. morphological tezture, due t o preferential orientation of the normals to the broad faces of the crystalline lamellae faces; and 3. macromolecular tezture in the amorphous phase, promoted by molecular alignment with the direction of maximum stretch. The evolution of texture with large strain plastic deformation strongly affects the macroscopic mechanical behaviour of semicrystalline polymers. For instance, a strong textural hardening is observed in tension and plane strain compression but not in simple shear and uniaxial compression [7,9,10]. Here we report on the results of a computer simulation of large strain plastic deformation in HDPE, using a micromechanically based model, to predict the evolution of textural anisotropy and macroscopic mechanical behaviour under different modes of straining [14]. In our visco-plastic composite model, plastic deformation in each phase is based on well established microstructural mechanisms and their relative resistances. The model uses a two-phase composite inclusion consisting of a crystalline lamella and its corresponding amorphous layer attached to it, as shown in Figure l ( b ) . Each of the two components of the composite inclusion is assumed t o deform homogeneously. Moreover, crystalline/amorphous interface compatibility and equilibrium are satisfied throughout the entire deformation history. In the proposed model, a so-called Sachs-like aggregate interaction law is employed t o relate the volume average deformation and stress of a composite inclusion t o the respective macroscopic fields, in preference t o a so-called Taylor-like interaction law. While we have chosen HDPE as a model material for the present study because of the large amount of existing experimental information on its deformation mechanisms, we consider the developed methodology t o be equally well adaptable to other semicrystalline polymers with different crystal structures, provided their deformation mechanisms are well understood. Undeformed HDPE has a spherulitic morphology with spherical packing of crystalline lamellae separated by layers of amorphous phases. The thickness of the lamellar inclusions ranges from 50A t o 250d; and the lateral dimensions from 1 p m to 50 pm. HDPE crystals have an orthorhombic structure. At room temperature, the amorphous phase of HDPE is in the rubbery regime [15]. The crystalline phase can deform plastically by crystallographic slip, twinning and stress-induced martensitic transformations. However, each of these mechanisms leaves the material direction parallel t o the crystallographic chain direction inextensible, so they provide fewer than

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the five independent deformation modes required to accommodate arbitrary plastic deformation [3,4]. Plastic deformation of the crystalline phase is accompanied by deformation of the amorphous phase. In the absence of cavitation, the amorphous phase deforms primarily by interlamellar shear [8,10,11]. While interlamellar separation has also been suggested [16,17], we do not consider that here as an acceptable mode for bulk deformation without cavitation. The simultaneous activity of several deformation mechanisms allows the initial structure to be transformed in a continuous manner t o any and all final oriented states. Thus, we consider the often observed transitional cavitational processes (micronecking, etc.) as not fundamental, but as unessential artifacts of tensile deformation. We have used the newly developed composite model to simulate stress-strain response and texture evolution during deformation of HDPE to large plastic strain under several different modes of straining. Predicted results have been compared t o experimental observations of earlier investigations as well as our own more recent results reported in greater detail elsewhere [6,8,10,11]. Here we discuss only the results of uniaxial compression and plane strain compression. Operational notation used in this paper is based on the following conventions. Scalars are in mathematical italics ( A ,a, a),vectors are lower-case bold-face (a),second-order tensors are upper-case bold-face (A). The superscripts “I”, “c” and “a” designate inclusion, crystalline lamella, and amorphous layer, respectively. When required, repeated Cartesian subscripts are summed from 1 to 3. Greek subscripts range from 1 t o 2. 2. Model description

2.1. Basic assumptions To model large strain plastic deformation and texture evolution in HDPE we neglect elasticity and pressure sensitivity of the plastic resistances, but we account for intrinsic nonlinear visco-plastic behaviour of both crystalline and amorphous phases. The choice of neglecting elasticity is motivated both by the increased simplicity of the constitutive modeling and by the argument that at very large strains, elasticity does not contribute much effect on the development of texture. Incompressibility is assumed in both phases. We assume that the basic element constituting semicrystalline polymers is a two-phase composite inclusion represented by a crystalline lamella and its associated amorphous layer. Due t o their large aspect ratio, the composite inclusions are modeled as infinitely extended “sandwiches” with a planar crystalline/amorphous interface (see Figure l ( b ) ) . Each composite inclusion “I” is characterized by its interface normal, n’, and the relative thickness f” and f“ = 1 - f a of amorphous and crystalline phases, respectively. The relative thickness f a also represents the inclusion volume fraction of the amorphous phase which is assumed to be constant and identical for all inclusions. Furthermore, each composite inclusion is presumed to have

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equal volume and initial thickness. Parenthetically, we note that one of our associated recent experimental studies [ll]demonstrates conclusively that interfaces between amorphous and crystalline phases can translate or rotate without accompanying material shear during morphological restructuring, apparently, purely in response to reduction of interface free energy. These effects which occur at very large strains are not incorporated into our model with certain consequences on our predictions which we will point out. Thus, we make the assumption that the material interface between the two components of the inclusion remains distinct throughout and does not migrate. In the following, we will discuss first the constitutive models for amorphous and crystalline phases of HDPE and the behaviour of the composite inclusion. After that, we present the local interaction law and outline the solution procedure for the proposed composite model. We then apply this composite model t o predict stress-strain behaviour and texture evolution of HDPE under conditions of uniaxial compression and plane strain compression, and compare these predictions with experiments. 2.2. Constitutive relations 2.2.1. Crystalline phase

The experimentally observed mechanisms of plastic deformations in HDPE are: crystallographic slip, twinning, and str.ess-induced martensitic transformations [3,4,18]. The crystal lattice is orthorhombic with lattice parameters a = 7.4 A, b = 4.93 A and c = 2.54 hi, where c is the crystallographic axis coinciding with the chain direction. Experiments on HDPE have established that crystallographic deformation occurs on the (100)[001], (010)[001], {110}[001], (100)[010], (010)[100], {llO}(lTO), slip systems, and the (110), (310) twinning systems. The stress-induced martensitic transformation from the orthorhombic to the monoclinic lattice in HDPE was also detected by X-ray studies. For all of these modes of deformation, there is no experimental evidence for the occurrence of twinning or martensitic transformation in anything more than trace ammounts and then, occurring only in very late stages of deformation [8,10,11]. Therefore, we consider crystallographic slip as the only mechanism that accomplishes plastic straining in the crystalline lamellae. Two slip categories operate in the orthorhombic unit cell of HDPE crystals: chain slip with its slip direction parallel to the chain direction, such as (100)[001], (010)[001], and {110}[001] slip systems; and transverse slip with its slip direction perpendicular to the chain direction, such as (100)[010], (010)[100], and {110}(1~0)slip systems. These slip systems comprise only four linearly independent systems. The addition of twinning and martensitic transformation do not provide the missing degree of freedom due to chain inextensibility, but merely aid transverse slip in transverse shape changes. Moreover, we note that all these mechanisms leave the molecular chains inextensible, so that lamellae with their

Deformation induced texture: computer simulat.ion and experiments

27 1

chain directions parallel to the principal direction of extension act as rigid inclusions requiring special procedures t o deal with their deformation in aggregates. The resistances t o plastic flow of these slip systems can be measured experimentally using highly textured quasi-single crystalline HDPE obtained by plane strain compression in a channel die from initially spherulitic material [15]. Recently, Bartczak et a1 [6] have found that the easiest slip system Table 1. Slip systems of HDPE and their corresponding normalized initial resistances Slip System

Chain slip

Transverse slip

(100)[001] (0 10)[OO I] {100}[001]

( 100)[O lo] (OlO)[lOO] {iio}{iio}

Normalized Resistance

Normalized Resistance

ga/ro

ga/ro

(experimental evidence)'

(current choice)

E l

>2 >2

E l 2.5 2.5

1.66

1.66

2.00 2.2

2.5 2.2

The normalized initial resistances measured by Bartczak et al. [6].

in such quasi-single crystalline HDPE is the chain slip system (100)[001] and that the other slip systems listed above have progressively higher plastic resistance. Based on these experiments, possible slip systems in the crystalline phase of HDPE are summerized in Table 1 with their measured or estimated initial shear resistances normalized to T O , the resistance (at room temperature) of the easiest chain slip system, (100)[001]. To derive a constitutive law for the crystalline lamella, we first introduce a visco-plastic power law [19,20] relating the shear rate of a given slip system a to the corresponding resolved shear stress, on the same slip system as

+"

where 40 is a reference strain-rate (of the order of s-')} nc is the non-linear rate exponent (the inverse rate sensitivity coefficient) and gQ is the reference shear resistance of slip system a. In the model we neglect strain hardening and normal pressure effects on the shear resistance, so that gQ remains constant during the deformation. The neglect of intrinsic strain hardening in the crystalline lamellae is justified because they are very thin and cannot retain dislocations in them. The plastic shear rate on a slip system is known to be temperature dependent. We consider this

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temperature dependence to reside in the reference strain rate '0, but will not discuss its form further. Because of chain inextensibility, the shear rate of any slip system is not dependent on the normal stress component in the chain direction [21]. This renders the crystalline lamellae rigid in the chain direction. To cope with this problem we have introduced some special procedures, as mentioned above. Let us denote by Sc*, a special modification of the deviatoric Cauchy stress tensor, S c , in the crystalline lamella, with zero normal component in the chain direction (i.e. S:ej*cicj = 0) [14]. The resolved shear stress in slip system (Y can then be expressed as P = S"RG, where R" is the '? symmetric, traceless Schmid tensor of stress resolution associated with the slip system a . The components of the symmetric part of the Schmid tensor, R"8 1 ' can be defined as RG = f(spn7 npsja) where sp and np are the unit vector components of the slip direction and the slip plane normal of the given slip system a , respectively. resulting from the contributions of The plastic strain rate tensor DC, all K active slip systems in the crystalline lamella is given by

+

Relation (2) represents a three-dimensional constitutive law for the plastic behaviour of the crystalline lamellae through active slip systems and accounts for chain inextensibility, i.e. Dfjcicj = 0, by virtue of the special geometrical restriction imposed on the deviatoric stress tensor as discussed above. The principal cause of the crystallographic texture development is lattice rotation resulting from the change of external shape in relation to the material lattice. We call the rate of lattice rotation, W*, the lattice spin tensor. The concepts are illustrated schematically in Figure 2. The lower left figure illustrates a reference material element in a crystalline domain, along with the unit vectors n" and s" representing slip plane normal and the slip direction of the slip system a . Without loss of generality the instantaneous configuration can be taken as the external shape reference. At fixed lattice orientation the rate of crystallographic shearing of a magnitude on system a generates a strain rate of T" RG and a plastic spin '"A!, where A; = a(ssns - npsp) is the skew part of the Schmid tensor for slip system a , introduced above. The resulting (intermediate) deformed configuration is shown in the lower right portion of Figure 2, where it is noted that the total crystallographic strain rate DC,and plastic spin WP are given by sums over all slip systems Ii',and represented in purely kinematic form as:

+"

K

K

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____t

DC+W

Figure 2. T h e kinematics of the various components of spin: (a) initial undeformed lattice, (b) plastically sheared lattice, (c) plastically sheared and rotated lattice

We note that homogeneous slipping alone, in general, alters lengths and orientations of material line elements represented by fiducial lines and angles drawn on the element (e.g., “diagonald’ of the material element), but leaves the lattice unchanged. Lastly, the intermediate configuration is subject t o a strain-free rigid body rotation rate W * , which carries both material line elements and the lattice vectors t o their final orientations. This is shown by the top frame of Figure 2. The crystalline velocity gradient L‘ bringing a material line element directly from the initial to the final configuration is: L‘ = D‘ W‘, as also shown in Figure 2. The skew part of this tensor W cis the sum of the skew parts due t o plastic spin and rigid body spin: Wc = WP W*. Thus, the lattice spin controlling the rate of change of crystallographic axes, relative to the initial reference fiducial body axes, can be expressed in terms of total crystallographic spin and the slip rates by:

+

+

K

W?. ‘3 = W.”. $1 - W?. $1 = - Wc. ZJ - z y a A G .

(3)

Cr=l

The rate of change of crystallographic axes, for instance the chain axis, c , can be expressed in component form as

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274

2.2.2. A m o r p h o u s p h a s e

For the viscc-plastic response of the amorphous component we have taken as a guide the plastic shear resistance theory of Argon [23] for glassy polymers. While modern developments by computer simulation [24] make the molecular interpretations of that theory no longer acceptable, the functional forms put forth by the old theory are still the most accurate. In a further departure we note that in HDPE the amorphous component is rubbery at room temperature while the theory of Argon is intended only as an iso-structural one for the glassy state, well below the glass transition temperature, Tg. We nevertheless apply a power-law approximation of it to the rubbery state of HDPE for operational ease. Then, the simple viscoplastic relation that we propose t o relate the plastic shear rate 7" and the revolved shear stress F in the amorphous phase of HDPE is of the form ' n

+a=.(&)

,

(5)

where $0 is a reference strain-rate and na is the rate exponent. Without much loss in precision, we choose the reference strain-rate equal t o that of the crystalline phase. Moreover, for simplicity and convenience, we also set the rate exponent in the amorphous phase, n a ,equal t o n c , that of the crystalline phase, so na = ne G n. The reference shear strength TO g('oo)[ool] is the initial shear resistance of the easiest slip system in the crystalline phase. Thus, "UTO" is the reference shear strength of the amorphous domain, with the parameter a characterizing the relative strength between the initial deformation resistance in the amorphous phase and that of the easiest slip system in the crystalline phase. Once the barrier to the chain motion is overcome, the molecular chains of the amorphous phase tend to align in the direction of the maximum plastic stretch resulting in directionally-specific changes in the resistance t o plastic flow. To derive a three-dimensional constitutive relation for the amorphous phase, we again neglect elasticity and introduce a back stress tensor, Ha, in the flow rule, which accounts for the strain hardening produced by molecular alignment [25]. Let Da and S" be the strain-rate (stretching) and the deviatoric Cauchy stress present in the amorphous phase. The driving stress (often called effective stress) within the amorphous phase is then defined as S" - Ha. Thus, the resolved shear stress 7' is defined as a norm of the driving stress by

Then, the three-dimensional power-law constitutive relation which we pro-

Deformation induced texture: computer simulation and experiments

275

pose for the rubbery amorphous polymer is

Using the eight-chain network model of rubber elasticity recently proposed by Arruda and Boyce [26], the back stress is conveniently expressed as

where N is the number of rigid links between entanglements and is proportional to the square of the tensile locking stretch; C R is approximately the rubbery modulus; Ba is the so-called left Cauchy-Green deformation tensor obtained from the deformation gradient tensor Fa of the amorphous phase: BG = FGFj"k; I1 = BE; 6,j is the Kronecker delta; and L is the with a Langevin function defined by L ( p ) = coth(P) - 1/p = symbolic inverse function L - ' ( , / w ) = p.'

d m ,

2.3. Composite inclusion

We have modeled the composite inclusion by a generalized threedimensional lamination theory, such that the deformation and stress within each phase are uniform but not necessarily identical and satisfy the constrains of interface compatibility and equilibrium. Let D' and W' be the inclusion-averaged strain-rate and spin, respectively, that can be expressed as

where superscripts "a" and "c" denote the uniform quantities within the amorphous and crystalline phases, respectively. Similarly, the inclusionaveraged deviatoric stress, s', can be written as

s!. '3 = f"SP.'3 + (1 - fa)sij.

(9c)

We assume there is no relative slippage at the crystalline/amorphous interface. Then the interface compatibility condition demands velocity continuity across the crystalline/amorphous interface. Let ef denote a local *We note here that representing the rubbery behaviour of the amorphous component between crystalline lamellae by the formalism of rubber elasticity is done primarily for operational expediency because it does successfully represent the macroscopic mechanical response. Clearly, caution is required in the literal interpretation of the behaviour of this well-defined material on the molecular level.

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orthonormal Cartesian basis vector fixed to inclusion " I " , with e i = n'. Relative to this basis, the compatibility conditions in conjunction with incompressibility in both phases, require the following continuity conditions on strain-rate and spin components:

D' aP - D& = DZp;

(104

Di3 = Dg3 = Di3;

(lob)

w:,= w,c, = Wf2;

(10c)

where the Greek subscripts a,p, range from 1 t o 2. The crystalline/amorphous interface also enforces shear traction equilibrium across the interface which can be expressed in terms of stress deviator components relative to the local Cartesian basis vector ef as

Si3= s:3 = sz3.

(114

Since we assume incompressibility and neglect pressure sensitivity of decomponent of traction continuity can be formation, the normal (n' or satisfied by assuming that any jump of the normal component of deviatoric stress is equilibrated by a corresponding jump in the pressure as

ei)

where pa and p c are the pressure in the crystalline lamella and amorphous layer, respectively. 2.4. Interaction law and solution procedure

A local/global interaction relation must be imposed t o relate the average mechanical behaviour of each composite inclusion t o the macroscopically imposed boundary conditions. The collective plastic deformation of aggregates, such as grains in a polycrystalline assembly, has been the subject of many studies in crystal plasticity and mechanics of heterogeneous plastic media. Since exact solutions satisfying all local conditions of equilibrium and compatibility are intractable, a number of approximate approaches have been developed throughout the years. The most prominent of these are the Sachs model [27], and the Taylor model [28]. In the Sachs model, local and global equilibrium is satisfied trivially by considering the stress as uniform in all component parts, the global compatibility is enforced as a global volume average while local compatibility is not attended to. In comparison, in the Taylor model, compatibility of deformation is satisfied everywhere by considering the local deformation to be related to the global one in an affine sense, while equilibrium is satisfied only as a global volume average. In an earlier model based on the crystalline component alone, we have successfully implemented a Taylor model of HDPE, where textures were

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predicted for several different modes of straining, but where the predicted aggregate plastic resistances were unrealistically higher than the corresponding experimental measurements [21]. As a result it was concluded that since compatibility is already enforced between the crystalline and amorphous layers in the composite inclusion, it is less important t o constrain the deformation of the composite inclusion further t o satisfy additional compatibility restrictions between inclusions than t o satisfy local/global equilibrium. Consequently, we have developed a modified Sachs-like model which satisfies local/global equilibrium but satisfies compatibility only as a global volume average of the compatible deformations and spins of the individual composite inclusions. In our new proposed composite model, a Sachs-like interaction law was employed, which, as we have demonstrated elsewhere [14,29], has been quite successful in predicting both the stressstrain curve and the texture for different modes of deformation. Consider an aggregate of composite inclusions_subject _ t o a prescribed homogeneous boundary condition. Let us denote S , D, and the macroscopic deviatoric Cauchy stress, the macroscopic strain-rate and the macroscopic spin, respectively. Relative to the fixed macroscopic orthonormal baDij and v i j must be prescribed sis vectors E*,specific components of in accordance with a well-posed boundary value problem. For example, in the case of constant strain-rate uniaxial tension _ _ or compression along the relative t o the E3-direction, the prescribed components of S , D and basis vector Ei, are

w

sij,

w,

s

The other (five) (work-conjugate) components of and which are not prescribed must be obtained from conditions of global compatibility and equilibrium. In applying the Sachs-inclusion model, the inclusion-averaged deviatoric stress in each inclusion, S', is approximated as constant, and equal t o the macroscopic deviatoric stress, 3, imposed on the aggregate such that

s'

= 3.

(13.3)

To complete the model for large deformation, we simply equate the inclusion-averaged spin, W', with the macroscopic one,

w:

W' =

w.

(13b)

The self-consistent conditions for global equilibrium and compatibility within the aggregate are that suitable volume averages of local fields equal

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the corresponding macroscopic quantities [30]. The Sachs-inclusion model (13a,13b) satisfies the following requirements trivially:

s; (WI) = w, (S') =

(144 (14b)

where (.) designates the volume average over the aggregate. The remaining self-consistent conditions provide global compatibility, i.e., the volume average of the inclusion strain-rate must equal the macroscopic strain-rate:

(D') =

n.

(14c)

When using the Sachs-inclusion interaction law, (14a-c) can be used t o obtain the five components of and not specified in the definition of the macroscopic boundary value problem. Full details of the solution procedure can be found elsewhere [14]. To simulate the large plastic deformation of semicrystalline polymers, the evolution of texture in these materials has to be taken into account, and is, of course, of primary interest here. The procedure of updating the crystallographic texture, morphological texture and macromolecular texture during the numerical simulation is also available elsewhere [ 141.

s

2.5. Parameter selection

Consider an aggregate consisting of M composite inclusions as described above. This aggregate may represent an isotropic initial state or even oriented semicrystalline polymer depending on the initial orientation distribution assigned to this set of inclusions. Here we consider only an initially isotropic HDPE and neglect interactions between spherulites so that the initial spherulitic morphology is not accounted for explicitly. However, it is possible to generate an isotropic texture corresponding to a "quasispherulitic" structure. In the modeling of initially isotropic HDPE, we have taken an aggregate consisting of 244 composite inclusions, embedded in the collective field of each other. The initial distributions of crystallographic orientations given by the (002) pole figures (or chain axes, c ) and (200) pole figures (or a-axes) in equal area stereographic projection are shown in Figure 3(a) for these 244 inclusions. Since the distributions of (002) and (200) pole figures are essentially uniform (also true for the (020) pole figure due to the orthogonality of the crystal axes), the initial crystallographic texture of the aggregate can be considered as isotropic. It has been reported that for spherulitic polyethylene, the chain axis c and the lamellar normal n' are not parallel [31-331. The initial angle between these two axes varies between 17' and 40'. We take this angle to be initially 30" between c and the ' in the local crystal corresponding n', along with a random projection of n plane spanned by a and b. The initial distribution of lamellar normals for these 244 inclusions is shown in Figure 3(b).

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279

‘l(CD)

(4

Figure 3. Pole figures representing the initially isotropic texture for undeformed HDPE: (a) crystallographic texture and (b) distribution of lamellar normals For the (common) strain-rate sensitivity exponent, we use the value of n = 9 in each phase, based on the measurements of G’Sell and Dahoun [34]. A typical level of crystallinity of HDPE is about 70%; therefore, we take f” = 0.3. Based on published data in the literature, our own extensive experiments, and fitting the behaviour of our model to simple experimental tests we pick the following magnitudes for the parameters of our model: 70 = 7.2MPa [6]; ~ O / T O = 2 - 4.2; a = 1.2; C R = 0.170. To pick the values for a , N , and C R just mentioned, the response of the macroscopic stress-strain behaviour on these constants was studied parametrically [14]. 3. Predicted results and comparison with experiments

3.1. Modes of straining We have applied the proposed composite model to simulate stress-strain response and texture evolution in initially isotropic HDPE for several different modes of straining. Predicted results were compared with both the

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experimental results of previous investigations and with the results of our own recent extensive experiments. The different modes of straining that were considered are, constant strain-rate uniaxial tension and compression, simple shear, and plane strain compression. According to their deformation patterns, these modes of straining can be divided into convergent molecular flow, such as in uniaxial tension and plain strain compression; and divergent molecular flow such as in uniaxial compression, with simple shear and plane strain compression being essentially neutral. A differentiating feature of these classes of deformation is that in convergent molecular flow, and in neutral flow, a process of fragmentation of stretched lamellae ultimately occurs in the course of deformation, at very large strain, which can result in a major restructuring of crystalline and amorphous domain morphology. These phenomena of restructuring of morphology introduce into the deformation important additional considerations such as interface migration. Such restructuring has not been detected in divergent deformation or in simple shear, where in the latter the lamellae are transformed t o fibrils, but no new long period is established [lo]. In the following sections, we first present the predicted results and then compare them with experimental observations for only uniaxial compression and plane strain compression as examples of divergent molecular flow and neutral molecular flow, and over only the deformation history unaffected by the morphological restructuring. 3.2. Uniaxial compression

The first application is the prediction of stress-strain response and texture evolution in deformed HDPE under constant strain-rate uniaxial compression (with D'qQli.0 = 1). The calculated equivalent macroscopic stress, PJ, as a function of equivalent macroscopic strain, Eeq = J,"Deqdt is shown in Figure 4. Also shown in Figure 4 are the corresponding curves for the other deformations that have been simulated of which we will discuss only plane strain compression. As can be seen from Figure 4, our predicted uniaxial compression curve compares well with the experimental data obtained by Bartczak et al. [8], including the level of locking stretch and strain hardening slope. Parenthetically, we note that the predicted stress-strain curves in Figure 4 show a jerky behaviour. These frequent, short stress drops result from the Sachs-inclusion model when during the course of deformation some composite inclusions are caught in momentary soft orientations where they tend t o undergo local "run-away" deformation until these local deformations and their accompanying spins naturally rectify the soft condition. Meanwhile, however, the accelerated volume average deformation results in the stress drops. Figures 5(a) and 5(b) give the predicted crystallographic textures for equivalent strains of 1 and 1.8, respectively. In each pole figure, the axis perpendicular to the projection plane is the compression direction. An equal

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0

Bartczak et al. IS]

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Gaierki et al. [Ill

t

9 I d

28 1

compression

/I+

9':

Tension

oi

I;

Compression

5

v-

i 0.0

Simple shear

ro = 7.8MPa 0.5

1.o

1.5

2.0

Figure 4. T h e normalized equivalent macroscopic stress as function of equivalent macroscopic strain of HDPE subjected to different modes of straining. Experimental d a t a points shown were normalized using TO = 8.0MPa. (from Lee et al. [29], courtesy of Butterworth)

area stereographic projection is used for each pole figure. These figures show that with increasing compressive strain, the pole of the (200) planes (the planes with the lowest chain slip resistance) migrates toward the compression direction, and that the poles of the (002) and (020) planes tend t o align circumferentially uniformly in the radial direction. However, in both cases, the final goals - i.e., for the (200) poles t o reach the compression axis and for the (002) and (020) poles t o reach the radial direction - are not attained. The (011) planes also spread toward the radial direction and evacuate the centre of the pole figure (compression direction) as strain increases. The predicted morphological texture (distribution of the lamellar normals) and macromolecular texture (distribution of orientations of maximum principal stress within the amorphous layers) are also plotted in Figures 5(a) and 5(b). With increasing strain, the normals to the crystalline-amorphous interfaces strongly congregate around the compression axis and the molecular segment alignment in the amorphous domains becomes strongly focused toward the radial direction. At large macroscopic strain, predicted crystallographic textures clearly

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1

(020)

Molecules

Normals

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t 3 =

Figure 5(a). The predicted crystallographic textures, morphological texture, (lamellae normals) and the amorphous phase molecular alignment for HDPE subjected to uniaxial compression at F q = 1.0

-

show two general groups of crystals: a larger group with a axes oriented 30° away from the compression direction and both b and c about 20' axes oriented toward the radial direction; and a smaller group having their b axes oriented about 20' 30' away from the compression direction and both a and c axes oriented toward the radial direction. This agrees with the experimental observations obtained by Krause and Hosford [35].

-

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1

(020)

Molecules

Normals

.w

Figure 5( b). T h e predicted crystallographic textures, morphological texture, (lamellae normals) and the amorphous phase molecular alignment for HDPE subjected to uniaxial compression a t F q = 1.8 (Compression direction is along %axis)

Detailed experimental studies of uniaxial compression on HDPE were also made by Bartczak et al. [8]. Figures S(a)-S(c) show the wide angle X-ray scattering (WAXS) intensity profiles of the (200), (020) and (011) planes as a function of altitude angle measured away from the compression direction for several equivalent macroscopic strain levels including those

10

a0

a0 40

so so

10

eo s

Figure 6. Plots of WAXS intensities of the diffraction by particular crystallographic planes on the altitude angle between the plane normal and the loading direction at macroscopic strains between 0.02and 1.86 of HDPE subjected to uniaxial compression: (a) (200) planes; (b) (020) planes, and (c) (011) planes. The curves were shifted along the intensity axis for clarity. (from Bartczak et al. [8], courtesy of ACS)

0

l . . . . . . . . I

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given in Figures 5(a) and 5(b). The experimental results of Figure 6(a) confirm the model predictions that the scattered intensity of (200) planes show a peak at an altitude angle of around 25' away from the compression direction, while those of Figure 6(c) show that the intensity of (011) planes generally increases as the altitude angle increases away from the compression direction. Between strains of 1 5 Eeg 5 1.8, the model (011) pole figures in Figures 5(a) and 5(b) show a clearing of the region of altitude angles less than 35O, the development of a monotonically increasing intensity within 35' to 70' altitude, where a weak peak appears, and a filling-in of the region with altitude angle > 70'. These features are in remarkable agreement with experimental trends shown in Figure 6(c). At the highest strains, the scattered intensity of (020) planes in Figure 6(b) shows a broad bimodal distribution. These results are consistent with the numerical predictions that there are two groups of crystal orientations (see also Krause and Hosford [35]), a conclusion which is especially evident in the (020) pole figure of Figure 5(a) at Eeq = 1. Direct WAXS information of the (002) planes is difficult to collect because of very low signal-to-background ratio for the (002) diffraction peak [8]. However, the orientation of the (002) poles (or chain direction) may be deduced from either (200) and (020) pole figures or from the pole figures for (011) and (020) planes. Experimental results support the prediction that the (002) pole of sheared crystalline lamellae progressively aligns in the direction of divergent radial flow. The monotonic migration of the amorphous layer normals toward the compression axis predicted in Figures 5(a) and 5(b) is shown best experimentally in the small angle X-ray scattering (SAXS) patterns of Bartczak et al. [8]. Figure 7 shows the SAXS patterns of the deformed material viewed from a radial direction, for overall equivalent strain levels close to those in Figures 5(a) and 5(b). Figure 7(a) shows the initial isotropic SAXS (uniform ring) pattern of the undeformed sample. At an equivalent strain of 0.35 (Figure 7(b)), a distinct clustering of the SAXS intensity in the region closer to the compression direction is discernible, as well as a perceptible outward motion of the maximum of the intensity peak. This clustering of lamellae sharpens further as an equivalent strain of 0.82 (Figure 7(c)) is reached, where a definite congregation of the lamellar normals has taken shape in the compression direction region, with a further outward motion of the intensity peak indicating continued compression induced thinning of the planar lamellae. Finally, in Figure 7(d), at an equivalent strain of 1.86, the location of the intensity maximum has moved out much further, but the overall scattering has also decreased, indicating further thinning of the lamellae, with lamellar normals now being aligned predominantly parallel to the compression direction, but showing a larger variation in thickness and becoming less regular. The SAXS patterns of deformed HDPE can be constructed numerically in a very idealized way based on the calculated information of orientation of lamellar normals, n', and corresponding lamellar thicknesses of the 244

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LD

0.82

1.86

Figure 7. Plots of SAXS patterns viewed from the radial direction for P q of 0, 0.35, 0.82 and 1.86, in uniaxially compressed sample (from Bartczak et al. [8], courtesy of ACS) composite inclusions for different stages of the simulation. In the numerical construction of the SAXS pattern, each composite inclusion is represented by two centrally symmetric diffraction points in a polar coordinate plane with the radial distance of the points from the origin being proportional to the reciprocal of the lamellar thickness. The angle of the point in the synthesized SAXS pattern is in the same direction as the projection of the lamellar normal on the plane perpendicular to the direction of viewing (or incident beam). Because all computational inclusions were initially of identical thickness, the numerical SAXS pattern at zero strain would show all points at equal radius from the origin, in contrast to the distribution of long periods experimentally noted in Figure 7. This lack of initial thickness distribution in the model must be kept in mind when comparing the predicted and experimental SAXS patterns. Figure 8 shows the numerically

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+ *+ ++

LD

+

+

+*

++ +

Figure 8. Plots of numerically-constructed SAXS patterns viewed from a radial direction for Seq of 0.5, 1.0 and 1.5, for a uniaxially compressed sample (from Lee et al. [29], courtesy of Butterworth)

constructed SAXS patterns viewed from a radial direction of the uniaxial compression test for macroscopic equivalent strains of 0.5, 1.0 and 1.5, respectively. Both the numerically constructed and the experimental SAXS patterns indicate that, as strain increases, the SAXS images change progressively from a uniform ring pattern to an elliptic pattern with the longer axis aligned with the compression direction t o an eventual two-point pattern. This change in SAXS patterns implies that the lamellar normals migrate toward the compression direction (as is also evident in Figures 5(a) and 5(b)), and that the lamellae that are oriented perpendicular to the compression direction show both a decrease in thickness and an increasing spread in this thickness. The number of lamellae oriented parallel t o the compression direction (normals perpendicular to compression direction) monotonically decreases, while their thickness progressively increases. These features are all in very good agreement with the experimental observations of Bartczak et al. [8], shown in Figures 7(a)-7(d). In order to gain a deeper understanding regarding the roles of the crystalline and amorphous phases in the texture evolution, the volume averaged strain rate and stress were calculated for each phase. The equivalent phase-volume-averaged strain-rate and stress in the crystalline domains are defined as

ac =

{G,

where [.] denotes the volume average over the domain occupied by the designated phase. The equivalent phase-volume-averaged strain-rate and stress

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I

10

"

"

I

.

'

"

I

.

'

'

'

-

I

I I

I

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I I I I I

Crystalline Ib

II I I

0 ~ " " ' " " ' " " ' " " ~ 0.5 1.o 1.5 0.0 ZeQ

-

2.0

m la"

Figure 9. (a) The equivalent phase-volume-averaged stress, normalized by T O , in both phases in uniaxially compressed sample, as a function of F q and (b) the equivalent-volume-averaged strain-rate normalized by the applied macroscopic strain-rate, in both cases, as a function of F q (from Lee et al. [29], courtesy of Butterworth)

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in the amorphous domains, Da and a“, can be analogously defined. The normalized equivalent strain-rate and stress of each domain obtained in this manner are shown in Figures 9(a) and 9(b) as a function of the macroscopic equivalent strain. At low strain, the amorphous phase supports less stress and deforms considerably more rapidly than the crystalline phase. As deformation progresses, the amorphous phase hardens due t o network locking, resulting in near equalization of the equivalent phase-volume-averaged strain-rates. Strong amorphous phase hardening is predicted in Figure 9(a) at E“Q 2 1.5; in Figure 4, rapid macroscopic hardening in uniaxial compression begins at a similar point. Similarly, the relative magnitude of crystalline phase deformation rate steadily increases with increasing large strain, comparing well with the considerable sharpening of crystallographic texture evident in Figures 5(a) and 5(b). Referring to the crystallographic texture shown in Figures 5(a) and 5(b), we interpret the behaviour t o result from a competition of chain slip and shearing of amorphous domains that allows the (200) poles to reach a “stand-off’ orientation away from the compression direction as shown in both experimental observation and numerical simulation. 3.3. Plane strain compression

The second deformation mode that we wish to present as an example of neutral flow is plane strain compression of HDPE as it develops in a channel die. The channel die compression experiment was performed by Galeski et al. [ll]at a temperature of 8OOC. In order to compare properly with the experimental observations, the (common) strain-rate sensitivity exponent n, the relative resistance of the slip systems in the crystalline phase of HDPE and the material constants of the amorphous phase, a , N and C R , should be chosen accordingly. Due to insufficient experimental information about HDPE at different temperatures, we have employed the same set of material constants used in the previous tests to simulate the constant strain-rate plain strain compression test of HDPE. Our predicted Feq vs. Zeq response is included in Figure 4 (with -=(I D l i . 0 = l ) , together with the experimental curve of Galeski et al. [ l l ] . Again, the agreement is as good as for uniaxial compression. Texture evolution is shown in Figures lO(a) and 10(b) for Teq = 0.8 and 1.3, respectively. In each pole figure, the direction perpendicular to the projection plane is the flow direction. The loading direction and the constraint direction are marked as “LD” and “CD”, respectively. In these figures there is a monotonic migration of the (200) poles toward the loading direction and a corresponding monotonic migration of the (002) poles toward the flow direction. In both cases, however, full alignment is stifled, never quite reaching the geometrical goals, resulting from the competition between crystallographic slip and shear in the amorphous layers. The orientations of directions of maximum stretch in the amorphous phase show strong alignment in the

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CD

CD

Normals

Molecules

LD

LD

CD

CD

Figure lO(a). The predicted crystallographic textures, morphological texture (lamellae normals), and the amorphous phase molecular alignment for HDPE subjected to plane strain compression at F q = 0.8 (Flow direction is along 3axis) (from Lee et al. [as], courtesy of Butterworth)

flow direction. As in the previous case of uniaxial compression the lamellar normals and the chain axes rotate in opposite directions. The simulations predict a monotonic migration of the lamellar normals toward the loading direction. The numerically-constructed SAXS patterns at equivalent macroscopic strain levels of 0.4, 0.8 and 1.2, its viewed from the constraint direction (the neutral direction for plane strain compression) and the flow direction are shown in Figure 11. As strain increses, the predicted SAXS patterns viewed from the constraint direction change progressively from a uniform ring pattern to a four-point pattern, while those viewed from the flow direction develop a two-point pattern. At large strain, the SAXS patterns viewed from both directions predict that the lamellar normals rotate toward the loading direction with decreasing lamellar thickness. Plane strain compression and uniaxial tension belong to a class of

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!CD

Molecules LD

Normals LD

CD

CD

Figure 10(b). T h e predicted crystallographic textures, morphological texture (lamellae normals), and the amorphous phase molecular alignment for HDPE subjected t o plane strain compression at F q = 1.3 (Flow direction is along 3axis) (from Lee et al. [29], courtesy of Butterworth)

macroscopically irrotational large strain deformations, which differ quite significantly in their consequences from uniaxial compression and simple shear. To highlight these differences, here we compare the predictions of our simulation of channel die compression with the experimental results of Galeski et al. [Ill. Figures 12(a) and 13(a) show experimental pole figure patterns of the (002) and (200) planes at Zeq = 0.92 and 1.86, respectively. The orientations of normals to segments of macromolecular chain in the amorphous domain obtained from an X-ray peak deconvolution process discussed in detail by Galeski et al. [36] are shown in Figures 12(b) and 13(b) for those same levels of equivalent strain. In these figures, the view is from the flow direction. Information on the clustering of the lamellar normals is given in Figures 14(a) and 14(b) in the form of the associated SAXS patterns viewing the deformed material from the constraint direction and the flow direction, respectively, for four equivalent strain levels of 0.44, 0.92, 1.15 and 1.86.

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LD

LD

LCD 0.4

Figure 11. Plots of numericallyconstructed SAXS patterns viewed from the constraint direction and the flow direction for samples deformed by plane strain compression, for 2* of 0.4, 0.8 and 1.2 (from Lee et al. [29], courtesy of Butterworth)

0.8

1.2

In Figure 12, for Feq = 0.92, the (200) poles have distinctly rotated toward the loading direction, and the (002) poles have rotated toward the flow direction. Both of these rotations have reached a position roughly 20" from their ultimate target, very much like the trend shown in the simulation reselts in Figures 10(a) and 10(b). In Figure 13, at Feq = 1.86, a high degree of crystallographic orientation is obtained, producing a texture resembling a monocrystal, with (002) poles oriented in the flow direction and (200) poles oriented in the loading direction. Moreover, from Figures 12(b) and 13(b), the orientation of the normals to macromolecular chain segments in the amorphous regions rotate perpendicular to the flow direction and thus the chains in the amorphous phase form an orientation parallel to the flow

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CD

Figure 12. Plots of (a) the WAXS intensities of the diffraction by (002) and (200) planes and (b) the orientation of normals to segments of macromolecular chains in the amorphous region obtained from an X-ray peak deconvolution process of HDPE subjected to plain strain compression at Teq of 0.92 (from Galeski et al. [ll],courtesy of ACS) direction, in continuity with the chains in the crystalline lamellae. This is in good agreement with the simulation results shown in Figures lO(a) and 10(b). The experimental SAXS patterns in Figure 14 for re' = 0.44, 0.92 and 1.15 show that the lamellar normals have very discernibly begun t o cluster around the loading direction, as predicted in Figure 11 (also Figures 1O(a) and 10(b)). The progressive thinning of the lamellae is also confirmed by the SAXS patterns. In Figure 14(a), the SAXS patterns viewed from the constraint direction show a continuous change from a uniform ring into an elongated elliptic shape with a visible four-point pattern. On the other hand, the SAXS patterns viewed from the flow direction change contin-

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(002 I

CD

CD

6Q= 1.86

CD

Figure 13. Plots of (a) the WAXS intensities of the diffraction of (002) and (200) planes and (b) the orientation of normals to segments of macromolecular chains in the amorphous region obtained from an X-ray peak deconvolution process of HDPE subjected to plane strain compression at Feq of 1.86 (from Galeski et al. [ll],courtesy of ACS)

uously from a uniform ring into an elongated ellipse with practically a two-point pattern. These features are qualitatively in excellent agreement with the simulation results of Figure 11. The SAXS patterns in Figure 14(a) show that beyond Seq = 1.15, some new events are beginning to happen. The clear clustering of the lamellar normals has distinctly bifurcated away from the loading direction and toward the flow direction. As reQis increased to 1.86, the four-point pattern viewed from the constraint direction transforms into two arcs normal to the flow direction. The two-point pattern viewed from the loading direction shown in Figure 14(b), is now much better outlined. These data indicate that the lamellae were oriented first preferentially perpendicular to

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LD

0.92

Figure 14(a). Plots of the SAXS patterns viewing the material from the constraint direction for P q of 0.44, 0.92, 1.15 and 1.86 (from Galeski et al. [ll], courtesy of ACS) the loading direction, as predicted by the model, and then, for Feq 2 1.15, the SAXS patterns viewed from the flow direction become progressively fainter, showing a gradual elimination of those lamellae previously oriented with their normals parallel to the loading direction. The SAXS pattern for Eeq = 1.86 in Figure 14(a) shows evidence for restructuring of a new set of lamellae and amorphous regions, i.e., a new long period. Thus, the lamellar normals in the final, fully-textured material are nearly parallel with the flow direction, or the direction of the principal molecular alignment. The formation of these new lamellae, as a major morphological restructuring process, had not been fully elucidated until recently. Galeski et al. [11]proposed a scenario based on their TEM observations and the SAXS results to explain how this newly evolving amorphous material is topologically

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LD

1.15

,:,’

1.86

Figure 14(b). Plots of the SAXS patterns viewing the material from the flow direction for samples deformed by plane strain compression for Te* of 0.44, 0.92, 1.15 and 1.86 (from Galeski et al. [ll],courtesy of ACS) related to the initial amorphous material. In the past this restructuring process leading to the establishment of a new long period, that had been studied only in tension, was associated with the so-called “micro-necking” mechanism proposed by Peterlin [37], in which a fine scale cavitation process was considered to be essential to decouple lamellae from each other prior t o their unravelling. Galeski et al. [ll],who have followed this process in great detail by combined WAXS, SAXS, and TEM experiments in the plane strain compression experiment, have observed no cavitation, but instead a series of continuous transformations, albeit associated with an apparent internal deformation instability. Their observations are outlined in a scenario illustrated in Figure 15, where 15(a) shows the initial stack of parallel lamellae and interspersed amorphous layers. With increasing strain the lamellae shear and become stretched out, as shown in Figure 15(b), as

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tF D

e

. .

Figure 15. Sketch of the process of the formation of a new long period during plane strain compression (from Galeski et al. [Ill, courtesy of ACS)

they also rotate t o redirect their plane normals toward the loading direction as shown in Figure 15(c). As the lamellae progressively thin down, a stage is reached when their interface stretching resistance becomes comparable with the internal plastic resistance of the thin lamellae. Under these conditions thickness perturbations should grow and the lamellae should pinch off on a wholesale basis as depicted in Figure 15(d). The newly formed extensively fragmented crystallites (observed in detail by TEM) which have an excess of interface energy can now lower this energy (without material rotation or shear) purely by interface migration in a state of fixed molecular segment alignment to restructure a new long period, as outlined in Figures 15(f) and 15(g). These restructuring processes were not incorporated into the current model, thus limiting the predictions to deformation to equivalent strains less than the experimentally observed onset of restructuring. However, the predictions are in very good agreement with the experiments up to that point.

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4. Discussion

Development of deformation induced texture in HDPE resulting in large stiffness and strength anisotropies has been known for decades [39,40].The importance of this in technological applications in production of high modulus fibres and ribbons and precursors for high modulus carbon fibre is widely appreciated. In view of this importance there had been intense research activity in the late 60s and early 70s in the study of the mechanisms of the morphological alterations that produce such texture (for a review see Lin and Argon [MI). With few exceptions [40,41] this early research has relied heavily on the uniaxial tension experiment and on a multitude of imaginative microexperiments carried out on electron transparent thin films by means of TEM. These experiments have produced a bewildering collection of deformation features. Many of these experiments have been invaluable in clarifying the crystal structure and forms of crystallization of long chain polymers as well as how these chain molecular lamellar crystals are associated with an ubiquous amorphous phase. On the other hand, they were instrumental in establishing a distorted picture of how the deformation evolved and resulted in texture. Since most investigations concentrated on the details of the tension experiment, which undergoes a variety of unessential and often confusing deformation instabilities, it was believed that large strain texture development necessitates a stage of release of interlamellar constraints by a widespread fine cavitation which then permits unraveling of the lamella followed by unhindered chain alignment, in a process labelled by the picturesque title of “micro-necking” [37]. The early rolling experiments of Keller and Pope [40] and channel die compression experiments of Young and Bowden [41] and the much more detailed recent experiments of Galeski et al. [ll],also in plain strain compression, all have demonstrated that the same very high degree of texture evolution, molecular alignment and long-period restructuring occur in large strain compression flow as in uniaxial tension - but without the cavitation or so-called micro-necking stage. How this occurs quite naturally in the course of large strain extensional flow through eventual repeated pinch-off in the stretched lamellae has been discussed above. This emerging new mechanistic understanding has established the point of view that development of deformation induced texture in semicrystalline polymers can be described by a continued succession of volume preserving shear transformations occurring in the crystalline lamellae and the associated amorphous layers compatibly. This is the approach which we have developed in a series of computational models [14,21,42,43],for HDPE, in association with our experimental studies of this phenomenon [6,8,10,11]in this material. Here we have compared the results of the computer simulation with these experimental results for the two cases of uniaxial compression and plane strain compression. While the computer simulation has been specifically tailored to the orthorhombic crystal structure of HDPE, the developed methodology can be readily

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adapted t o the corresponding deformation induced texturing of monoclinic Nylon-6 [44] and triclinic P E T [45], and any other semicrystalline aggregation, the initial morphology and the deformation mechanisms of which can be definitively stated as initial conditions and constitutive behaviour (see Chapter 2). As we have demonstrated above, our computer model has a high degree of precision in the simulation of both the evolving plastic resistances and deformation induced textures in the “divergent” flow mode of straining of uniaxial compression where no long period restructuring by lamellar pinchoff occurs. In the case of plane strain compression by means of channel die compression our simulation is able to follow the evolution of texture in all respects up to the occurrence of the long period restructuring a t an equivalent strain larger than 1.15. Above this critical strain our simulation is still able to predict the crystallographic texture correctly, but does not predict the further evolution of the lamellar morphology, since this involves lamella pinch-off and apparently extensive interface migration t o reduce stored interfacial free energy. Such processes could be simulated separately but this has not yet been done. 5 . Conclusions

We have employed a newly developed micromechanically based composite model [14] t o study plastic deformation and texture evolution in initially isotropic HDPE subject t o uniaxial compression and plane strain compression. The predicted results agree with the experimental observations of macroscopic stress-strain behaviour and texture evolution in nearly all respects. In the case of channel die compression, the predicted morphological texture for large strain was in some contradiction with existing experimental results. The contradiction arises from a long period restructuring process that appears in large strain extensional flow due to extensive lamella pinchoff and interface migration. This process which has been studied in detail by us and reported elsewhere [ll] has not been incorporated into the present simulation. Nevertheless, our model, even lacking this restructuring, has sharpened the focus on the complex process of texture development. This present micromechanically based composite model can also be applied t o study plastic deformation and texture evolution in other initially isotropic semicrystalline polymers, e.g. P E T and Nylon-6, as well as in initially oriented semicrystalline polymers. 6. Acknowledgements

This work was supported by a DAPRA/U.R.I. program under ONR Contract #N00014-86-K-0768. We acknowledge the important contributions

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of Dr. S. Ahzi to t h e early stages of t h e deformation simulation problem, a n d useful discussions with Prof. C. G’Sell.

References 1. 2. 3. 4. 5.

F. C. Frank, A. Keller, A. O’Connor, Phil. Mag. 3, 64 (1958) T. Seto, T. Hara, T. Tanaka, Japan J . Appl. Phys. 7, 31 (1968) R. J. Young, P. B. Bowden, J. Richie, J. G. Rider, J. Mater. Sci. 8, 23 (1973) P. B. Bowden, R. J. Young, J. Mater. Sci. 9, 2034 (1974) J. M. Haudin, in: Plastic Deformation of Amorphous and Semi-Crystalline Materials, edited by B. Escaig, C. G’Sell, Les Editions de Physique, Les Ulis

6. 7. 8. 9. 10. 11.

Z. Bartczak, A. S. Argon, R. E. Cohen, Macromolecules 25, 5036 (1992) C. G’Sell, J. J. Jonas, J. Mater. Sci. 14, 583 (1979) Z. Bartczak, R. E. Cohen, A. S. Argon, Macromolecules 25, 4692 (1992) C. G’Sell, S. Boni, S. Shrivastava, J. Mater. Sci. 18, 903 (1983) Z. Bartczak, A. S. Argon, R. E. Cohen, submitted to Polymer A. Galeski, Z. Bartczak, A. S. Argon, R. E. Cohen, Macromolecules 25, 5705

1982, p. 291

(1992) 12. F. Khoury, E. Passaglia, in: Treatise on Solid State Chemistry, edited by N. B. Hannay, Plenum Press, New York 1976, vo13, p. 335 13. J. D. Hoffman, G. T. Davis, J. I. Lauritzen, in: Treatise on Solid State Chemistry, edited by N . B. Hannay, Plenum Press, New York 1976, vol.3, p. 497 14. B. J. Lee, D. M. Parks, S. Ahzi, submitted to J. Mech. Phys. Solids 15. L. Lin, Ph.D. Dissertation, 1991, Department of Mechanical Engineering, 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33.

MIT. D. P. Pope, A. Keller, J . Polym. Sci., Polym. Phys. 13, 533 (1975) G. S. Burney, G. W. Groves, J. Mater. Sci. 13, 639 (1978) L. Lin, A. S. Argon, J. Mater. Sci. in press J. W. Hutchinson, Proc. Roy. SOC. London 348, 101 (1976) R. J. Asaro, A. Needleman, Acta Metall. 33, 923 (1985) D. M. Parks, S. Ahzi, J . Mech. Phys. Solids 38, 701 (1990) R. J. Asaro, J. R. Rice, J. Mech. Phys. Solids 25, 309 (1977) A. S. Argon, Phil. Mag. 28, 39 (1973) P. H. Mott, A. S. Argon, U. W. Suter, Phil. Mag., 41, 389 (1993) M. C. Boyce, D. M. Parks, A. S. Argon, Mech. Mater. 7, 15 (1988) E. Arruda, M. C. Boyce, J. Mech. Phys. Solids 41, 389 (1993) G. Sachs, 2. Verein Duet. Ing. 72, 734 (1928) G. I. Taylor, J. Inst. Metals 62, 307 (1938) B. J. Lee, A.S. Argon, D.M. Parks, A. Ahzi, Z. Bartczak, Polymer, in press R. Hill, Proc. Roy. SOC. LondonA326, 131 (1972) A. Keller, S. Sawada, Macromol. Chem. 74, 190 (1964) D. S. Bassett, A. M. Hodge, Proc. Roy. SOC. LondonA377, 25 (1981) W. D. Varnell, E. Ryba, I. R. Harrison, J. Macromol. Sci., Phys. B 26, 135

(1987) 34. C. G’Sell, A. Dahoun, to be published 35. S. J. Krause, W. F. Hosford, J . Polym. Sci., Polym. Phys. Ed. 27, 1853 (1989)

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36. A. Galeski, A. S. Argon, R. E. Cohen, Macromolecules 24, 3953 (1991) 37. A. Peterlin, J. Muter. Sci. 6, 490 (1971) 38. I. M. Ward, in: Structure and Properties of Oriented Polymers, Halsted Press, New York 1975 39. A. Ciferri, I. M. Ward, in: Ultra High Modulus Polymers, Applied Science Publishers, London 1979 40. A. Keller, D. P. Pope, J . Muter. Sci. 6, 453 (1971) 41. R. J. Young, P. B. Bowden, Phil. Mag. 29, 1061 (1974) 42. S. Ahzi, D. M. Parks, A. S. Argon, in: Computer Modeling and Simulation of Manufactoring Processes, edited by B. Singh et al., ASME, New York 1990, p. 287 43. D. M. Parks, S. Ahzi, in: IUTAM Symposium on Inelastic Behauiour of Composite Materials, edited by G. J. Dvorak, Springer Verlag, New York 1990, p. 325 44. L. Lin, A. S. Argon, Macromolecules 25, 4011 (1992) 45. A. Bellare, R. E. Cohen, A. S. Argon, Polymer, in press

Oriented Polymer Material> Stoyko Fakirov Copyright 0 2002 Wiley-VCH Verlag GmbH & Co. KGaP

Chapter 10

Intrinsic anisotropy of highly oriented polymeric systems in relation to molecular orientation and crystallinity

M. Matsuo

1. Introduction

Polymer molecules are intrinsically anisotropic in physical (e.g. , mechanical and optical) properties. This causes the bulk properties of polymer aggregates to be anisotropic when the macromolecules are oriented. To estimate the anisotropy of polymeric systems, the intrinsic values of physical constants have been measured for many kinds of polymers using melt drawn fibres and films. The resulting values, however, are ambiguous because of a complex morphology with superstructures such as deformed rods and spherulites. The estimation of the intrinsic anisotropy of polymeric systems would be correct if the chains of a test specimen are fully aligned and extended and if the specimen is almost completely crystalline. At present, such a simple morphology as perfect molecular orientation and crystallinity can be achieved by gelation/crystallization from semidilute solutions only with two polymers, polyethylene and polypropylene. Accordingly, several interesting phenomena concerning the crystal lattice modulus and the crystal dispersions are discussed by using ultradrawn polyethylene and polypropylene films. Furthermore, ultradrawn films were prepared from a dilute so-

Intrinsic anisotropy in relation to molecular orientation and crystallinity

303

lution of polyethylene and polypropylene, in spite of their incompatibility in solution, and the morphology and mechanical properties were discussed as dependent of the composition. 2. Crystal lattice moduli of crystalline polymers In recent years, research on the preparation of fibres and films with high modulus and high strength has become a topic of increasing interest [l-121. The utimate value of Young’s modulus is well-known t o be equivalent t o the crystal lattice modulus along the chain axes. The crystal lattice modulus has been studied by X-ray diffraction [13-161, Raman spectroscopy [17], and inelastic neutron scattering [18]. The values obtained by Raman and neutron scattering are significantly higher than that determined by X-ray diffraction. The difference may be due to essential problems in determining the crystal lattice modulus by Raman spectroscopy and neutron scattering. In addition to the difficulty in estimating the exact value of lamellar length by small angle X-ray scattering, both methods contain an unavoidable assumption concerning the frequency of absorption bands in a polymeric system. On the other hand, theoretical treatments of the crystal lattice modulus were reported by Odajima et al. [19] and Tashiro et al. [20]. The calculated values, however, are different because of difficulties in estimating the effects of intermolecular interactions, which cannot be ignored. X-ray diffraction measurements were carried out by Sakurada et al. [13,14], Nakamae et al. [15-161 and Matsuo et al. using several kinds of polymers having different crystallinities and molecular orientation [1,2].

set tin g apparatus \

unit : mm

plane

Figure 1. WAXD optical system used to detect the crystal lattice strain of the crystal plane

304

M. M a t s u o

They concluded that the value of crystal lattice modulus is hardly affected solely by these two factors. An essential question, however, arises as to whether the homogeneous stress is valid in such a case. That is, whether the stress within a specimen is everywhere the same as the external stress applied. If this hypothesis may be used, X-ray diffraction has the advantage of determining the crystal lattice modulus directly. Figure 1 is a sketch showing the optical system of the wide-angleX-ray diffraction (WAXD) with a scintillation counter in our laboratory [l]. The incident beam was monochromatized and collimated by a curved graphite monochromator. The intensity distribution was measured with a step-scanning device at a step of 0.05-0.1, each at a fixed time of 20-100 s , in the desired range of twice the Bragg angles. Figure 2 shows the constant-tension stretching apparatus. The specimen was mounted horizontally in the stretching clamps and the diffraction intensity from the crystal plane was detected by the diffractometer shown in Figure 1. A load cell was fixed at the right end of the clamp. The load cell consists of a steel ring whose deformation during elongation is negligibly small compared to that of the specimen. The deformation of the ring due to the tensile strength of the specimen is electronically transformed as analogue voltage. The deviation of the peak position was estimated visually by Sakurada et al. [13,14] and Nakamae et al. [15,16], while in this chapter it was estimated as the deviation of the centre of gravity of the intensity distribution which was described elsewhere in detail. In order to check the homogeneous stress hypothesis, ultradrawn films

I

-4

I

I)

(k)

Figure 2. Stretching device providing constant tension: (a) fixed clamp, (b) beryllium plate, (c) constant temperature chamber, (d) sample, (e) movable clamp, (f) axis to stretch a test specimen, (g) mechanical detector, (h) ball bearing, (i) gear, (j) motor, (k) plate to fix mechanical part, (1) rotational axis

Intrinsic anisotropy in relation t o molecular o r i e n t a t i o n and crystallinity

305

are suitable as test specimens, because of their simple morphology, i.e. perfect crystallinity and molecular orientation. To this purpose, the dried gel films of ultra-high molecular weight polyethylene (UHMWPE) with molecular weight of 6 x l o 6 were prepared by crystallization from dilute decalin solutions according to Smith et al. [7-91. The films were elongated up t o 300 times at 135°C under nitrogen. The specimen elongation was found t o be negligibly small during the measurements of the crystal strain. Under such conditions, it may be postulated that the stress within the test specimen is equal to the external stress applied. Table 1 shows the crystal lattice modulus of polyethylene measured from the crystal strain of the (002) plane [l].These results indicate that the crystal lattice modulus is in the range of 213-229 GPa and is unaffected by small differences in crystal size, crystallinity, and the second order orientation factor but the corresponding Young’s modulus is very sensitive to these differences. Such independence of the crystal lattice modulus supports the assumption that the stress within a specimen is homogeneous. Table 1. Characteristics of specimens used to measure the crystal lattice modulus Specimen Elongation Crystal lattice Crystallinity Crystal Orientation Young’s ratio modulus (GPa) (%) size (A) factor modulus (GPa)

A- 1 A- 2 B- 1 B- 2 c -1 c-2 c-3 c-4 c-5 C-6 D-1 D- 2 D-3

50 50 100 100 200 200 200 200 200 200 300 300 300

222 205 201 225 213 213 219 222 214 217 200 215 229

90.4 87.0 94.3 90.0 92.3 94.9 92.3 94.9 92.3 94.9 95.4 95.4 96.2

350 330 350 400 330 430 300 310 360 350 450 380 430

0.9943 0.9957 0.9978 0.9975 0.9986 0.9990 0.9997 0.9996 0.9979 0.9976 0.9999 0.9996 0.9994

25-30 45-55

110-1 20

151-202

To check this concept, the crystal lattice modulus of ultradrawn isotactic polypropylene was also measured “4. The specimens were prepared similarly to polyethylene dried gel films and were elongated up t o 80 times at 170OC. It should be noted that a crystal plane with reciprocal lattice vector parallel to the molecular chain axis was not detected. In the unit cell, the reciprocal lattice vector of the (713) plane most closely parallels the caxis among all the crystal planes. Hence, the apparent crystal modulus E, of the (713) plane was measured. Using the apparent value, the real value of the crystal lattice modulus E: was calculated through a complicated mathematical treatment. 2

E,O = {cos 43

+ (1

-

cos2 43)(S13/S33)}Ec

306

M . Matsuo

where 5’13/&3 corresponding to the Poisson’s ratio can be written by using the elastic stiffness Cij as follows:

These values of the elastic stiffness at 24OC were measured by Leung and Choy using an ultrasonic technique. They were reported to be C11 = 5 GN/m2, C12 = 3 GN/m2, and c13 = 4 GN/m2. From the crystallographic viewpoint, cos 43 is given by

~ 0 ~ =4 (3absinp)/(b2c2 3 + 9a2b2+ a2c2s i n 2 p+ 6 ~ b ~ c c o s p ) (3) ~/~, where the coefficients in Eq.(3) represent the constant values of the unit cell. They are given as a = 6.65A, b = 20.96A, c = 6.50A, and ,8 = 99.20’ Using Eqs. (1)-(3), E: takes the following values:

E: = 38.7 GPa, if E, = 41 GPa E: = 40.6 GPa, if E, = 43 GPa E: = 42.5 GPa, if E, = 45 GPa

(4)

Table 2. Characteristics of ultradrawn po1ypropy.-ne films Draw Crystal lattice Young’s Tensile Birefrigence Crystallinity ratio modulus (GPa) modulus (GPa) strength (GPa) x ~ O - ~ (%I 30 40 60 80 100

42.5 42.5 38.7 40.6 41.6

13.6-19.6 19.2-21.4 24.0-30.2 26.1-37.6 33.8-40.4

0.542-0.889 0.750-0.994 1.04-1.24 1.15-1.43 1.36-1.56

19 21 23 25 27

77.4-78.9 78.9-79.8 80.4-81.3 81.1-83.3 82.6-84.4

Table 2 shows the crystal lattice modulus modified by using the above relationship, Young’s modulus, tensile strength, birefringence, and crystallinity. The crystal lattice modulus of polyethylene is also independent of the draw ratio > 30. This tendency is similar to the results of ultradrawn polyethylene films listed in Table 1, indicating the validity of the homogeneous stress hypothesis. The Young’s moduli of polyethylene and polypropylene reached 216 and 40.4 GPa, respectively. This implies that the Young’s moduli of ultradrawn polyethylene and polypropylene gel films attain almost their ultimate theoretical values. Here it should be noted that the crystal lattice moduli of polyethylene and polypropylene measured using ultradrawn films are almost equal to those measured by Sakurada et al. using melt films with low crystallinity and molecular orientation [13]. The study of these peculiarities requires a theoretical approach.

Intrinsic anisotropy in relation to molecular orientation and crystallinity

307

3. Theoretical approach t o the estimation of the c r y s t a l lattice modulus as measured by X-ray diffraction

A mathematical treatment is proposed for the estimation of the crystal lattice modulus as measured by X-ray diffraction and the Young’s modulus in the bulk as a function of molecular orientation and crystallinity. The procedure for calculating the mechanical anisotropy of a single phase system from the orientation of the structural units is discussed in terms of the mutual conversion of the orientation distribution function of the structural unit with respect t o Cartesian coordinate fixed within the bulk specimen [21-241. In this chapter, a composite unit as shown in Figure 3 [25,26] is proposed t o describe the polymer specimen, in which anisotropic amorphous layers lie adjacent to oriented crystalline layers with the interface perpendicular t o the three principal directions. The volume crystallinity X , is represented by pb2 using the fraction lengths 6 and p in the directions of X 3 and X 2 . In this model system, the X 3 axis is along the stretching direction and the X 2 X 3 plane is parallel t o the film surface and 5 is assumed t o be unity, since ultradrawn films can be represented as a series model [all. When the uniaxial external tensile stress is applied along the X 3 axis in this model system, the crystal lattice modulus and bulk strain within XS

Figure 3. Composite structural unit of a semicrystalline polymer with crystallites surrounded by amorphous phase

308

M. Matsuo

this composite model could be estimated as a function of molecular orientation and crystallinity based on a somewhat complicated mathematical treatment associated with tensor analysis. The Young's modulus E is given by [21]

E=

Xc[H(SiV,,Si;,Xc)+ Sj;] +

1 (5) (1 - xc)[G(SiV,,Si;,Xc) St:30]

+

where

and

The crystal lattice modulus E," along a chain axis is given by [21]

1/E: = l/Ec

+ F(StO,,Sg , St:,X,)

(8)

where

In Eqs.(5)-(9), the volume fraction of crystallinity corresponds to the fractional length X, of the crystallites along the X3 axis. Assuming the homegeneous stress hypothesis for a polycrystalline material, the relation between the intrinsic compliance of a structural unit and the bulk compliance is given by

and 3

siojvki

=

3

3

3

~~(aioajpakqalr)s~~qr

(11)

r = l q=1 p = l o = l

where Si:k, and Siojvkl are bulk compliances of the crystal and amorphous phases, respectively, and S:oqr and S:iq,, are their intrinsic compliances.

Intrinsic anisotropy in relation to molecular orientation and crystallinity

309

I

I_

' 0

20

40

60

80

Crystallinlty cx)

Kx)

Figure 4. Young's modulus ( E ) calculated as a function of crystallinity for various draw ratios (A)

is, for example, the direction cosine of the @axis of the structural unit and the i-axis of the bulk specimen. In accordance with the analysis of Krigbaum and Roe [27,28], the distribution funtion w(0,cj) may be expanded in a series of spherical harmonics and the brackets in Eqs. (10) and (11) can be represented by using the fourth and second order orientation factors. Here, it is evident that the crystal lattice modulus along a chain axis as measured by X-ray diffraction is essentially not equal to the intrinsic crystal lattice modulus. Only in the case of F(S:", SiV,,SzE,X , ) << 1/E:, the measurable crystal lattice modulus is almost equal t o the intrinsic crystal lattice modulus. Accordingly, the numerical calculation plays an important role to check whether this relation can be formulated. Figure 4 shows the crystallinity dependence of Young's modulus ( E ) for various draw ratios. The Young's modulus ( E ) increases as crystallinity increases. This tendency becomes considerable with increasing draw ratio. In the range from X = 50 t o 100,the magnitude of the increase becomes very high but the crystallinity dependence of the Young's modulus becomes less pronounced with the further rise of X beyond 200. In the case of X = 400, E is close to the theoretical value proposed by Odajima et al. (191 as the crystallinity increases. This supports the experimental results of Young's modulus listed in Table 1. Figures 5 and 6 show the crystallinity dependence of the crystal lattice modulus E, for various draw ratios. The value of E, increases with decreasing crystallinity but this tendency is not significant. Especially, as shown in Figure 5, E, for specimens drawn beyond X = 20 is hardly affected by the crystallinity. It should be noted that, even at A = 10, E, for a specimen with X, > 60% is almost equal to the value at X = 300 and the small difference between E: and E, is within the experimental error. This supports ai,

310

M. Matsuo I

300-

I

I

1

-

Figure 5. Crystal lattice modulus

E, calculated as a function of crystallinity for various draw ratios up to 20

254

Figure 6. Crystal lattice modulus E, calculated as a function of crystallinity for various draw ratios between 50 and 400

that the value measured by Sakurada et al. using a melt film with X = 10 and crystallinity > 60% [13] is almost equal to the results in Table 1. 4. Effect of crystallinity and molecular orientation on Young’s

modulus in UHMWPE and LMWPE blend films The data in Tables 1 and 2, suggest that Young’s modulus is sensitive to the molecular orientation and crystallinity. To check further this observation, blend gel films with different crystallinities were prepared by using UHMWPE with M, = 6 x l o 6 and LMWPE (Sumikathen G201) with Mu = 4 x lo4 and high degree of branching, 2.5 CH3/100C. The UHMWPELMWPE compositions chosen were 91/9, 67/33, and 50/50. Table 3 shows the changes in Young’s modulus, crystallinity, and birefringence as dependent of the draw ratio. The crystallinity value for undrawn films becomes higher as the UHMWPE content increases. Crystallinity increases with increasing draw ratio. The crystallinities of the 100/0 and 91/9 blend films with X = 200 reached 95 and 9496, respectively, and those of the 67/33 and 50/50 blends reached about 84 and 81%. This indicates that LMWPE with a high degree of branching hampers the increase in crystallinity. The birefringence increases with A; its values for the 91/9, 67/33 and 50150 blend 61 x and 60 x respectively. films at X = 200 reached 63 x

lntririsic anisotropy in relation to molecular orientation and crystallinity

3 11

Table 3. Characteristics of UHMWPE-LMWPE blend films as dependent of the draw ratio [29] Draw ratio

200 50

20

Composition

91/9 67/33 50150 91/9 67/33 50/50 91/9 67/33 50/50

Birefringence x10-~

Crystallinity

(%)

Young’s modulus (GPa)

63 61 60 55 54 51 48 41 37

94 84 81 87 77 71 82 73 67

138 90 86 72 52 30 27 22 16

These values are higher than the intrinsic birefringence of the cryscalculated on the basis of the assumption, that talline phase, 58.5 x the principal refractive indices can be estimated by assuming the atomic arrangements within the crystal unit cell and neglecting the uncertain effect of the internal field. Thus, the intrinsic birefringence of the crystalline phase is calculated from the three principal refractive indices of the crystal of n-paraffin (C36H74) reported by Bunn and de Daubeny [30]. This discrepancy is probably due to the fact that the value of crystalline birefringence may be incorrect and that form birefringence, which has been neglected, may be significant. Anyway, the birefringence data indicate that molecular chains within the three kinds of blend films drawn to X = 200 show high orientations in the stretching direction. The small difference in birefringence values among the blends is probably due to the difference in crystallinity as listed in Table 3 but it is almost independent of the orientational degree of molecular chains. Young’s modulus increases with A; its values for the 9119, 67/33 and 50150 blend films reached 135, 93 and 85 GPa, respectively, at X = 200. Young’s modulus is sensitive t o the composition. Judging from the values of crystallinity and birefringence at X = 200, the decrease of Young’s modulus with increasing the content of LMWPE is attributed to the decrease in crystallinity. This assumption is in good agreement with the calculated results in Figure 3. 5 . Temperature dependence of the cr ystal lattice modulus and

Young’s modulus

For the exact measurement of the temperature dependence of the crystal lattice modulus, care should be taken t o avoid further elongation of the drawn test specimen under external stress applied at elevated temperature [31,32]. Furthermore, elongation under a constant stress, termed creep, is

312

M. Matsuo ( c ) at 130%

( b ) at I I 0 " C

( a ) a t 140'1:

0.I 0 Crystal strain 1

'

uGPa

1

~

(%I 1

Crystal ~

1

- ~

strain (%I 1

~

Crystal strain

1

v ~ 1 1

aGPa

'2 0.055 '3 0.083 04 0.133

'3

a

#

8

;

t

1

74 28

8p 8. 0

75 ( Bragg

76 angle I

Figure 7. Relationship between X-ray diffraction intensity distribution and the crystal lattice modulus: (a) wrong result, (b) wrong result, (c) correct result associated with viscoelastic properties and results in unreliable values of the crystal strain. This creep phenomenon can be negligible if the molecular chains are fully aligned and extended and if the test specimen is almost completely crystalline. Figure 7 shows examples of the change in the X-ray intensity distribution with increasing external stress a t the indicated temperature above 110OC. These profiles serve to determine whether the test specimens are suitable for measuring the crystal lattice modulus as a function of temperature. It is obvious that the change in the profile of the diffraction intensity is extremely sensitive to creep and the resulting data become wrong. A correct result is obtained when the intensity distribution remains constant under different external stresses. For the retention of a sample strain of less than 10% even at 145OC, all specimens drawn beyond X = 300 were annealed for 2 h at 14OOC and cooled slowly to room temperature at a constant stress of 0.1 GPa, prior to the measurement of the crystal lattice strain. In this way, the sample strain under an applied constant stress of 0.15 GPa was confirmed to be less than 10% at 145OC. Therefore it can be assumed that this procedure causes further increases in molecular orientation and crystallinity and plays an important role in avoiding creep, thus leading to a correct result, as shown in Figure 7(c). Figure 8 shows the temperature dependence of the complex dynamic

Intrinsic anisotropy in relation to molecular orientation and crystallinity

- -20 LLJ 40

313

60 80 100 120 I

1

1

I

0 0

0 0 0

0 0

0 0

0 0 0

0 0 0 0

0 0 0 0

0

0 0 0

O

I

0

W 20 40 60 80 I00 I20 140

Temperature

("C1

Figure 8. Temperature dependence of the complex dynamic tensile modulus for an ultradrawn film with a draw ratio of 400

tensile modulus of an ultradrawn film with a draw ratio of 400. This specimen has a modulus of 216 G P a a t 20°C, corresponding to the crystal lattice modulus. The dynamic modulus was measured for various temperatures from 10 to 14OOC at 10 Hz. The storage modulus E' decreases with increas-

314

M . Matsuo

ing temperature. This tendency is similar to the results generally observed with semicrystalline polymers. The value, however, is beyond 130 GP a at 14OOC in spite of the drastic drop of E' of commercial polyethylene films (or fibres). To elucidate this fact, the temperature dependence of the crystal lattice modulus was followed for ultradrawn polyethylene and polypropylene together with the temperature dependences of Young's modulus and crystallinity. Table 4. Temperature dependence of the crystal lattice modulus, Young's modulus, and crystallinity of polyethylene (PE) and polypropylene (PP)

PE

PP

Temperature ("C)

Crystal lattice modulus (GPa)

Young's modulus (GPa)

Crystallinity

20 50 70 100 110 120 130 140 145 150

219 211 216 214 219 222 221 211 219 130

217 204 192 172 164 158 147 137 130 110

97 96 94 89 87 84 81 78 75 -

20 70 100 130 150 155 160

41 41 41 41 41 41 20

37 35 34 32 30 29 28

86 86 85 84 83 82 -

(%I

It is interesting t o note (see the results in Table 4), that within the experimental error, the measured values of the crystal lattice modulus are temperature independent below the melting point (145.5OC) [33].This behaviour can be explained by assuming that the polymer chains in the melt retain their extended arrangement and therefore the entropy of fusion is smaller than the value calculated for random coils in the molten state. Actually, the apparent melting point was 155OC by differential scanning calorimetry (DSC) measurement at a heating rate of 10°C/min. This effect is characteristic of ultradrawn films at temperatures near the theoretical melting point. The sample remains intact above the melting point because of superheating effects. Beyond the melting point, however, the crystal lattice modulus decreases considerably. As for ultradrawn polypropylene films, the crystal lattice modulus is 41 GPa at temperatures below 155OC but at 160°C this value decreases and becomes 20 GPa. This means that the crystal lattice modulus decreases at temperatures below the melting point (187OC) [34]. Anyway, this observation is due to the fact that the crystal lattice modulus is unaffected by temperatures close to the melting

Intrinsic anisotropy in relation to molecular orientation and crystallinity

315

point despite the drastic decrease in Young's modulus of bulk specimen. This difference suggests that the temperature dependence of the Young's modulus is strongly affected by the rise in amorphous content with increasing temperature; this result is in good agreement with that in Table 3 (see also Chapter 2). Incidentally, the thermal expansion coefficient of the c-axis of polyethylene was measured against temperature in the free state without applied stress and at various stresses. When the crystal strain a t 2OoC was set to be zero, the linear thermal expansion coefficient was estimated to be -2.27 x 10-5/0C [31]. As for polypropylene, the value for the (T13) plane was -6.18 x 10-5/0C [32]. These values for polyethylene and polypropylene are almost independent of the applied stress. This observation is very important to check the validity of the obtained values (see Chapter 6). As shown in Table 4, the crystallinity decreases with increasing temperature, remaining about 74% even at 145OC. This observation is based on the decrease in the area of the X-ray diffraction intensity distribution curve from the (002) plane, attributed to a decrease in crystallinity and to an increase in thermal fluctuation arising from lattice distortion. The two contributions can be separated by using the methods proposed by Ruland [35] and Killian [36] for undrawn films. Similarly, the temperature dependence of crystallinity was followed for ultradrawn polypropylene films; the value decreases from 86 to 82%. The effect of temperature on crystallinity is not so significant as in the case of ultradrawn polypropylene. Hence, the degree of decrease in Young's modulus for ultradrawn polypropylene films with temperature is less pronounced than that for ultradrawn polyethylene. Figure 9 shows the changes in birefringence with increasing temperan

-

0

X

a

lo

0

0

0

0

0

0

0

0

0

0

0

50

Temperature ( "C Figure 9. Temperature dependence of birefringence for a n ultradrawn film with a draw ratio of 400

M. Matsuo

316

Figure 10. Composite structural unit of a crystalline polymer with crystallites surrounded by amorphous phases: (a) without voids; (b) containing voids ture. The measurements were performed using the specimen with X = 400 in a fixed dimension. The values are temperature independent up to 145OC, indicating perfect molecular orientation. Here it should be noted that, in is contrast to what is normally observed, the total birefringence 67.6 x as dismuch higher than the intrinsic crystal birefringence A:, 58.5 x cussed before. This discrepancy is probably due to the fact that the value of A: may be incorrect and that the value of form birefringence, Af , which has been neglected, may be significant. Furthermore, the form birefringence cannot be neglected because a number of voids were observed by scanning electron microscopy [ll]within the drawn specimens. Unfortunately, it was impossible to estimate experimentally the form birefringence effect. Thus, a model is proposed as shown in Figure 10 to analyze the form birefringence effect [39]. In this model system, oriented crystallites are surrounded by amorphous phases. Diagram (b) represents the system containing voids, while diagram (a) represents the system obtained by removing voids from diagram (b). In both cases, amorphous layers are adjacent to oriented crystalline layers with the interfaces perpendicular to the 2 and Table 5. Parameter sets to calculate birefringence Case

1 - lo/Lo 1 - &/Do

I

0.9999 0.9700

Case

I1

0.9700 0.9999

Intrinsic anisotropy in relation to molecular o r i e n t a t i o n a n d crystallinity

317

1.4

~

L/Lo- 1.00I

-8. 1.3 a c 9. n \

9

4

1-29

E

% a 1. I

1.00

1.005 O/ Do

I.o

)

Figure 11. Birefringence against DIDO at L/Lo = 1.001 z axes. In diagram (a), the fraction of length corresponds to lo/Lo in the z-direction and &/Do in the z-direction, while in diagram (b), the fraction corresponds to l / L and d / D in the z- and x-directions, respectively. Of course, these models correspond to a series model at d o l l l o (= d / D ) = 0 , while they correspond t o a parallel model at lo/Lo(= l / L ) = 0. The detailed method is described elsewhere [39]. In numerical calculations, volume crystallinity, X,,is fixed at 0.97 (97%) to represent the morphology of ultradrawn polyethylene. The values of (1 - lo/Lo) and (1 - do/&) must be set to assume X, = 0.97. Two cases are considered and each set of parameters is listed in Table 5. In Case I, parallel coupling between amorphous and crystal phases is predominant, while in Case 11, series coupling is predominant. Figure 11 shows birefringence with increasing D/Do when L/Lo is fixed at 1.001. In Case I, corresponding to parallel coupling, the birefringence in

318

M . Matsuo

this system containing no voids is about 58.25 x loA3,which is close to the value of the intrinsic crystalline birefringence. On the other hand, in Case 11, corresponding to series coupling, the value is about 54.7 x This indicates that birefringence is very sensitive to morphology even in ultradrawn films with cystallinity of 97%. With increasing D I D O ,i.e. volume fraction, de, birefringence in Case I increases. The increase in voids in Case I corresponds to a model system where voids exist only in the amorphous region, dL, showing parallel coupling and no voids are present in the very narrow amorphous region, 1D. Here it can be noted that at DIDO > 1.085 (i.e. q5 > 0.24), birefringence is beyond 60 x This has been reported generally for ultradrawn polyethylene films. On the contrary, birefringence in Case I1 decreases with the rise of voids. The increase in voids in Case I1 can be represented as the model where voids exist only in the very narrow amorphous phase, d L , indicating parallel coupling. Anyway, the results in Figure 11 indicate that the form birefringence effect attributed to the existence of voids leads to higher values of the observed birefringence than the intrinsic birefringence of the crystal phase. 6. Viscoelastic properties of ultradrawn polyethylene

The crystal dispersion (a-transition) of polyethylene has been reported to consist of two or more relaxation mechanisms [38,39]. The resolution of the a-transition into two components was first reported by Nakayasu et al. [40] for melt-crystallized polyethylene. Since then, multiple types of crystalline relaxation mechanisms have been studied by many authors. Numerous rheooptical studies on the a-transition have indicated that the a1 mechanism is associated with grain boundary phenomena related to deformation and/or rotation of crystallites (crystal mosaic blocks) within a viscous medium and the a2 mechanism - with the crystal disordering transition due to the onset of torsional oscillation of polymer chains within the crystal lattice [41,42].In these studies, however, it has been difficult to give an unambiguous interpretation of the relaxation mechanism because of the structural complexity of the semicrystalline samples [43-461. Therefore, crystal dispersion must be investigated by a system that is morphologically simpler than a semicrystalline spherulitic one. Thus, ultradrawn polyethylene films were used as test specimens. Figure 12 shows the master curves of the storage modulus E' and loss modulus E" for the dry undrawn gel films, reduced to the common reference temperature of 65OC. Each curve is obtained by shifting horizontally and then vertically until good superposition is achieved. It is seen that the frequency dispersion of E" exhibits a quite broad dispersion peak and the profile is asymmetrical with respect to the logarithmic frequency axis. From these observations, it can be inferred that although the broad dispersion

Intrinsic anisotropy in relation to molecular orientation and crystallinity

319

Figure 12. Master curves of the storage modulus E' and loss modulus E" for the undrawn dry gel film

curves may be expected to consist of two mechanisms, the direct separation of the reduced moduli into the respective contributions cannot be carried out owing t o the lack of adequate data, especially in the lower frequency range. In order to divide the broad dispersion curve into two components, the logarithm of the temperature dependence of the horizontal shift factor was plotted against the reciprocal absolute temperature. The Arrhenius plots thus obtained are represented by two straight lines and the activation energies obtained from the slopes of these lines are given as 110 and 163 kJ/mol, respectively. These values are within the two ranges of the literature values of high-density polyethylene, i.e. from 98 to 117 kJ/mol for a1 and from 147 to 193 kJ/mol for ag. Figure 13 shows the master curves of El and El' for the ultradrawn film (A = 400) annealed for 1 h at 130°C, prior to the measurements. The profile of El shows that the frequency dependence is much weaker than that observed generally with other specimens. The value of E" decreases considerably with the rise of frequency beyond 10 Hz. This tendency indicates that the specimen with X = 400 behaves like elastic materials. The storage modulus at 20°C was 216 GPa in the frequency range beyond 10 Hz,which corresponds t o Young's modulus of steel. The master curve of E" shows a sharper dispersion than those of the specimens with X = 20, 60 and 100 [38].

320

M. Matsuo

3

2-41

2.2 2.0

I

-I

,

“.B I

0

,

I

I

,

, 2

0

,

I

3

,

o o q

4

L O G p a l (Hz) Figure 13. Master curves of the storage modulus E’ and loss modulus E” for the dry gel film with X = 400 Figure 14(a) shows the Arrhenius plots of the horizontal shift factor aT(T,To) and Figure 14(b) shows the logarithms of the vertical shift facT , versus temperature. The Arrhenius plots are represented as tor ~ T ( To) straight lines. This result indicates that only one mechanical dispersion exists with activation energy of 79 kJ/mol. Here it should be noted that the superposition of E” required only a horizontal shift along the logarithmic frequency axis and that of El required a very small vertical shift in addition to the horizontal one. According to the concept of Takayanagi et al. [38], the temperature-frequency superposition associated with the a2 mechanism requires only a horizontal shift but the superposition associated with the 01 mechanism can be realized by horizontal and vertical shifts. The question arises whether his concept for single crystal mats is applicable to systems with higher molecular orientations. In order to propose a general concept of crystal dispersion, the results derived from rheooptical studies by Suehiro et al. [45] should be taken into

Intrinsic anisotropy in relation to molecular orientation and crystallinity

lo

1

2.0

~

1

.

1

32 1

r

0 c,

1

3.2 3.4 2 0 4 0 6 0 8 0 I / T x lo3 (K? Temperature ("C1 3 . 0

Figure 14. Arrhenius plots (a) of the horizontal shift factor aT(T,To) and (b) the logarithm of t h e vertical shift factor ~T(T, TO)versus temperature for the dry gel film with X = 400

-4

-2

0 2 4 LOG t,, (sac)

6

8

Figure 15. Master curves of the stress relaxation modulus for drawn films (A = 300) with the indicated molecular weights

account. These authors pointed out that the 122 mechanism is affected by the temperature dependence of the crystal modulus of crystallites in the horizontal direction within the spherulites. This indicates that the contribution of the 122 mechanism is significant when the c-axes are oriented perpendicular to the external applied excitation. On the contrary, the a2

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mechanism does not appear for the ultradrawn film with X = 400. Thus, it may be concluded that dispersion with an activation energy of 79 kJ/mol corresponds to the a1 mechanism, since the second order orientation factor of this specimen was almost unity, revealing the perfect orientation of crystallites. Figure 15 shows the master curves obtained from stress relaxation modulus measured [39] at various temperatures for gel films with X = 300 prepared from three kinds of polyethylene films with molecular weights of lo6,3 x lo6 , and 6 x l o 6 , which are reduced to the common reference temperature of 7OOC. Each curve is obtained by shifting horizontally and then vertically until good superposition is achieved. It is seen that the master curves exhibit a smooth decreasing trend and the profiles of the curves depend on the molecular weight. Namely the stress relaxation modulus of the drawn film with M , = lo6 exhibits a drastic decrease in magnitude with time. This phenomenon is of interest in the consideration of the relationship between molecular weight and durability. Among the three kinds of specimens prepared from their optimum concentration, the specimen with M , = 6 x l o 6 is the most advantageous as an industrial material because it exhibits the smallest decrease in stress relaxation modulus on long-term standing in the time scale > lo6 s . This is probably due to the fact that the higher the molecular weight, the greater the number of entanglement mesh per molecule. Table 6 summarizes the change in activation energies of the a1, a2 and a3 mechanisms with draw ratio, estimated from the complex dynamic modulus and stress relaxation modulus. The a3 dispersion appeared at the highest temperature range by the measurements of the stress relaxation modulus; it could not be observed with the measurements of the complex dynamic modulus, since the loss modulus above 90°C exhibited an unusual behaviour to hamper the superposition. This mechanism is unknown, but is probably due to a greater contribution to the stress relaxation modulus than in the mechanism I11 reported by Nakayasu et al. [40]. Accordingly, the a1 and a2 mechanisms will be mainly discussed in this chapter on the basis of the superposition of the complex dynamic modulus. As listed in Table 6, the values of the activation energies for both mechanisms are almost independent of the indicated molecular weight but they decrease with the draw ratio. That is, the dispersion strength of the a2 mechanism becomes smaller with increasing draw ratio and finally becomes zero at X = 400. As discussed before, it was inferred that the a2 mechanism is observed when the external excitation applied is perpendicular to the c-axis but is less obvious when the applied excitation is parallel to the c-axis. Therefore, if the a2 mechanism is ascribed to the smearing-out effect of the crystal lattice potential due to onset of rotational oscillation of polymer chains within the crystal grain as pointed out by Kawai et al. [46], the smearing-out effect must be most active, when the direction of the external stress is perpendicular to the c-axis. Thus, it may be concluded

Intrinsic anisotropy in relation to molecular orientation and crystallinity

Table 6. Change in activation energies of the a l , a2 and

a3

323

mechanisms. (A) by

complex dynamic modulus and (B) by stress relaxation modulus A ) by complex dynamic modulus Molecular weight Draw ratio

6 x

lo6

1 20 60 100 400

B) by stress relaxation modulus Molecular weight Draw ratio 1 x 106 3 x 106 6 x

lo6

Activation energy, kJ/mol a , mechanism a2 mechanism

1 50 300 1 50 300 1 50 300 400

110 100 86 80 79 a1

163 118 104 99

-

Activation energy, kJ/mol mechanism a2 mechanism a3 mechanism

90 81 -

95 80

-

100 81 78

163 145 107 163 159 106 162 170 106

-

330 343 253 334 342 231 335 331 214 216

that the a2 mechanism is related to the anisotropy of crystallites. The activation enegy of the a1 mechanism decreases with increasing draw ratio but it tends to a constant value beyond X = 100, indicating a draw ratio which reflects a limiting high orientation of the c-axes. This result indicates that the a1 mechanism must be considered in relation t o the relative orientation of polymer chains in the case of the a2 mechanism. If the a1 mechanism for a spherulitic system is assigned to interlamellar grain boundary phenomena associated with reorientation of crystal grains due t o their own preferential rotation within the orienting crystal lamellae, it may be expected that the a1 mechanism of the ultradrawn film with X = 400 is related t o the slippage of crystal grains in the direction of the c-axes, when the external excitation is parallel t o the c-axes. This is due t o the fact that rotation of the crystallites cannot occur in ultradrawn films. Furthermore, if the morphological properties of grain boundaries are correlated with the activation energy, the value of the energy associated with the shear deformation parallel t o the c-axis should differ from that associated with the deformation perpendicular to the c-axis. Thus, it may be concluded that the activation energy of the a1 mechanism decreases with increasing draw ratio. For the ultradrawn film (A = 400) with perfect orientation of the c-axes, the temperature-frequency superposition of E" does not require a vertical shift. This is in good agreement with the previous results indicating that the crystal lattice modulus along the c-axis is temperature independent below 145OC and the thermal expansion coefficient is very small.

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7. Morphological and mechanical properties of UHMWPE-UHMWPP blend gel films On the basis of some mechanical properties of ultradrawn UHMWPE and UHMWPP gel films, our attention was focussed on the ultradrawing of blend films produced by gelation/crystallization from semidilute solutions. The polyethylene/polypropylene (PE/PP) compositions chosen were 75/25, 50150, and 25/75. Because of entanglements between polyethylene and polypropylene chains in the mixed solutions, the blend gel films could be prepared despite their incompatibility. The blend gels were drawn in a poly(ethy1ene glycol) bath at 14OOC [47,48]. Figure 16 shows the difference in the appearance of the specimens with different P E / P P compositions in the scanning electron microscope. The texture of polyethylene and polypropylene blend films is apparently composed of fibrillar interconnected lamellar crystals seen edgewise. With increasing content of polypropylene, the fibrillar texture becomes extremely fine, like the smooth surface of a melt film. More important, however, is the fact that distinct domains, corresponding to the polyethylene and polypropylene components cannot be reorganized. Thus, it may be concluded that the two components become intimately mixed in the gelation/crystallization process in spite of their incompatibility in solution. These scanning electron micrographs differ from those reported by Lovinger et al. [49] for films blended in a two-roll mixer. According t o their report, very short lamellae (1 p m or less) were observed in polyethylene, while those in polypropylene were very broad and many micrometers in length. Their 50/50 blend incorporated both these features and also showed clearly a two-phase structure of the sample with islands of polyethylene of the order of 2-10 pm dispersed within the continuous matrix of polypropylene. The islands of polyethylene become smaller as the polypropylene content increases. They confirmed that the polypropylene lamellae were also smaller than those in the pure polymer, since the rapidly crystallizing polyethylene regions promote nucleation of polypropylene lamellae. On the contrary, in the present case a two-phase structure is not observed in the blend films and the fibrillar texture of the blends is less pronounced than in the individual homopolymers. This suggests that the entanglements between polyethylene and polypropylene chains hamper the formation of large lamellae of the individual components, as already indicated above. Figure 17 shows the results for the 25/75 blend film with X = 60, when the sample was fixed at a constant stress of 0.018 G P a t o avoid shrinkage of the film [47]. The specimens were annealed for 20 min at the indicated temperatures prior to photographing. As can be seen in the series of patterns, the strong equatorial reflections from the (110) and (200) planes shift t o smaller scattering angles and their intensities become weaker as the temperature increases to 16OOC. This tendency becomes considerable for the (200) plane associated with the thermal expansion of the a-axis. At 17OoC,

Intrinsic anisotropy in relation to molecular orientation and crystallinity

325

Figure 16. Scanning electron micrographs of dry gel films in undeformed state: (a) 100/0; (b) 75/25; (c) 50/50; (d) 25/75; (e) 0/100

the reflections from the (110) and (200) planes disappeared due to melting. This behaviour is quite different from that of cross-linked polyethylene, where a transformation into the hexagonal rotator phase is observed. This difference can be understood on the basis of the assumption that the ex-

326

M . Matsuo

Figure 17. Change in WAXS patterns (through view) in the horizontal direction from the 25/75 blend films ( A = 60) at the indicated temperatures during heating and cooling

tended polyethylene chains in a polypropylene matrix have higher mobility than those in an amorphous cross-linked polyethylene matrix. Here it should be noted that the polyethylene crystallites within the polyethylene matrix are obviously not free to allow a random orientation in the molten state. This is revealed by the wide angle X-ray diffraction patterns at 20 and 100°C, which show the equatorial reflections of the (110) and (200) planes, indicating that the c-axes are highly oriented with respect to the stretching direction. This type of intensity distribution is attributed to the existence of entanglements between polyethylene and polypropylene chains, hampering the random orientation of polyethylene chains in the molten state. Figure 18 shows Young’s modulus of the blend films with the indicated draw ratio measured at 20°C [48]. Young’s modulus of the specimens decreases with increasing polypropylene content except for the specimen with X = 20 for which Young’s modulus increases with increasing polypropylene content. The result at X = 20 contradicts the general concept of polymer science, since the crystal lattice modulus in the chain direction of polyethy-

Intrinsic anisotropy in relation to molecular orientation and crystallinity

PE/PP

327

CIO

Figure 18. Young's modulus of the polyethylene-polypropylene compositions at various draw ratios lene (213-229 GPa) is much higher than that of polypropylene (41 GPa). This phenomenon was found t o be due t o the decrease in orientational degree of the c-axis of polyethylene with increasing polyethylene content at X = 20 [48]. 8. Conclusion

Throughout this chapter, several intrinsic anisotropical properties of polyethylene and polypropylene were clarified by using ultradrawn films with almost perfect molecular orientation and crystallinity: (1) The crystal lattice moduli of polyethylene and polypropylene measured by X-ray diffraction technique are 215-229 and 41-43 GPa, respectively. They do not dependt on the orientational degree and crystallinity as long as the draw ratio of the test specimens is greater than 50 and 30 for polyethylene and polypropylene films, respectively. These results indicate that a state of homogeneous stress can be achieved. (2) The maximum values of Young's moduli of ultradrawn polyethylene

328

M . Matsuo

and polypropylene are 216 and 40.4 GPa, respectively. These values are close to their crystal lattice moduli, indicating that the respective ultimate values can be realized. (3) Mathematical treatment indicates that the crystal lattice modulus as measured by X-ray diffraction differs from the intrinsic crystal lattice modulus. The numerical calculation for polyethylene, however, indicates that the calculated value is almost unaffected by the molecular orientation and crystallinity except for the case of a low draw ratio (< 10) and low crystallinity (< 60%). This suggests that the crystal lattice modulus measured in ultradrawn films is quite close to the value measured by Sakurada et al. [I21 using melt films. (4) The total birefringence of polyethylene with a draw ratio of 400 is This value is higher than that of the intrinsic crystal birefringence 67 x A:, 58.5 x calculated from the three principal refractive indices of the n-paraffin (C36H74) crystal reported by Bunn and de Daubeny. This is the opposite of what is normally observed and the discrepancy is due t o the fact that the form birefringence is neglected. When birefringence is calculated using a parallel model as a function of the content of voids, the calculated result is beyond 60 x lop3. This indicates that the unusual value of the total birefringence is due to the existence of a number of voids within ultradrawn polyethylene films. (5) The crystal lattice moduli of polyethylene and polypropylene are in the range 211-222 GPa and 41 GPa, respectively. They are temperature independent up to 145 and 155OC, respectively, these values being close to the equilibrium temperatures. On the contrary, their Young's moduli decrease with temperature due to decrease in crystallinity. (6) The value of the activation energy associated with the a1 mechanism decreases as the draw ratio increases and tends t o level off at draw ratios > 100. The a1 mechanism depends on the relative molecular orientation of a test specimen. For ultradrawn polyethylene, the a1 mechanism is related t o the slippage of the crystal grains along the c-axis. The component of the a2 mechanism decreases with increasing draw ratio and becomes zero at the extremely high draw ratio of 400. This means that the a2 mechanism cannot be observed when the external excitation is parallel to the c-axis. (7) Films of a polyethylene-polypropylene blend could be prepared by gelation/crystallization from a semidilute solution in decalin by using ultrahigh molecular weight polyethylene (6 x lo6) and polypropylene (4.4 x lo6) in spite of their incompatibility in solution. The maximum drawability is affected by the morphology of the blend films which is sensitive to the composition. That is, the draw ratio increases, as the lamellar size becomes smaller. Therefore, it can be expected that an effective entanglement between polyethylene and polypropylene chains takes place, hampering the growth of large lamellae.

Intrinsic anisotropy in relation to molecular orientation and crystallinity

329

References 1. M. Matsuo, C. Sawatari, Macromolecules 19, 2036 (1986) 2. C. Sawatari, M. Matsuo, Macromolecules 19, 2653 (1986) 3. J . Smook, J. C. Torf, P. F. van Hulten, A. J. Pennings, Polymer Bull. 2, 293 (1980) 4. G. Capaccio and I. M. Ward, Polymer 15, 233 (1974) 5 . S. Kojima, S. R. Desper and R. S. Stein, J. Polym. Sci., Polym. Phys. Ed. 19, 1721 (1987) 6. P. J. Barham and A. Keller, J. Mater. Sci. 15, 2229 (1980) 7. P. Smith, P. J . Lemstra, B. Kalb, A. J. Pennings, Polym. Bull. 1,733 (1979) 8. P. Smith, P. J. Lemstra, H. C. Booij, J. Polym. Sci., Polym. Phys. Ed. 19, 877 (1981) 9. P. Smith, P. J. Lemstra, J. P. L. Pijppers, A.M. Kiel, Colloid Polym. Sci. 258, 1070 (1981) 10. M. Matsuo, R. St. J. Manley, Macromolecules 15, 985 (1982) 31. M. Matsuo, K. Inoue, N. Abumiya, Sen-i-Gakkaishi40, 275 (1984) 12. C. Sawatari, M. Matsuo, Colloid Polym. Sci. 263, 783 (1985) 13. I. Sakurada, Y. Nukushina, T. Ito, J. Polym. Sci. 57, 651 (1962) 14. I. Sakurada, T. Ito, K. Nakamae, J . Polym. Sci., P a r t C 15, 75 (1966) 15. K. Nakamae, T. Nishino, Y . Shimizu, T. Matsumoto, Polymer J. 19, 451 (1987) 16. K. Nakamae, T. Nishino, H. Ohkubo, J. Macromol. Sci., Phys. B30, l ( l 9 9 1 ) 17. G. R. Strobl, R. Eckel, J. Polym. Sci., Polym. Phys. Ed. 14, 913 (1976) 18. L. Holliday, J. W. White, Pure Appl. Chem. 26, 545 (1971) 19. A. Odajima, T. Maeda, J . Polym. Sci., P a r t C 1 5 , 55 (1966) 20. K. Tashiro, M. Kobayashi and H. Tadokoro, Macromolecules 11,914 (1978) 21. C. Sawatari, M. Matsuo, Macromolecules 19, 2726 (1986) 22. M. Matsuo, Macromolecules 23, 3261 (1990) 23. M. Matsuo, C. Sawatari, Y. Iwai, F. Ozaki, Macromolecules 23, 3266 (1990) 24. M. Matsuo, R. Sato, Y. Shimizu, Colloid Polym. Sci. 271 11 (1993) 25. M. Maeda, S. Hibi, F. Ito, S. Nomura, T. Kawaguchi, H. Kawai, J. Polym. Sci., Polym. Phys. Ed. 8, 1303 (1970) 26. S. Hibi, M. Maeda, S. Makino, S. Nomura, H. Kawai, Sen-i-Gakkaishi29, 79 (1973) 27. R. J. Roe and W. R. Krigbaum, J. Chem. Phys. 40, 2608 (1964) 28. W. R. Krigbaum, R. J. Roe, J. Chem. Phys. 41, 737 (1964) 29. C. Sawatari, M. Matsuo, Polymer 3 0 , 1603 (1989) 5 0 , 1173 (1954) 30. C. W. Bunn, R. d e Daubeny, Trans. Faraday SOC. 31. M. Matsuo, C. Sawatari, Macromolecules 21, 1653 (1988) 32. C. Sawatari, M. Matsuo, Macromolecules 22, 2968 (1989) 33. P. J. Flory, A. J . Vrij, J. Am. Chem. SOC. 85, 3548 (1963) 34. W . R. Krigbaum, I. Uematsu, J. Polym. Sci. A3, 767 (1965) 35. W. Ruland, Acta Crystallogr. 14, 1180 (1961) 36. H. G. Killian, Kolloid Z. Z. Polym. 183, 13 (1962) 37. M. Matsuo, T. Ogita, Polymer J. 23, 1149 (1991) 38. M. Matsuo, C. Sawatari, T. Ohhata, Macromolecules 21, 1317 (1988) 39. T. Ogita, R. Yamamoto, N. Suzuki, F. Ozaki and M. Matsuo, Polymer 32, 822 (1991)

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40. H. Nakayasu, H. Markovitz and D. J . Plazek, J. Trans. SOC.Rheol. 5, 261 (1961) 41. M. Takayanagi, M. Matsuo, J. Macromol. Sci., Phys. B 1 , 407 (1967) 42. T. Kajiyama, T. Okada, A. Katada, M. Takayanagi, J . Macromol. Sci., Phys. B7, 583 (1973) 43. T. Kawaguchi, T. Ito, H. Kawai, D. A. Keedy, R. S. Stein, Macromolecules 1, 126 (1968) 44. A. Tanaka, E. Chang, B. Delf, I. Kimura, R. S. Stein, J. Polym. Sci., Polym. Phys. Ed. 11, 1891 (1973) 45. S. Suehiro, T. Kyu, K. Fujita, H. Kawai, Polymer J. 1 1 , 331 (1979) 46. H. Kawai, S. Suehiro, T. Kyu, A. Shimomura, Polym. Eng. Rev. 3,109 (1983) 47. C. Sawatari, S. Shimogiri, M. Matsuo, Macromolecules 20, 1033 (1987) 48. C. Sawatari, S. Satoh, M. Matsuo, Polymer 31, 1456 (1990) 49. A. J. Lovinger, M. L. Williams, J. Polym. Sci., Polym. Phys. Ed. 18, 1703 (1980)

Oriented Polymer Material> Stoyko Fakirov Copyright 0 2002 Wiley-VCH Verlag GmbH & Co. KGaP

Chapter 11

Nature of the crystalline and amorphous phases in oriented polymers and their influence on physical properties

V. B. Gupta

1. Introduction Polymers in the form of natural fibres like cotton and wool, which are products of synthesis in a plant and an animal respectively, have been known to be used as clothing for many centuries and have provided human beings with protection and comfort in all seasons. However, it was only around 1930, that the proposal of Staudinger, made on the basis of results obtained through viscometry, that polymers were composed of long chains of covalently bonded molecules was taken with some degree of seriousness by the scientific community. Following this, the possibility of finite deformation through rotation around C-C and other single valence bonds in the main chain was immediately recognized; it was appreciated that this was responsible for one of the most essential and desirable characteristics of the fibre, viz. an extension of 5 percent or greater without breaking on application of a load and near complete recovery on release of the load, a characteristic, which is absent in non-polymeric materials. With the advent of X-ray diffraction and its application to textile fibres around the same time, it became clear that the fibres contained small but highly ordered crystalline entities embedded in an amorphous matrix. Since the molecules

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were much longer than these “micelles” or crystallites, it was concluded that individual molecules pass through a number of crystallites, alternating with segments in the amorphous or disordered regions and thus provide integrity t o the system. These features were the basis of the fringed micellar model which was also proposed around 1930. The structural basis of this model was that the favoured arrangement that molecules take on coming together is one in which the free energy is a minimum. The free energy state at high temperatures, when the mobility is too high for intermolecular bonds t o be effective, is the random state; with decrease in temperature the molecules become relatively less mobile and a local alignment of neighbouring sections of various molecules can occur to minimize free energy. As crystallization starts at many places, the same molecules get trapped in several growing crystals. Each crystal continues to grow giving rise to entangled and strained regions between crystals which prevent the large scale growth of crystals. As a natural corollary of the fringed micelle model, the roles played by the two phases were understood more clearly, viz. that cohesion, stability, strength and durability were provided by crystals while the non-crystalline regions were mainly responsible for extensibility, recovery, toughness and a path for diffusion. It is thus not surprising that all successful textile fibres, which have since been synthesized, are based on intrinsically crystallizable polymeric structures which have the potential to be oriented (see also Chapters 1 and 2). This chapter deals with anisotropic polymeric products with emphasis being placed on axially oriented semicrystalline fibres which are produced from the melt, though fibres formed from solutions and gels have also been briefly considered. It is intructive to start the discussion with the way polymeric products form under quiescent conditions. When dilute solutions of flexible chain polymers with sufficient order to crystallize are supercooled, thin lamellar crystals with folded chains are formed. At higher concentration, multilamellar structures called hedrites or axialites are formed. Change in crystallization conditions can lead to formation of rounded structures of lamellar ribbons in the form of prespherulitic structure. Melt crystallization under quiescent conditions, on the other hand, generally leads to multilamellar ribbons in the form of spherulites [l]. For crystallization to occur with the molecules in the extended state, the chains have to be stretched first. This may be achieved in different ways. If a dilute polymer solution is agitated by stirring, the elongational flow field stretches the longest molecules preferentially and around these nuclei, lamellar chain-folded crystals form during cooling; such structures are called shish-kebabs. It is noteworthy that stretched rubbers also show such structures. The second route to such anisotropic products is through the spinning of a gel and then drawing the gel-spun filament. The resultant product has a structure composed of predominantly extended molecules. Both the shish-kebab and the extended molecular fibrous structures represent departures from the conventional fringed micellar model. The third

Nature of the crystalline and amorphous phases in oriented polymers Fibril n

333

Amorphous region

X \ &

>(

a

C

Figure 1. Schematic representation of the morphologies of some oriented products: (a) shish-kebab, (b) gel spun and drawn high density polyethylene fibre, and ( c ) poly(ethy1ene terephthalate) textile fibre (Figure l(c) taken from [ a ] )

method of producing oriented products is the conventional melt or solution spinning of flexible chain polymers by extruding or spinning a melt or a solution in an elongational field and then in a subsequent operation, drawing the spun filament in the solid state. The morphologies of the resultant products in the three cases considered are shown schematically in Figures l(a), (b) and (c) [2]. It may be noted that the differences in molecular organization are considerable. They lead to very significant differences in physical properties. The commercial textile fibres and other uniaxial products have a structure close to that shown in Figure l(c), though products having the structure shown in Figure l ( b ) are also now commercially available for special applications requiring high performance. The shish-kebab structure (Figure l(a)) has too few extended molecules and very limited chain continuity along the fibre axis and is therefore of limited practical usefulness. Hence it will not be considered further. The differences in properties are mainly related to the roles played by the two phases; in products represented by Figure l(b) the crystalline phase plays a predominant role while the amorphous phase plays a more significant role in the products represented by Figure l(c) (see also Chapters 2, 5, and 12). In this chapter the roles of crystalline and amorphous phases in determining the macroscopic properties of the two phases and of the oriented product will be considered in terms of their relative content, perfection, orientation distribution, size and size distribution and the nature of coupling between the two phases. The influence of these phase characteristics

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V . B. Gupta

and also of molecular architecture on a number of important physical properties like stiffness, strength, mechanical and thermal transitions, thermal expansion, birefringence, and transport of dyes will be critically examined. Some aspects of structure formation and characterization will also be considered. The emphasis throughout will be on poly(ethy1ene terephthalate) fibres though the various structure-property correlations would apply to a wider spectrum of manufactured fibres. 2. Nature and role of molecular architecture

The term “molecular architecture” will be used here in its wider connotation, viz. to cover such important polymer characteristics as its constitutional composition, molecular conformation, the way individual macromolecular chains are bonded to each other and their aggregation or organization in the product. The role of molecular architecture in determining mechanical and thermal properties will be illustrated by taking three wellknown polymer systems, viz. (i) high density polyethylene (HDPE), an aliphatic flexible chain polymer, (ii) poly(ethy1ene terephthalate) (PET), an aliphatic-aromatic semirigid chain polymer, and (iii) poly(p-phenylene terephthalamide), a wholly aromatic rigid chain polymer, which will henceforth be called “Kevlar” . The role of molecular architecture in these three cases will now be considered with respect t o axial modulus, axial strength, thermal expansion and melting behaviour. 2.1. Axial modulus

The axial modulus of a product represents the resistance offered by it to initial deformation. When fibres with structures represented by Figure l(b) are subjected t o an axial force, the stronger covalent bonds offer high resistance to deformation. On the other hand, in the case of fibres with structures shown in Figure l(c), the amorphous regions play an important role and the weaker intermolecular forces that characterize the amorphous phase offer low resistance to deformation. The difference is very clearly evident in the case of HDPE fibres produced through the gel-spinning and melt-spinning routes respectively, as shown in Table 1, which also contains data on other fibres. The gel-spun HDPE fibre has a modulus very close to the crystal modulus whereas the melt-spun fibre has much lower modulus. These differences in structure can be traced to a number of factors. The gel contains less entanglements than the melt; consequently it allows much higher molecular weight material to be spun and then drawn to very high draw ratios to give a product with high chain continuity in the axial direction. On the other hand, due to high viscosity and high entanglement density of the melt, only relatively low molecular weight polymers can be spun and the draw ratios that can be achieved are also much lower. Under these

Nature of the crystalline and amorphous phases in oriented polymers

335

Table 1 . Axial modulus data Polymer

Measured elastic modulus, GPa (g/den) Fibre: Melt-spun and drawn

Fibre: Gel-spun and drawn or liquid crystal spun

HDPE

5 [31

288 [4]

324 [4] (3745)

PET

10 [31

30 [Sa]

110 [6] (903)

Cannot be melt-spun

125 [4]

194 [7] (1515)

Kevlar 49

Crystal

conditions significant chain folding occurs and thus there is only limited chain continuity. The Kevlar fibres contain rigid rod-like molecules and are produced by liquid crystal spinning which results in high orientation and a high degree of chain continuity, consequently the fibre is highly crystalline and its structure is close to that of ultra-high molecular weight gel-spun HDPE fibre[10] as shown in Figure l (b) , in spite of its relatively lower molecular weight. The gel-spinning of P E T is more problematic compared to the gel-spinning of HDPE because of its rigid chain structure. Therefore though the molecular weight of gel-spun P E T fibres is relatively higher than that of the corresponding melt-spun fibres, it is much less than that of gel-spun HDPE. The morphology of gel-spun P E T fibre is consequently different and its crystallinity is low; the differences in elastic modulus can be traced to these factors (see also Chapters 2, 10, and 15). It is noteworthy that in the above illustration, the polymer with the most flexible chain has the highest crystal modulus and also the highest measured fibre modulus. An elegant explanation of the physical basis for this was offered by Frank [8] as follows: “The Young’s modulus for diamond in the [110] direction is 1160 GPa. In the [110] direction diamond is composed of fully aligned zig-zag chains of carbon just like those in polyethylene, utilizing half the neighbour-to-neighbour bonds in the crystal, while the other half of the bonds are at right angles to this direction, contributing nothing to the Young’s modulus in this direction, just as the carbon-to-hydrogen bonds in fully aligned polyethylene contribute nothing to its longitudinal Young’s modulus. The cross-sectional area per chain in diamond is 0.0488 nm2, four times smaller than polyethylene, 0.182 nm2 . Hence, from this analogy, we could expect a modulus of 285 GPa for fully aligned polyethylene, well above that of steel.” The cross-sectional area per chain of the three polymers being considered are: 0.182, 0.217 and 0.205 nm2 for HDPE, PET and Kevlar respectively. Thus the small cross-sectional area of HDPE contributes to its

V . B. G u p t a

336

I

I

a

b

C

Figure 2. Skeletal structure of the molecule in the crystal of (a) polyethylene, (b) poly(ethy1ene terephthalate), and (c) Kevlar high crystal modulus in the chain direction as it ensures that a relatively large number of chains per unit cross-sectional area take the load. Also the HDPE molecules in the crystal are in the extended trans comformation, as shown in Figure 2(a), whereas the P E T molecules (Figure 2(b)) are not exactly straight; their extended length per repeat unit being 12.75A whereas the measured length is 2.2 A. The Kevlar molecules, though in the extended trans conformation (Figure 2(c)) are believed [9] to aggregate in the form of a radial system of axially pleated lamellae and consequently deviate from linearity[lO] by 5' . The recently introduced Kevlar 149 fibre is reported [ll]to have a measured modulus of 170 GPa (1343 g/den), which has been achieved by producing a more perfect highly oriented fibre without a pleated structure in which the molecules do not deviate from linearity [ 121. That chain conformation is of primary significance has been adequately demonstrated by a study of the crystal moduli of around twenty five polymer-based fibres and films [13]. For crystals with helical molecules like isotactic polypropylene with 3/1 helix, the cross-sectional area is about twice that for HDPE, the force required for 1%extension is around one fifth and the axial modulus is 30 GPa. Crystals with more loosely packed helices have still lower axial moduli: 7 GPa for 7/2 helix and 4 GPa for 4/1

Nature of the crystalline and amorphous phases in oriented polymers

337

CHAIN CROSS SECTIONAL AREA (nm-’) Figure 3. Dependence of Young’s modulus of some polymer crystals vs. the reciprocal of their molecular cross sectional area. 1. Poly(ethy1eneoxybenzoate) (a-form); 2. Poly(pivalo1actone) (a-form) (helix 2/1); 3. Poly(isobuty1eneoxide) (distorted planar zig-zag 2/1); 4. Poly(ethy1ene oxide) (helix 7/2); 5. Poly(oxymethy1ene) (helix 9/5); 6. Poly(tetrahydr0furan) (planar zig-zag); 7. Poly(ethy1ene terephthalate) (nearly planar); 8. Isotactic polystyrene (helix 3/1); 9. Isotactic polybutene-1 (helix 3/1); 10. Isotactic polypropylene (helix 3/1); l l . Poly[l,6-di(N-carbazolyl)-2,4-hexadiene] (planar zig-zag); 12. Poly(tetrafluoroethy1ene) (helix 15/7); 13. Poly(viny1idene fluoride) (slightly deflected planar zig-zag); 14. Poly(viny1 alcohol) (planar zig-zag); 15. Polyethylene (planar zig-zag); 16. Diamond (extended)

helix. In a helix, various combinations of trans and gauche conformations are possible due to which bond rotation becomes the predominant deformation mechanism on axial loading. It needs t o be emphasized that even for extended trans structures, the presence of bulky side groups can result in a large cross-sectional area.

338

V . B. Gupta

The Young’s modulus of the crystalline regions of a number of polymerbased fibres and films in the chain direction, mostly taken from [13], are plotted as a function of the reciprocal of cross-sectional area of the corresponding molecules in Figure 3. The data points appear t o form three broad groups. The polymers with a carbon backbone in the planar zig-zag or nearly zig-zag conformation are seen to fall on line A. Polymers with a carbon backbone in a helical conformation tend t o fall on line B. Polymers which, in addition t o carbon, contain oxygen in their backbone and have a helical or planar conformation, have the lowest moduli for any chosen crosssectional area and fall on line C. P E T (marked as number 7 in Figure 3) which also contains oxygen in the backbone, however, does not fall on line C; it has a relatively higher modulus apparently due t o the stiffening of the structure due t o the presence of the aromatic ring. The development of rigid-rod, aromatic heterocyclic ordered fibres with extended chain-molecules has made it possible to extend the stiffness range still further. An example of such a system is the high performance poly(pphenylene benzobisoxazole) (PBO) fibre with a density of 1.58 g/cm3, a theoretical tensile modulus of 730 GPa, measured crystal modulus (by Xray diffraction) of 477 GPa and measured fibre modulus of 318 G P a [lo]. 2.2. Axial strength

Like modulus, the axial strength of the polymer in the chain direction would also be expected t o depend predominantly on the area supported by each chain. Since the limiting value of the load is defined by chain rupture, Ohta [14] estimated the ultimate axial strength of various polymer crystals along the chain length assuming that at the breaking point, the carbon-carbon or other bonds in the backbone are ruptured. The estimated ultimate strength values of the crystal along with the highest measured values and the measured values for conventional fibres for the three cases Table 2. Ultimate axial strength data Polymer

HDPE PET Kevlar 49

Measured elastic modulus, GPa (g/den) Fibre: Melt-spun and drawn

Fibre: Gel-spun and drawn or liquid crystal spun

0.76 (9)

6.80

(80)

31.60 (372)

1.15 (9.5)

1.9 [5b] (15)

28.13 (232)

cannot be melt-spun

3.50 (27.66)

29.74 (235)

Crystal

Nature of the crystalline and amorphous phases in oriented polymers

339

considered earlier are given in Table 2. It is noteworthy that in two respects the trend shown by the strength data (Table 2) differs from that shown by the modulus data (Table 1). First the values of crystal strength in G P a are quite close for the three polymer crystals. This is obviously due to the very approximate nature of the model used in calculating the theoretical strength. Second, the highest reported measured axial strength values are much less than the corresponding crystal strength values unlike in the case of modulus where it has been possible t o achieve values which are much closer t o the theoretical maximum. The highest reported [15] strength (80 g/den) is for a gel-spun ultra-high molecular weight HDPE; it is less than one fourth the estimated theoretical maximum value for this polymer. This is primarily because in considering the axial strength of fibres, account must also be taken of the flaws that are present in the fibre such as microvoids, particulates, microscopic cracks, chain ends and other sources of stress concentration. These flaws have little effect on axial modulus, which involves very low strain, but have significant effect on axial strength which is measured at the limiting strain of the material. 2.3. Thermal expansion

Polymer crystals like those of HDPE, P E T , polyvinyl alcohol, Kevlar and Nylon 6 with extended chain structures exhibit negative thermal expansion along the chain direction and positive expansion in the transverse direction [6]. The latter reflects the weakness of the interchain interactions, while the former is postulated to arise from the strong elastic anisotropy in a polymer crystal, due to which torsional and bending motions in the chains are more highly excited than the stretching modes. This can lead t o an effective reduction in the interatomic distance along the chain axis. An alternate model [4] postulates that internal stresses are responsible for this negative thermal expansion. Since the interchain interactions are relatively weaker in the amorphous phase, the linear thermal expansivity is higher. However chain alignment results in a large drop in the expansivity along the draw direction. In semicrystalline oriented structures, the taut tie molecules between the crystals constrain the expansion of the amorphous region. In HDPE of draw ratio 18, the thermal expansivity along the draw direction is 90% of the thermal expansivity of the crystal along the chain axis [17] (see also Chapter 6). 2.4. Melting point

At the melting point, equilibrium exists between the liquid and crystal phases. The equilibrium melting point of a crystal, T: is given by AH,,, (enthalpy of melting)/AS,,, (entropy of melting). This definition would apply to crystals of infinite size (no surface effects) which contain

340

V. B. G u p t a

only equilibrium defects, if any. The crystals in the fibres are metastable and contain non-equilibrium defects. The melting point of a fibre, Tm, may, however, also be considered in terms of the thermodynamic relationship given above. The simplest approaches identify large heat of fusion with strong intermolecular forces [18]. It has been pointed out by Mandelkern [19] that attempts to correlate the melting points of polymers with intermolecular interactions utilizing the cohesive energy density of the repeating units as a measure of these interactions has been notably unsuccessful since no simple correlation is observed between Tmand AHm, as is clear from the extensive data available in the literature. It was, therefore, thought that it is more likely that AS,,, may be of prime importance in establishing the value of T, (see also Chapters 2 and 6). Dole and Wunderlich [20] emphasized that in the thermodynamic equation the heats and entropies of fusion represent the differences in enthalpy and entropy between the liquid and crystalline states; it is, therefore, necessary that both these states of matter should be considered in any interpretation of the melting point. They further suggested that the high melting point of polyamides is due to the low entropy of the liquid phase (perhaps due to the presence of hydrogen bonds) while the low melting point of aliphatic polyesters results chiefly from a low heat of fusion. Some interesting thermal studies [21] have been recently made on two liquid crystal polyesters (polymers A and B) with molecular weights in the range 10,000-39,000. Polymer B had a stiffer chain than polymer A and both were, in turn, stiffer than the P E T chain. The X-ray crystallinities of the polymers were determined and were combined with the area of the DSC melting peak to obtain the values for the heat of fusion of a unit mass of three-dimensional crystals (AHF). Results based on the data for the samples prepared by slow cooling are listed in Table 3 along with the value for the conventional PET. The table also lists values for the entropy of fusion ASF = AHF/Tm. As shown in Table 3, AHF for the liquid crystal polymers is significantly less than that for PET. Table 3. The heat and entropy of fusion for some polymers [21] Polymer PolymerA Polymer B

PET

(K)

X-ray crystallinity, %

513 563 530

17 21 Typically 50

T 7 T l

AH, (kJkg-') 40 20 135

AS, (kJkg-'K-') 0.08 0.04 0.25

This has been attributed to the imperfections within the crystal lattice causing poor cohesion of chains. The reason for the imperfections is stated to be the non-regular nature of the chain in which the probability of long runs of regular sequences is low. Since the melting points of the two rigid chain polymers are not very different to that of PET, the low enthalpy of

Nature of the crystalline and amorphous phases in oriented polymers

34 1

fusion also reflects a much lower entropy of fusion than in P E T (Table 3). The reduced ASF is a direct consequence of the extra stiffness of the chains, and the melting process is very different in the liquid crystalline and the conventional polymer systems. It is concluded from this study that chain stiffness is the main property that will determine whether the polymer melt will exist as a mesophase or as a conventional isotropic melt. If the enthalpy of fusion is not made low, the polymer will have a very high T,. Thus, t o make processable liquid crystal polymers, one must introduce irregularitues in the chain t o limit the effective bonding of the crystals. It has been shown later in Section 4.4 that the orientation of the amorphous phase can also influence the melting behaviour of PET fibre. 3. Nature and role of defects

3.1. Nature of defects It is generally believed that crystals in fibres are hard and undeformable [22]. Bueche [23] has, however, emphasized that “the crystallites cannot be as perfect as to impart great rigidity t o the polymer, however, or the material will be too brittle t o be useful. It is important, nevertheless, that the crystallites are stable to rather high temperatures, so that they will not melt out during normal handling of the fibre.” Crystalline polymers are much less perfect from the point of view of crystal regularity than simple substances [24], the possible imperfections ranging from point defects in the lattice to a truly amorphous phase. Amongst the defects within the lattice, the chain ends represent a discontinuity that can form edge dislocations whose density in polydiacetylene single crystals has been reported t o be of the order of 1013/m2 [25]. The fold surface, particularly the gross crystallinity deficiency at the fold surface, represents a significant source of imperfection. It is noteworthy that rigid chain polymers usually crystallize as extended molecules while flexible chain polymers often form folded chain crystals [26], and that the rigid chain structures like Kevlar have a relatively more imperfect lattice than the flexible chain structures like polyamides and polyolefins[27]. From the point of view of defects, polyethylene has been studied in detail. Some lattice deffects in polyethylene which are conformational in nature are: kinks, jogs and Reneker defects. In the case of kinks and jogs, a part of the chain is displaced perpendicular t o the long axis. A combined study using wide-angle and small-angle X-ray diffraction of a series of polyethylenes, mostly low density, with a wide range of chain defect concentration (0.1-7%) crystallized from the melt has been reported [29]. The concurrent unit cell expansion and long period decrease with increasing chain defect concentration lead to a picture of chain defects (branches, unsaturations) being distributed between the crystalline lamellae and the surface layer. Based on a model, which assumes inclusion of defects within the lattice by means of generation of kinks, an estimation

342

V . B. G u p t a

of the concentration of chain defects incorporated into the crystal lattice (< 1%)is attempted. The density of defects in non-crystalline regions turns out to be much larger (greater than 80%) than their concentration in the crystalline regions and supports the view of a clustering of defects. It is seen that branching has a most dramatic effect on the density of defects in the amorphous phase; the average chain separation in the amorphous regions registers an increase as increasing number of defects enter this layer. The effect of defects on fibre properties will now be briefly considered. 3.2. Effect on thermal properties

During rapid crystallization of polymers, defects such as kinks and chain ends are incorporated in the fibrillar crystals. It has been estimated [30] that in commercial P E T fibre, a chain end is likely t o be present in each volume element of 22A as a side - a very high density of chain ends. The crystals with high defect density have been shown to have low melting points while drawn fibres annealed for long durations have relatively higher melting points [31,32], the difference being of the order of 10°C (247OC to 257OC) in the case of PET. When the fibre is constrained in the DSC cell so that it cannot shrink, the melting point of the heat-set P E T fibre can go up to 264OC [33]. The crystalline density of P E T ori&nally calculated a t 1.455 g/cm3 [34] is now believed to be closer to 1.515 g/cm3 [35]; it appears to be morphology-dependent. 3.3. Effect on optical properties

The intrinsic crystalline birefringence of PET which represents the limiting birefrigence of its perfectly oriented crystalline unit, assuming it to be transversely isotropic, has been reported to be anywhere between 0.212 and 0.31 [36]. It was observed [36] that the lower values arose from studies on cold-drown fibres while the higher values were based on studies on heatset fibres. It was suggested[37] that if a perfect crystal had an intrinsic birefringence of Anco, then a crystal with perfection index Pc will have birefringence PcAnc0, assuming that an ideally perfect crystal will have Pc = 1. The measured birefringence A n of a fibre of crystallinity ,f3 and crystallite orientation f c can then be written as

+

A n = PcAnco,f3fc PamAnamo(1-

P)fam

where Pamis the perfection index of the amorphous phase, Anamo its intrinsic birefringence and fam its orientation. Since cold-drawn fibres have crystals with high defect density compared to the heat-set fibres, the dependence of measured intrinsic birefringence on sample morphology reported in the literature is not surprising. Similar considerations apply to intrinsic birefringence of the amorphous phase.

Nature of the crystalline and amorphous phases in oriented polymers 1.390

343

a

TIME (h)

Figure 4. (a) Density of samples of draw ratio around 4.2 as a function of heat treatment time upto 72 hours a t 85OC (inset shows the d a t a upto 5 min). 0 water-drawn film, A - water-drawn monofilament, 0 - LOY based yarn [39]; (b) Crystal disorder parameter of samples of draw ratio around 4.2 as a function of heat treatment temperature (symbols same as in Figure 4(a)) [39]

344

V . B. C u p t a

3.4. Effect o n crystallization It has been pointed out [38] that defects within the lattice reduce the energy for molecular motion and their presence can therefore result in faster crystallization. The crystallization kinetics of three P E T samples in the form of film, monofilament and yarn of draw ratio around 4.2 produced at different speeds have been recently studied [39]. The data relating to crystallization kinetics and crystal disorder parameter are presented in Figures 4(a) and (b), respectively. It is noteworthy, that the samples which undergo rapid crystallization, are the ones which have high crystal defect density. These samples also show very rapid reduction in defect density on heat-setting (Figure 4(b)). They also show low shrinkage at elevated temperatures as they crystallize very fast [39]. 4. Coupling effects

4.1. Nature of coupling In a fibre, a single molecule can form part of several ordered regions (crystals) as can be concluded from the following observation. The usual length of a molecular chain is, in general, far greater than the size of the crystallites. For example, considering only the extended molecule, the length of the zig-zag polyethylene molecule of molecular weight 50,000 is about 4500A [40]. A crystallite, on the other hand, may be only 100-500A long and hence one molecular chain is considered to pass through many crystalline and non-crystalline regions successively. The ordered and disordered regions are thus coupled through these threading molecules. The coupling may be in series or in parallel and the nature of coupling can have important consequences on fibre properties. The nature of coupling in a textile fibre is best understood with the help of structural models for these fibres. A common feature in all these models is the presence of intercrystalline links in fibrils, which assist in load transfer and whose number is less than the number of molecules in the crystal, as is clearly seen in Heuvel and Huisman’s model, Figure l(c). This provides a straightforward example of the predominance of series coupling. A good illustration of the predominance of parallel coupling is provided by the model of Prevorsek et al. [41] for PET fibre (not reproduced here) in which the interfibrillar extended molecules form a distinct oriented amorphous phase (the third phase); a feature on which opinions are divided. The model for as-drawn HDPE fibre proposed by Fischer et al. [42] (Figure 5(a)) shows randomized disorder; on slack heat-setting (Figure 5(b)), zone refining occurs in which defects become clustered and amorphous regions now form a distinct mobile phase. While in the as-drawn fibre, parallel coupling predominates providing considerable constraints to molecular motion, on annealing, the coupling

Nature of the crystalline and amorphous phases in oriented polymers

345

Ir;

b a

Figure 5. Schematic model for high-density polyethylene fibre: (a) as-drawn; (b) drawn and annealed [42]

a

b

Figure 6 . Schematic representation of changes in structure of oriented PET during crystallization a t different temperatures : (a) after anealing a t lower temperature; (b) after annealing a t higher temperature [43]

346

V. B. G u p t a

becomes predominantly of the series type and the motional constraints are now less. Fischer and Fakirov [43] studied the reorganization that occurs in oriented crystalline P E T fibre on annealing under different tensions and temperatures. At low temperature and high tension, the phase separation was represented by the model shown in Figure 6(a), while at higher temperatures and lower tensions, there was a very distinct phase separation (Figure 6(b)), as observed by small-angle X-ray diffraction. Ward [44] has recently considered the mechanical anisotropy at low strains in polymers and has pointed out that the various models for anisotropic polymers fall in two distinct categories, depending on whether molecular orientation or the composite nature of a crystalline polymer is the starting point. The two model hierarchies are then applicable to different polymer systems. On the basis of molecular orientation, the single-phase aggregate model [45] may be successfully applied to amorphous polymers, low-crystallinity PET, drawn low-density PE, Kevlar and carbon fibre; the single phase sonic modulus model [46] is applicable to all oriented polymers. The two-phase sonic modulus model [47] is applicable to polypropylene fibres and to a limited extent to PET fibres. If the composite model approach is used, the series-parallel unit cube model [48] can be applied to annealed drawn linear PE and PP and the lamellar orientation model [49] to oriented sheets of PE, annealed P P and PET. If tie molecules are added to composite models[50], they can be applied t.o all drawn polymers. For high modulus polyethylene, the addition of crystalline bridges to composite models [4] allows their mechanical anisotropy to be understood. The short fibre reinforced polymer composite model [51] has also been applied to high modulus polyethylene. The above considerations suggest that there can be no unique model for a fibre since the structure and morphology of the fibre are so sensitive to thermo-mechanical treatments. The models of Huisman and Heuvel[2] and of Prevorsek et al. for P E T are thus representative of very specific morphologies out of a wide spectrum of possible morphologies of P E T fibre. 4.2. Effect on mechanical properties of fibres

Extensive studies [52,53] on heat-set P E T have shown that high temperature (200'C and above) slack annealing of P E T fibres and films results in predominantly series type of coupling; the amorphous orientation factor shows a drastic reduction and the elastic modulus decreases by a very large amount. Annealing at low temperature, on the other hand, retains significant amount of parallel coupling and the samples have a relatively higher amorphous orientation and elastic modulus. The samples heat-set with their ends clamped have greater degree of parallel coupling. It is interesting to recall that in industrial processes, the fibres and fabrics are subjected to heat setting treatment under considerable constraint.

Nature of the crystalline and amorphous phases in oriented polymers

0 Series (A)

Freeannealed

-

347

Parallel (4)

Tau t-annealed

Control a5

I

I

I

I

I

100

140

180

220

260

HEAT SETTING TEMPERATURE,'C Figure 7. Coupling parameters as functions of heat-setting temperature for PET fibre [53] To illustrate the above observations, the experimental data [53] on series and parallel coupling parameters for free-annealed and taut-annealed PET fibres, estimated on the basis of the Takayanagi model [48]along with the Instron and sonic modulus data are presented in Figures 7 and 8, respectively. The correlation between modulus and coupling parameters is quite apparent. In taut-annealed samples, the parallel coupling is higher and so is the modulus. In free annealed samples, the series coupling is relatively

V . B. G u p t a

348

a

Instron

sonic

Control

h

a

6oh Control

SO 100

140

180

aao

100

HEAT SETTING TEMPER.4TURE, ("C)

140

180

220

HEAT SETTING TEMPER.4TURE. ("C)

Figure 8. Dependence of (a) Instron modulus and (b) sonic modulus of PET fibres on heat-setting temperature [53]

higher and they have low moduli. The recovery behaviour of these two sets of P E T fibres for tensile strains up to 0.15 was also investigated [54]. The taut-annealed samples showed superior recovery behaviour which was dominated by both the crystalline and amorphous phases; the recovery behaviour of the free-annealed samples, on the other hand, was controlled principally by the amorphous phase. It has recently been reported [55] that the dynamic mechanical relaxation with peaks at around 5OoC and 90°C in HDPE seem to arise due to defect diffusion in the crystallites with some influence of the amorphous matter in the interfacial region. This type of interaction between the two phases would be expected if they are in tandem or are coupled in series. Series coupling is significant in fibrillar fibrous structures, as is evident from the following two examples. In six HDPE fibre and film samples with crystallinity ranging from 50 to 85% the macroscopic moduli ranged from 0.7 t o 15 GPa [13], though the crystal modulus was constant (around 250 GPa). The resistance to initial deformation (stiffness or modulus) is thus apparently dominated by the more compliant amorphous phase and, therefore, homogeneity of stress or series coupling may be assumed to be predominant. In another study [56] though the crystal modulus of P E T remained constant at 110 GPa from 25 to 215°C the axial modulus of the filament decreased from 9 GPa at 25OC to 1 GPa at 200OC. This decrease is apparently due to a decrease in amorphous modulus; a series coupling is again indicated. Wool has a very compliant matrix reinforced by a-helices, which form the crystalline phase. It has been quite convincingly shown that the helices dominate the axial deformation of wool [57] and this is attributed to the

Nature of the crystalline and amorphous phases in oriented polymers

349

parallel coupling between the globular protein matrix and the helix; the stress is in fact transferred from the spring-like helix, as it deforms, to the matrix. Takayanagi [48] realized quite early that in fibres both series and parallel coupling are present and his unit cube model has been very successful. 4.3. Effect on deformation mechanisms

Fourier-transform infrared (FTIR) studies were made on oriented semicrystalline P E T films prepared by heat-setting at elevated temperatures as the films were axially deformed [58]. It was observed that in the sample heat-set under constraint, crystal deformation commenced at a very low strain while the deformation of the slack-set sample was dominated by chain uncoiling in the amorphous phase. Only beyond 20% strain, chain unfolding could be detected in the slack-set sample. These effects are related to the nature of coupling and are consistent with the data presented in Section 4.2. 4.4. Effect on thermal behaviour

Heat-set P E T filaments, subjected t o DSC tests for studying the melting characteristics with the sample in the unconstrained and constrained states, showed some interesting features [33]; the relevant data are summarized in Table 4. Table 4. Structural and thermal characteristics of heat-set PET filaments [33] Sample

Crystallite

Amorphous

Melting temp.('C)

orientation

Unconstrained technique

Constrained technique

Control 0.940 Taut-annealed

0.582

254.7

263.5

0.952 0.947 0.947 0.934 0.937 0.936 0.944

0.519 0.494 0.470 0.433 0.416 0.369 0.318

254.6 254.9 255.1 255.5 256.6 256.0 256.2

263.8 263.8 263.8 263.6 263.0 262.4 262.0

0.944 0.952 0.922 0.912 0.877 0.859 0.860

0.522 0.505 0.430 0.258 0.200 0.156 0.039

255.6 255.0 255.2 254.8 254.8 255.0 255.0

263.7 262.0 263.0 262.2 262.2 261.8 261.4

orientation

< p2(q >c 1000 140' 180' 2200 230' 240' 250'

< Pz(q

Free-annealed 1000 140' 180' 2200 230' 240' 250'

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V . B. Gupta

It is interesting to note that in the constrained state, when reorganization of the structure is inhibited and the orientation is expected to be retained right up to melting, the melting point is enhanced by 6" t o 9°C over the melting point observed in the inconstrained state. This enhancement was attributed to the entropic restrictions on chain conformation in the amorphous regions. The degree, perfection and size of the crystallites are slightly higher in the free-annealed samples [33,52] heat-set between 220 and 25OoC, but their melting points are lower. This could be attributed to the lower degree of parallel coupling and is also a reflection of relatively low orientation in these samples as is clear from Table 4. 5. Content and size of the phase The most dramatic effect of crystallinity is observed for isotropic polymers in the rubber-like state. For example, the Young's modulus of raw rubber (smoked sheet) increases by a factor of the order of 100 by the presence of about 24% crystallinity [59]. The rubbery modulus of amorphous unoriented PET at 90°C also increases by about 100 times on crystallization [37]. In both cases, the T, also increases on crystallization. The situation for oriented, semicrystalline fibres is more complex. For example, when commercial PET fibre is heat-set isothermally at temperatures between 100°C and 255OC for 5 min., the Tg first increases with increase in heat-setting tempearture (or with crystallinity), reaches a peak value at about 16OOC and then shows a decrease [32], as shown in Figure 9. The dye uptake or diffusion coefficient of PET, say at 13OoC,on the other hand, first decreases with increasing temperature of heat-setting and then registers an increase [60] as shown in Figure 10 [61]; the minimum in dye uptake coincides approximately with the maximum in Tg [60] as may be seen by comparison of Figures 9 and 10. These observtions have been explained as follows: Upto heat-setting temperature of 160"C, new crystals are formed by coming together of wellparallelized chains in the amorphous regions which increase the number of small crystals in the fibre. As a result, at a heat-setting temperature of 16OoC,the fibre contains a large number of small crystals so the amorphous regions are highly constrained. Heat-setting at higher temperatures can result in the formation of crystals of larger size. The fibre consequently contains a small number of large crystals and the amorphous volume per crystal increases; as a result, molecular mobility is enhanced. Figure 11 [62] shows this effect very clearly. Thus the crystallites may be considered as forming a network in an amorphous matrix. When the density of this network is the highest, the Tgshows a maximum and dye uptake a minimum because high density of crystallites makes the path of entry of the dye molecule very tortuous.

35 1

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SETTING TEMPERATURE] O C Figure 10. Effect of setting temperature on dye uptake at 100'C for 90 min for PET fibre [61] Crystal size can have a significant effect on the melting point of fibres; larger crystals showing higher melting temperatures than smaller crystals. 6. Crystal and amorphous orientation The orientation of the molecules in the crystalline and amorphous regions with respect to the fibre axis can have important consequences on mechanical, thermal and optical properties of the fibre. The measured crystal modulus of PET reported in the literature ranges between 75 GPa and 137 GPa. This wide range of values has been shown [6] to arise because the angle between the crystalline c-axis and the fibre direction can vary in

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Figure 11. Dependence of amorphous volume per crystal of P E T on heat-setting temperature [62] different samples which, if not accounted for, can lead to an underestimate of crystal modulus. When suitabe correction was applied, a constant value of 110 GPa was obtained [6] (see Chapter 13). It must be emphasized that the mechanical properties of extended chain fibres like gel-spun HDPE, Kevlar and carbon fibres are very sensitive to crystal orientation; in the standard melt-spun fibres, the mechanical properties are not equally sensitive to crystal orientation. This is because the latter are predominantly dependent upon the state of the amorphous phase, in particular its orientation. For PET fibres, the strain in the crystalline regions was shown [63] to be a factor of about ten less than the macroscopic strain for macroscopic strains up to 1.8%. On the basis of X-ray diffraction studies on conventional P E T fibres, in particular from the azimuthal intensity distribution of the amorphous halo, it has been inferred that the amorphous regions in the fibre may be divided into two fractions, viz. isotropic non-crystalline (amorphous) and oriented non-crystalline, the latter being identified with Lindner's third phase [64].It has been shown that on heat-setting, the third phase fraction decreases with increase in heat-setting temperature. An interesting

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conclusion from the latter study [65] was that the Hermans orientation factor for the amorphous phase shows good correlation with the third phase fraction provided the amorphous part is comprised of a random unoriented amorphous phase and a highly oriented amorphous phase. A low strain mechanical property like elastic modulus is determined predominantly by the taut tie molecules which bear the external stress. A high strain mechanical property like strength, on the other hand, will be expected to depend on the average concentration of tie molecules. The dominant molecular mechanism in slow crack growth and environmental stress cracking as well as in the fatigue of polyethylene has been identified [66] to be disentanglement or rupture of the tie molecules. These important properties are thus strongly dependent on the tie molecule concentration. An analytical technique based on infrared dichroic measurements has been found [66] t o be useful for characterizing the relative tie molecule concentration in polyethylene. A number of indirect methods based on mechanical models have been used to determine the taut tie molecule fraction in oriented fibres [48,50,67].The effectiveness of zone annealing as a means of obtaining superior mechanical properties in oriented P ET has been attributed [68] to higher fraction of taut tie molecules in these samples. In recent years, the infra-red technique has been extensively used [69,70] to characterize the amorphous phase since it gives more meaningful data compared to the previous indirect methods [47,71]. Mechanical relaxation measurements have also been used [72] to characterise the state of the amorphous phase. The effect of amorphous orientation on the melting point and birefringence of P E T fibres has already been discussed earlier (Table 4). The dependence of elastic modulus [47,73], ultimate strength and elongationto-break on amorphous orientation in P E T fibres has been reported [47,74] in detail (see also Chapters 4 and 8). The orientation of the crystal or lamellar planes can also have a very significant effect on the Young’s modulus of fibres. The earliest studies were made on low-density polyethylene films [49] which showed that interlamellar shear could contribute t o the compliance of the film, particularly in samples showing four-point small-angle patterns with lamellar planes inclined t o the fibre axis. The low strain mechanical anisotropy of low density polyethylene was shown to relate to the orientation of the crystalline regions [75] and it was further shown that mechanical twins could also participte in deformation [76].

7. S t r u c t u r e f o r m a t i o n The formation of structure in polymers is a complex process and only some salient features which are relevant to the main theme of this chapter will be briefly described here. When molecules come together, depending on the nature of the molecule and the thermo-mechanical history to which the prod-

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uct is subjected, they may form amorphous or semicrystalline structures which are random or with varying degrees of orientation. It has already been stated in the introductory section that for crystallization to occur with the molecules in the oriented state the chains have to be stretched first. Fibre structure forms under uniaxial stress fields in the spin line and draw zone and is stabilized by heat setting. The structural changes that occur during drawing depend largely on whether the spun fibre is amorphous or semicrystalline [3,30]. This aspect will not be considered here. The formation of structure in the three polymer systems viz. in melt-spun P E T , gel-spun HDPE and solution spun Kevlar, will now be briefly considered. Most of the P E T fibres are spun from the melt at speeds upto around 3500 m/min and are essentially amorphous. Various models have been proposed for their structure. All these models recognize the presence of an entangled molecular network. However, it has been suggested that the structure is not homogeneous as in addition to the network, crystal nuclei [77] or extended chain molecules [78] are also present; however, there is need of further work to confirm their existence. The spun fibres are converted t o flat drawn yarn by uniaxial stretching or to textured yarn by simultaneous drawing and texturing. During drawing under uniaxial stress, parts of the neighbouring molecules come together and grow into small crystallites along long, thin fibrils; the entanglements prevent alignment of molecules over larger sections. The small crystals have a number of defects like chain ends and a relatively low lattice density. The residual stresses present in the fibre can result in high shrinkage of the as-drawn fibre at elevated temperatures; heat-setting relaxes these stresses and a stable structure results. Heat-setting results in significant structural changes and there are two major possibilities. First, smaller, imperfect crystals can melt at the setting temperature (150 to 225°C) followed by recrystallization into a new form. Second, solid state transformation can occur in which molecules in the amorphous regions, which are parallel but not in register (paracrystalline) can, with the aid of thermal energy, gain enough mobility to reduce their free energy by forming crystallites. In some interesting work on P E T , Wu et al. [79] monitored the small-angle X-ray scattering paterns in situ as the films deformed and concluded that the latter process predominates. Fakirov et al. [31] arrived at the same conclusion from DSC studies. However, Groeninckx and coworkers [80] state that P E T samples heat-set at low temperatures reorganize by the partial melting of small imperfect crystallites and their subsequent recrystallization. But when samples are heat-set at relatively higher temperatures, no large-scale melting occurs; the crystal thickening which occurs without any change in long period is presumed to arise from crystal perfection at the boundary layers of the crystalline and amorphous phases. During heat-setting, the crystal defects migrate out of the crystal and crystal size and crystallinity increases with considerable enhancement in the lateral order. Significant chain folding may also occur at higher tempertures. Structural rearrangement may also occur through

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chemical processes as a result of transesterification [82]. The structure of the oriented, heat-set fibre is rather complex and there is no unanimity either on the nature and number of tie molecules between crystalline blocks or between microfibrils or on their origin. Spinning speeds greater than 3500 m/min have also been used to produce P E T fibres. In high-speed spinning, the orienting influence of the uniaxial stress field overcomes t o a significant extent the disorienting influence of the thermal relaxation process [83]. During melt-spinning, the temperature at which crystal formation can commence is considerably enhanced at higher spinning speeds. However, molecular relaxation in the amorphous regions cannot be prevented. This has been a cause of disappointment to the fibre producers who had dreams of manufacturing oriented crystalline fibres in one step. Against this backdrop, a novel discovery [85] relating to one-step standard fibre production process for flexible chain polymers is noteworthy. The studies reported are on high molecular weight HDPE which is unprocessable at 16OOC but was found to have minimum viscosity between 150 and 152OC in which range it formed a highly mobile hexagonal crystalline mesophase making it possible to use the liquid crystal spinning with this flexible system which so far has been used only with rigid systems like Kevlar, aromatic copolyesters and cellulose and perhaps which the silk worm has been using for ages to spin silk, the queen of fibres (see Chapter 1). The spinline crystallization of P E T at high speeds involves significantly large undercooling; the melt temperature may decrease from 28OOC to 180°C in 0.005 sec. The nucleation rate is consequently very high and the concentration of nuclei is very dense. The crystal size of the nucleus for crystallization to proceed is considerably reduced and approaches the unit cell dimension of PET. This occurs because in an oriented melt, the entropy change on crystallization is small. At a given supercooling the free energy change is correspondingly increased. This has been termed as nucleative collapse [86] or as spinodal defect decomposition and is also referred to as regime I11 of crystallization. The large number of small nuclei come together t o form a crystallite. The crystallization is distinctly different compared to the usual nucleation and growth process that dominates the crystallization of a melt in the stress-free state or at low stresses (see Chapter 12). There is another type of crystallization that has received considerable attention viz. the crystallization of ultra-high molecular weight HDPE to give highly crystalline, extended chain morphology (Figure l(b)) and of Kevlar [lo]. As discussed in an earlier section, these high performance fibres are produced from a gel or a solution. Mackley and Sapsford [88] have made the interesting observation that high performance HDPE fibres had been earlier produced by Ward and coworkers [4] and Wu and Black [89] also from the melt; in both cases, high-strengh, high-modulus fibres could be obtained by processing at the elevated temperatures of the order of 25OOC and then rapidly cooling the filament to give an essencially isotropic fibre. The fibre is then subsequently drawn in the temperature range 80-

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125OC and draw ratio of the order of 30 can be achieved. Mackley and Sapsford [89] offer a physical explanation as to why these processing conditions should give such a high draw ratio. They believe that the processing conditions used result in a reduction in the entanglement concentration in the precursor melt and filament. As in gel drawing, this meant that the fibre could then be drawn t o a high draw ratio. It is concluded that the polymer must be processed in a manner to provide an entanglement concentration high enough t o ensure a connected network, yet sufficiently low t o enable high draw ratios; whilst increased molecular weight provides enhanced strength. A structural model for high modulus polyethylene has been derived from entanglement concepts by Grubb [go]. Starting from the concept that the entanglement network is a controlling factor in polymer deformation, a fibrillar morphology, rather than a crystalline-bridge type of morphology [4], similar to that derived for shish-kebab material, is proposed (see Chapter 15). Kevlar, a rigid rod polymer, is produced from a solution using the dry jet-wet spinning liquid crystal technique. The spun fibre itself is highly oriented and crystalline. The highly crystalline fibre has a structure like that of gel-spun HDPE and has superior mechanical properties. It is clear from the preceding discussion that though a number of significant contributions made by various researchers over the past few years have enhanced our understanding of fibre structure] a number of issues still remain to be resolved and some of these issues have been recently highlighted [91,92]. 8. Concluding remarks

The individual contributions made by the crystalline and amorphous phases t o the physical properties of axially oriented fibrous systems and the contributions that result from possible interactions between the two phases have been considered in this chapter in terms of various characteristics of tha two phases viz. their relative content, perfection, size and size distribution, orientation distribution and the nature of coupling. The influence of these phase characteristics and also of molecular architecture on stiffness, strength, mechanical and thermal transitions, birefringence and dye uptake characteristics of the individual phases and of the fibre has also been considered. The structure-property correlations that have been attempted clearly bring out the importance and usefulness of this approach and also highlight the limitations that arise from a lack of clear understanding of the fine structure of the two phases. There is a definite need to use the existing and newer techniques t o study these characteristics in greater detail and in a more precise way as this will allow the engineering of fibres for specific end-uses.

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Acknowledgement T h e author is grateful to Mr. J . Radhakrishnan of t h e Textile Department of IIT Delhi, for considerable assistance in preparing t h e chapter.

References 1. A. E. Woodward, “Atlas of Polymer Morphology”, Hanser Publishers, Munich 1989, p. 263 2 . R. Huisman, H. M. Heuvel, J. Appl. Polym. Sci. 37, 595 (1985) 3. I. M. Ward, “Mechanical Properties of Solid Polymers”, John Wiley & Sons, U.K. 1983 4. I. M. Ward, Advances in Polymer Science 70, 1 (1985) 5. (a) M. Ito, K. Takahashi, T. Kanamoto, Polymer31, 58 (1990) (b) M. Ito, K. Takahashi, T. Kanamoto, J . Appl. Polym. Sci. 40, 1257 (1990) 6. T. Thistlewaite, R. Jakeways, I. M. Ward, Polymer 29, 61 (1988) 7. K. Tashiro, M. Kobayashi, H. Tadokoro, Macromolecules 10, 413 (1977) 8. F. C. Frank, Proc. Roy. SOC.A319, 127 (1970) 9. M. G. Dobb, D. J. Johnson, B. P. Saville, Phil. Trans. Roy. SOC., London, A 2 4 9 , 483 (1980) 10. M. Panar, P. Avakian, R. C. Blume, K. H. Gardner, T . D. Gierkc, H. H. Yang, J . Polym. Sci., Polym. Phys. Ed. 21, 1955 (1983) 11. J.E. McIntyre, “High Performance Fibres for Industrial Textiles”, in: Textile Horizon, Oct. 1988, p. 43 12. S. Kumar, “Ordered Polymeric Fibres”, in: Encyclopedia of Composites, VCH Publishers, Weinheim 1990, Vol. 4 13. I. Sakaurada, K. Kaji, J . Polym. Sci. P a r t C 3 1 , 57 (1978) 14. T . Ohta, Polym. Eng. Sci. 23, 697 (1983) 15. W. Hoogsteen, G. ten Brinke, A. J. Pennings, Polymer 28, 923 (1987) 16. C. L. Choy, W. P. Leung, J. Polym. Sci., Polym. Phys. Ed. 28, 1965 (1990) 17. C. L. Choy, “Thermal Expansivity of Oriented Polymers”, in: Developments in Oriented Polymers-I, edited by I. M. Ward, Appl. Sci. Publishers, London 1962, p. 121 18. G. Allen, J . Appl. Chem. 14, l ( 1 9 6 4 ) 19. L. Mandelkern, Crystallization of Polymers, McGraw Hill Inc., USA 1964, p. 128 20. M. Dole, B. Wunderlich, Makromol. Chem. 34, 29 (1959) 21. D. J. Blundell, Polymer23, 359 (1982) 22. L. R. G. Treloar, “Introduction to Polymer Science”, Wykeham, London 1970, p. 96 23. F. Bueche, “Physical Properties of Polymers”, Interscience, John Wiley, New York 1967, p. 321 24. A. Keller, “Polymer Crystals”, in: Reports on the Progress of Physics, Inst. of Physics and the Physical Society, U.K. 31, 623 (1968)

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25. R. J . Youiig, “Polymer Single Crystal Fibres”, in: High Technology Fibres Part B, edited by M. Lewin, K. Preston, Marcel Dekker, New York 1989, p. 126 26. I. I. Perepechko, “An Introduction to Polymer Physics”, Mir Publishers, Moscow 1981, p. 53. 27. M. Fukuda, M. Ochi, M. Miyagawa, H. Kawai, T e d . Res. J. 61, 11, 668 (1991) 28. H . G. Elias, “Macromolecules 1” 2nd Ed., Plenum, New York 1984, p. 170. 29. F. J. Balta C d e j a , J. C. Gonzalez Ortega, J. Matinez de Salazar, Polymer 19,1094 (1978) 30.‘ J. M. Schultz, “Structure Development in Polyesters”, in: Solid State Behau:or of Linear Polyesters and Polyamides, edited by J. M. Schultz, S. Fakirov, Prentice Hall Inc., N.J. 1990, p. 84. 31. S. Fakirov, E. W. Fischer, R. Hoffman, G. F. Schmidt, Polymer 18, 1121 (1977) 32. V. B. Gupta, C. Ramesh, A. K. Gupta, J. Appl. Polym. Sci. 29,3727 (1984) 33. A. K. Jain, V. B. Gupta, J . Macromol. Sci., Phys. B29,49 (1990) 34. R. P. Daubeny, C. W. Bunn, C. J. Brown, Proc. Roy. SOC.A226,531 (1954) 35. S. Fakirov, E. W. Fischer, G. F. Schmidt, Makromol. Chem. 176,2459 (1975) 36. V. B. Gupta, S. Kumar, J. Polym. Sci., Polym. Phys. Ed. 17,1307 (1979) 37. V. B. Gupta, C. Ramesh, Polym. Commun. 28, 43 (1987) 38. P. H. Geil, “Polymer Single Crystals”, Interscience, John Wiley & Sons, New York 1963, p. 325 39. V. B. Gupta, J. Radhakrishnan, S. K. Sett, Polymer 34, 3814 (1993) 40. H. Tadokoro, “Structure of Crystalline Polymers”, Willey Interscience, U.S.A. 1979 41. D. C. Prevorsek, Y. D. Kwon, R. K. Sharma, J. Mater. Sci. 29,3115 (1977) 42. E. W. Fischer, H. Goddar, G. F. Schmidt, Makromol. Chem. 119,170 (1968) 43. E. W. Fischer, S. Fakirov, J. Mater. Sci. 11, 1041 (1976) 44. I. M. Ward, “Mechanical Anisotropy at Low Strains”, in: Developments in Oriented Polymers-I, edited by I. M. Ward, Applied Science Publishers, London 1982, p. 172 45. I. M. Ward, Proc. Phys. SOC.80,1176 (1962) 46. W. H. Charch, W. W. Moseley, Test. Res. J . 29,525 (1959) 47. R. J. Samuels, “Structured Polymer Properties”, John Wiley, New York 1974 48. M. Takayanagi, J. Imada, T . J. Kajiyama, J. Polym. Sci. Part C 15, 263 (1966) 49. V. B. Gupta, I. M. Ward, J. Macromol. Sci. Phys. B2, 89 (1969) 50. A. Peterlin, in: Ultra High Modulus Polymers, edited by A. Ciferri, I. M. Ward, Appl. Sci. Publishers, London 1979, Ch. 10. 51. P. J. Barham, R. G. C. Arridge, J . Polym. Sci., Polym. Phys. Ed. 15,1177 (1977) 52. V. B. Gupta, S. Kumar, J. Appl. Polym. Sci. 26,1885 (1981) 53. V. B. Gupta, C. Ramesh, A. K. Gupta, J . Appl. Polym. Sci. 29,3115 (1984) 54. V. B. Gupta, C. Ramesh, A. K. Gupta, J. Appl. Polym. Sci. 29,4219 (1984) 55. N. Alberpola, J. Y. Cavaille, J. J. Perez, J. Polym. Sci., Polym. Phys. Ed. 28,569 (1990) 56. K. Nakame, T. Nishino, F. Yokoyama, T. J. Matsumoto, J. Macromol. Sci., Phys. B27,407 (1988)

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57. D. Rama Rao, V. B. Gupta, Text. Res. J. 61,609 (1991) 58. V. B. Gupta, C. Ramesh, H. W . Siesler, J. Polym. Sci., Polym. Phys. Ed. 23,405 (1985) 59. L. R. G. Treloar, “The Physics of Rubber Elasticity”, Oxford Univ. Press U.K. 1958, p. 272 60. V. B. Gupta, A. K. Gupta, V. V. P. Rajan, N. Kasturia, Ted. Res. J. 54, 54 (1984) Dyers t3 Colourists70, 16 (1954) 61. D. N. Marvin, J. SOC. 62. J. H. Dumbleton, T. Murayama, Kolloid Z.Z. Polym. 220,41 (1964) 63. W. J. Dulmage, L. E. Contois, J. Polym. Sci. 28,273 (1958) 64. W. L. Lindner, Polymer 14,9 (1973) 65. V. B. Gupta, S. Kumar, Polymer 19,953 (1978) 66. A. Lustiger, N. Ishikawa, J. Polym. Sci., Polym. Phys. Ed. 29,1047 (1991) 67. A. Peterlin, J. Polym. Sci., A-2, 7,1151 (1969) 68. M. Evstatiev, S. Fakirov, A. Apostolov, H. Hristov, J. M. Schultz, Polym. Eng. Sci. 32,964 (1992) 69. S. R. Padibjo, I. M. Ward, Polymer 24, 1103 (1983) 70. A. K. Jain, V. B. Gupta, J. Appl. Polym. Sci. 41,2931 (1990) 71. J. H. Dumbleton, J. Polym. Sci., A-2, 6,795 (1968) 72. G. Valk, G. Jellinek, U. Schroder, T e d Res. J. 50,46 (1980) 73. V. B. Gupta, S. Kumar, J. Appl. Polym. Sci. 26,1877 (1981) 74. V. B. Gupta, S. Kumar, J. Appl. Polym. Sci. 26,1897 (1981) 75. V.B. Gupta, A. Keller, I. M. Ward, J. Macromol. Sci. B2, 138 (1968) 76. F. C. Frank, V. B. Gupta, I. M. Ward, Phil. Mag. 21,1127 (1979) 77. (a) P. Desai, A. S. Abhiraman, J. Polym. Sci., Polym. Phys. Ed. 23, 653 (1985) (b) M . Napolitano, A. Moet, J . Appl. Polym. Sci. 34,1285 (1987) 78. H. A. Hristov, J. M. Schultz, J. Polym. Sci., Polym. Phys. Ed. 28, 1647 (1990) 79. W . Wu, C. Riekel, H. G. Zachmann, Polym. Commun. 25,76 (1984) 80. G. Groeninckx, H. Reynaers, H. Berghmans, G. Smets, J. Polym. Sci., Polym. Phys. Ed. 18,1311 (1980) 81. G . Groeninckx, H. Reynaers, J. Polym. Sci., Polym. Phys. Ed. 18, 1325 (1980) 82. S. Fakirov, “Solid-state Reactions in Linear Polycondensates”, in: Solid State Behavior of Linear Polyesters a n d Polyamides, edited by J. M. Schultz, S. Fakirov, Prentice Hall Inc., N.J. 1990 83. P. Desai, A . S. Abhiraman, J. Polym. Sci., Polym. Phys. Ed. 26,1657 (1988) 84. P. N. Peszkin, J. M. Schultz, J. Polym. Sci., Polym. Phys. Ed. 24, 2591 (1986) 85. A. J. Waddon, A. Keller, J. Polym. Sci., Polym. Phys. Ed. 28, 1063 (1990) 86. H. H. George, “Spinline Crystallization of Poly(ethy1ene terephthalate)”, in: High-speed Fibre Spinning: Sctence and Engineering Aspects, edited by A. Ziabicki and H. Kawai, John Wiley, New York 1985, p. 271 87. E. W. Fischer, M. Stamm, Q. Fan, R. Zietz, Proc. Sixth Annual P.P.S. Meeting, Nice, France, April 17-20, 1990

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88. M. R. Mackley, G. S. Sapsford, “Techniques of Preparing High Strength, High Stifiness Polyethylene Fibres b y Solution Processes”, in: Developments in Oriented Polymers-I, edited by I. M. Ward, Applied Science Publishers, London 1982, p. 201 89. W. Wu, W. B. Black, Polym. Eng. Sci. 19,1163 (1979) 90. D.T . Grubb, J . Polym. Sci.,Polym. Phys. Ed. 21, 165 (1983) 91. J. W. S. Hearle, Ind. J . Fibre & Teztile Res. 16,1 (1991) 92. V. B. Gupta, “Fibre Structure: A Molecular Jigsaw Puzzle”, in: Polyester: Fifty Years of Achievement, Textile Institute, Manchester 1993

Oriented Polymer Material> Stoyko Fakirov Copyright 0 2002 Wiley-VCH Verlag GmbH & Co. KGaP

Chapter 12

Structure development in highly oriented PET

J. M. Schultz

1. Background Poly(ethy1ene terephthalate) (PET) is used commercially over a very wide product range: textile fibres, packaging films, moldings, and as a composite matrix material. Between and within these product areas the properties of the material can be varied over a wide range. For instance, the modulus of undrawn films [l] or fibres [2] is approximately 2.5 GPa, but this stiffness can be increased an order of magnitude, to some 20 GPa by drawing and zone-annealing [3,4]. These stiffer products are also stable against property degradation upon warming above the glass transition. Similar changes in stiffness and other behaviour can be effected by other thermomechanical routes. The variations in properties reflect changes in the physical microstructure of the material. It is intuitive that stiffness in the direction of the major normal stress (usually the extrusion, spinning or drawing direction) must reflect a high degree of alignment of the polymer chain axis with that direction. For such an oriented polymer system to be commercially viable, these chains must not re-coil upon modest heating, thereby losing stiffness and altering the dimensions of the product. The detailed microstructure must somehow inhibit such relaxation. In some instances, chains reside partially in crystalline and partially in noncrystalline regions. For such cases, the noncrystalline regions are fixed by their connection to the thermally invariable crystals. Important in such semicrystalline materials are the size, perfection and

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shape of the crystallites, and their degree of alignment with the loading axis. Also very important is the detailed nature of how the noncrystalline strands connect the crystallites. For instance, is the connectivity in parallel or in series with respect to the loading axis? And what fraction of the chains emerging from a crystallite enter the noncrystalline region and what fraction fold back into the crystallite? And what is the local state of extension of the noncrystalline chains? If one knows the microstuctural detail of a system, the properties of that system are implicit. Conversely, the structure of a material system can be inferred, but not unambiguosly, from its properties. An approach to correlating processing, structure and properties of P E T and nylon fibres through such considerations has recently been reviewed by Prevorsek and Oswald [ 5 ] . In such work, a combination of macroscopic property measurements is correlated to model systems and a best fit found. Such correlations, when carefully done, provide reasonable models for the structure-property correlation, but leave gaps in understanding how the specific microstructures develop and how processing variations may alter that structure. The work reviewed in this chapter relates to attempts to define structure development in a narrow range of cases. The great problem in following structure development in highly oriented systems is that the process goes very fast. Figure 1 is a good example. This figure shows the half-times of crystalization of P E T from the melt [6]

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and from as-spun fibres [7,8], which are oriented but noncrystalline, as a function of temperature. The fibre heat-treatments were performed under different axial stresses, as indicated in the figure. The half-times of the fibre transformation are normally tens, but sometimes hundreds, of milliseconds, some 4 to 5 orders of magnitude faster than for the unoriented material! Three approaches have been taken in the attempt to characterize structure development in these rapidly transforming systems. In post mortem studies, the process is taken t o completion and the polymer product then studied in great detail at room temperature. By varying the processing conditions and observing how the final microstructure changes, one can infer how the structure may have developed. In situ studies are carried out during processing. For instance, one might install an X-ray diffraction camera on a polymer spinline. Although the transformation of a volume element is very rapid, each given degree of transformation of each volume element occurs at a defined position along the spinline. Thus X-ray diffraction patterns taken from different positions along the spinline record different stages of transformation. Such investigations can be very fruitful, but they are also very expensive and are normally limited to one type of measurement. The third method, interrupted heat-treatment, is described in Section 1.3. 1.1. Post mortem studies The most direct post mortem characterization is that of electron microscopy, particularly transmission electron microscopy (TEM) (see Chapter 5). Both replica and thin film TEM studies of P E T fibres have been reported. Surface replicas of external surfaces of commercial fibres have not proven fruitful. Such fibres have a skin-core microstructure. If the skin is peeled back and a surface replica of the underlying material taken, a fibrous morphology is always observed [9-12]. Murray et al. have microtomed and stained thin axial sections of P E T fibres. Their TEM micrographs show a microfibrillar structure, the diameters of the microfibrils being in the 3-5 nm range [13]. Microtomed and stained transverse sections have been examined by Haggege [14]. These likewise show a fine structure in the n m range, consistent with a microfibrillar microstructure. Wide-angle X-ray scattering (WAXS) has likewise proved useful (see Chapter 3). Upon heat-treatment to crystallize oriented but as yet noncrystalline bristles, the azimuthal position (relative to the fibre axis) of the several hkO arcs show dramatic differences, depending on the initial orientation of the material [15,16].Heat-treated P E T bristles of low orientation exhibit a broad 100 arc centered on the meridian (parallel to the fibre axis). With higher and higher initial orientation, the 100 arc migrates toward the equator. Biangardi and Zachmann have studied this behaviour in detail [15,17-191, using a stereographic analysis suggested by Nadkarni and Schultz [no]. Biangardi and Zachmann conclude that the microstructure is as depicted in Figure 2. Here, crystals grow outward, along their b-axes,

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Figure 2. Model of the growth of lamellar crystals on a linear core: ( u ) low linear nucleation density, ( b ) high linear nucleation density

from linear nuclei or from microfibrils. The crystals initially have their chains, or c-axes (the thin direction of the lamelliform crystals), parallel to the fibre axis. But the crystals twist as they grow laterally. If the density of linear nuclei increases with orientation, then a very high orientation should have line nuclei so close together that crystallites from neighboring lines impinge before twisting significantly. In this case, one should observe all hkO reflections on the equator. For lower degrees of orientation, the line nuclei would be farther apart and there would be some lamellar twisting, resulting in hkO arcs about the equator. For very low orientations, the aaxis would be randomly oriented, since the crystals would be fully twisted. From this model, one would identify the fibrils observed in peel-back surface replicas as the sheaths of coherently growing lamellar crystals about the linear nuclei. Small-angle X-ray scattering (SAXS) has proved useful in suggesting crystallite sizes and arrangements (see Chapter 3). Figure 3 shows representative four-lobe and two-lobe SAXS patterns (intensity contour plot). Here the arrow indicates the fibre axis. The four-lobe pattern in Figure 3(a) consists of four streaks, indicated with shading in the figure. The streaks are elongated normal to the fibre axis. Under some conditions, the streaks merge along their long axes t o form a two-streak pattern, as shown in Figure 3(b). These types of patterns have been compared to model structures [21-231. The most recent and exhaustive of these studies, by Harburn et al. [23], concludes that the observed SAXS paterns are consistent only with systems comprised of columns of scatterers. A depiction of such a microstructure is given in Figure 4. Here the dark regions are crystallites and the light regions are noncrystalline matter. The columns may impinge, as in Figure 4(a), or not, as in Figure 4(b). The inferred column diameter is under 10 nm. If the crystallites are not laterally correlated, a two-streak pattern occurs. Lateral correlation results in the four-streak patterns. Analyses of the integrated intensities of SAXS patterns have been useful.

Structure development in highly oriented PET

Figure 3. Small-angle X-ray scattering patterns from PET fibres: ( a ) four-lobe pattern from fibre held for 200 ms a t 200 'C and 5.9 MPa; ( b ) two-lobe pattern from fibre held for 10 ms a t 220 OC and 6.4 MPa. Both fibres had an initial birefringence of 0.042

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Figure 4 . Models of segmented fibrillar crystallization: ( u ) with no noncrystalline layers separating microfibrils; ( b ) with microfibrillar separation

It has been observed that the absolute integrated intensity increases with the temperature of the crystallization transformation [12,24-291, indicating that the level of crystallization increases with transformation temperature. A very interesting result is that the absolute value, Q, of the integrated intensity is significantly lower than what is predicted from a simple axially alternating two-phase model of the type shown in Figure 4(a). T h e low

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value of Q may be attributed to axially intervening amorphous regions, as in Figure 4(b) [29] or to a large level of imperfection in the crystals [28,30]. In this latter model, it is envisioned that the defects are incorporated in broad interphase regions which axially separate the crystal and amorphous domains. The latter explanation is likely more correct, since the microstructure of Figure 4(b) also infers a transverse SAXS streak through the origin, and is often observed, while the Qo mismatch occurs even when no streak through the origin is observed. A rather remarkable result was obtained in the 70’s from N M R studies of PET. It had been noted earlier by Farrow and Ward [31] that the degree of crystallinity measured by N M R is consistently higher than that measured by WAXS. In general, N M R scans show a broad component, due to immobile chain segments, and a narrow component, due to more mobile segments. In computing the degree of crystallinity, it had been assumed that the broad and narrow components characterized the amorphous and crystalline portions, respectively. Eichhoff and Zachmann, however, showed that swelling of the material transfers a portion of the broad N M R signal to the narrow component, while producing no change in the intensity of the crystalline WAXS scattering [32]. Thus a portion of the broad N M R portion must reflect an immobile amorphous fraction. Biangardi and Zachmann later used very careful orientation studies of oriented P ET, in combination with N M R , SAXS and WAXS [15,19,33-351. They showed that the rigid noncrystalline portion consists of straight and highly oriented segments. It was separately noted that the amorphous halo in oriented P E T specimens appears to be a superposition of a random component and a highly oriented component [36]. On the basis of results such as these, it was suggested that a third phase, or “oriented mesophase” exists [37]. The fraction of this mesophase decreases with the temperature of heat-treatment of oriented material [37,38]. In summary, post mortem examinations indicate a fibrillar microstructure, in which the fibrils are segmented axially (crystal-amorphous alternation). The crystallites may be lamelliform and capable of twisting during growth. The breadth of the fibrils is in the 10 nm range and depends on the processing conditions. Additionally, an oriented mesophase is created in the initial processing, but gradually disappears as heat-treatment progresses. 1.2. I n situ studies: spinline observations

It is observed that crystallization in a spinline can occur, but only for threadline velocities above some threshold (ca. 4,000 m/min for PET). Commercial high-speed spinning makes use of this spinline crystallization. In an effort to understand the triggering mechanism(s) for spinline crystallization, on-line measurements have been performed. Ishizuka and Katayama have made WAXS measurements directly on a P E T spinline [39]. Other in situ spinline studies include measurements of fibre diameter

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[40-42], temperature [31,43] and birefringence [41]. Of special importance to us is the suggestion, based on on-line diameter changes and temperatures, that a critical level of deformation is needed t o initiate crystallization in the spinline. The corresponding stress level is 9.5 x 108dyne/cm2. It is by no means certain, however, that it is the stress, as opposed to chain extension, that is critical. Molecular orientation within a volume element increases as the element moves downstream from the spinneret. During that time, the volume element loses heat and becomes thinner (increasing the stress level). Bragato and Gianotti [41] show that the significant molecular orientation sets in in a rather narrow band of temperature and terminates near the glass transition. Only in this narrow range is the viscosity sufficiently high to oppose the re-coiling (relaxation) of the polymer chains, but not so low as to defeat the orientation process. The temperature range over which this balance is created depends on the local spinline stress and the velocity of the volume element through the potential orientation zone. The balance must be very delicate. 1.3. M odel s of structure development

It is clear that the very high transformation rate and the fibrillar morphology in PET fibres must relate to a large chain extension and the consequent large driving force. Two important considerations relating to the high transformation rate are the crystal nucleation rate and the removal of energy and uncrystallizable matter from the growing interface (see Chapter 2). The rate of nucleation of crystallites is an important consideration. Nucleation relates both to the creation of the primary crystals and can also be a mechanism in the propagation of the transformation front of such existing crystals. Ziabicki and Jarecki [44] have considered the sensitivity of crystal nucleation to chain orientation and have shown that profuse nucleation should occur under conditions of high-speed spinning. George [45] has likewise treated the dependence of the crystal nucleation rate on orientation. He shows that for the conditions encountered in high-speed spinning there is no activation barrier to nucleation; nucleation is instantaneous. Thus it is believed that under conditions of sufficiently high chain orientation crystals will form with little or no energetic hindrance. A second set of considerations relates to the effects of the rate a t which heat and noncrystallizing molecules can be removed from the growth interface. The heat of fusion is always released a t the, interface between transformed and untransformed material. If this heat cannot be removed quickly enough, one could envision the temperature rising ultimately to the melting point, halting the growth process. More realistically, the system alters its growth conditions so as to improve the removal of heat. This situation will be discussed below. Likewise, molecules which are not incorporated into the growing crystals must be removed from the growth front. Again, if these cannot be removed sufficiently rapidly, one can envision the accre-

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tion of such molecules to a level at which there are insufficient crystallizable molecules available at the growth front. Again the system will adjust its conditions somehow t o facilitate transformation. Such heat or solute removal problems can arise in any situation in which the transformation front moves with a very high velocity. Such high velocities occur during high-speed spinning (greater than some 4,000 m/min), in which the front moves with the speed of the spinline, and during the post-spinning heat-treatment of fibres spun at traditional speeds (less than some 4,000 m/min). The system can alter itself in several ways to accommodate the need t o dissipate heat or noncrystallizable molecules more rapidly. The possibilities are illustrated in Figure 5. In (a) is sketched a plane crystallization front propagating from left t o right at velocity V1. As indicated, normally uncrystallizable molecules and the liberated heat of fusion diffuse away from the interface with difusion coefficients D, and Dt, respectively. As indicated in (b), incorporation of a portion of the normally uncrystallizable material into the growing crystal can alleviate some of the concentration buildup of such matter near the interface (incorporation of a large defect content also raises the enthalpy of the crystal and thereby decreases the effective heat

C

d

Figure 5. Processes a t the transformation front. In ( a ) , the front moves with velocity V1, slow enough that both poorly crystallizable chains and the heat of transformation can diffuse away. When the front velocity is more rapid and poorly crystallizable material cannot diffuse away rapidly enough, one or more of the following actions can take place: ( b ) incorporation of defective chains in the crystal; (c) breakdown of the interface into sharp asperities to increase t h e dimensionality of diffusion, or ( d ) change in the local supercooling a t the interface, thereby lowering the velocity of the front

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of fusion). As indicated in ( c ) , sharp asperities in the growing front can increase the dimensionality of the heat and molecular flows from the interface and can thereby markedly increase the dissipation rate locally. Lastly, as sketched in (d), the interface propagation velocity can change. Since interface velocity increases with undercooling (the difference in temperature in the melt a t the interface between the equilibrium melting point and the actual temperature of the transformation), the velocity is controlled by the magnitude of the temperature in the melt at the interface. The processes outlined above are interrelated and an optimization principle of some sort acts to produce the interface temperature, interface morphology and crystal defect level a t an operating point consistent with external constraints. While the above is an acknowledged picture of possibilities, there is as yet no agreement among investigators as t o what optimization principle is used by nature in enforcing crystallization when heat and/or solute removal are important. What is qualitatively to be expected, however, is that the transformation product produced a t high extensions and high growth-front velocities should be to some extent imperfect and to some extent needlelike. More quantitative predictions of the morphology are found in our previous work [46-481 and will be reviewed in Section 6.

2. Interrupted transformation experiments Interrupted transformation experiments provide a means for creating a set of specimens which have been heat-treated isothermally for various times. Measurements of any type can then be made on these specimens. Such measurements enable the preparation of property isotherms. An example would be to measure the density of specimens prepared for various times a t some temperature T . From these data one determines the development of density with treatment time a t temperature T . In work reported from our laboratory, as-spun P E T fibres (oriented but not crystallized) are quickly raised in temperature from room temperature t o a temperature of interest, held there for a time t l , and then rapidly downquenched to a temperature well below T,. This can be repeated for other times t 2 , t 3 , t 4 , and so on. This procedure is shown schematically in Figure 6. A schematic drawing of the apparatus used [49] is shown in Figure 7. A fibre is fed at controlled velocity and tension through an annealing device and from there directly through a quenching device. The annealing device used here is a 4 mm deep silicone oil bath. The duration of time in the bath is controlled by the velocity of the fibre. The quenching device is a trichlorotrifluoroethane bath maintained a t approximately -40 "C. T h e nominal heat-treatment time interval can be as low as 5 ms. With the hot-bath maintained a t a constant temperature, fibres fed through the system a t various speeds create an isothermally treated speci-

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TIME Figure 6. T h e concept of an interrupted transformation experiment. Specimens are brought from room temperature to a given treatment temperature and held there for various times t l , t 2 , t 3 , t 4 before quenching t o below Tg

Figure 7. Schematic of heat-treatment apparatus [49]. Fibre is pulled from a spool, through a load-control device, an annealing device, a quenching device, and onto a take-up system

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men set available for characterization at room temperature. Specimens described in the next two sections have been prepared by such interrupted treatments.

3. Transmission electron microscopy Microstructural entities in semicrystalline polymer systems most usually have dimensions of some 10 nm. In principle, the most direct means of observing moieties of this size is transmission electron microscopy (TEM). However, two problems are inherent in TEM for polymers: difficulty in

Figure 8. T E M micrograph [50] of fibre spun a t 4,000 m/min and subsequently heat-treated a t 140°C for 10 ms. Double-headed arrow indicates the fibre axis. A , B, C point t o needlelike crystals

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Figure 9. TEM micrographs [50] of fibre spun at 4,000 m/min and subsequently heat-treated at 14OoC for ( u ) 20 ms and ( b ) 100 ms creating thin, electron-transmissible films and beam damage in the electron beam. It is difficult to thin polymeric materials chemically; so microtomy is the most reliable method for sectioning bulk polymers, even though polymeric specimens are easily deformed or otherwise damaged in this operation. Beam damage considerations require methods for minimizing the electron dose and dose rate. One must usually work rapidly, under conditions of very low illumination. Finally, the intrinsic contrast between crystalline and noncrystalline regions is best obtained using the phase contrast associated with optimal defocusing. This procedure requires taking a through-focus series of photographs of the same area, all before significant

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Figure 10. TEM micrographs [50] of fibre spun at 4,000 m/min and subsequently heat-treated at 160 'C for (u) 10 ms and ( b ) 20 ms beam damage occurs. Because of these problems, TEM of bulk polymer sections is rarely reported; the time, skill and effort to produce one useful micrograph can be very large. The effort being so large, we have concentrated on only two isotherms, sectioning and observing crystals a t three heat-treatment times for two different temperatures and one threadline tension. These results [50] are described a t this point because they set the stage for more complete experimentation using other methods. The specimens used here were spun a t 4,000 m/min into room temper-

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ature air. As-spun fibres exhibit a density greater than that of amorphous P E T at room temperature, but show no crystallinity by X-ray diffraction. Defocus TEM reveals no microstructure in the fibre interior, but shows the presence of a crystalline skin. It is what develops in the initially noncrystalline core that is of interest here. Figure 8 is from a fibre heat-treated for 10 ms at 140OC. The doubleheaded arrow indicates the fibre axis. The crystallization is fibrillar; the crystallites are thin dark streaks parallel to the fibre axis. Arrows at A, B and C point to such crystallites. The diameter of the fibrils is not more than 10 nm. Consequently these entities are seen only in very thin areas, since their images must overlap in thicker sections. After somewhat longer treatment, the situation changes remarkably. The fibrillar moieties can no longer be seen. The crystallites now extend normal to the fibre axis. This microstructure is seen developing at 20 ms at 140°C and is fully developed after 100 ms, as shown in Figure 9. The electron diffraction pattern below the micrograph shows that the chains within the crystallites are still oriented along the fibre axis (the double-headed arrow). The fibrillar microstructure has transformed to a row structure. The row structure is a long stack of thin lamellae in which the polymer chains and the stacking direction are both parallel to the fibre axis. At 16OOC the fibril to lamella transition is accelerated, narrow lamellae being observable after only 10 ms and fully developed after 20 ms as seen in Figure 10. As we shall see, the correlation of TEM results with wide-angle X-ray scattering provides a very instructive insight into the processes at hand. 4. Property isotherms

4.1. Structure Over the past decade three studies of P E T fibre property isotherms from interrupted heat-treatments have been reported from our laboratory, with increasing stress levels and threadline speeds and decreasing treatment time intervals over that period [7,49,51]. The development of structure in highly oriented PET reflects the competing mechanisms of relaxation and crystallization. Relaxation can be thought of as a re-coiling of extended chains. This process acts to lower the orientation of the system. Re-coiling should then result in shrinkage of a fibre. Crystallization, on the other hand, increases the local orientation of the system and, in systems of high prior orientation, can lock in and even improve this orientation. The result of crystallization then is to stabilize the fibre against shrinkage, and perhaps to produce some level of length increase. Which of the competing processes dominates is defined by the temperature and stress under which the transformation takes place. Low stress levels and low temperatures favor the kinetics of relaxation; high stresses and high temperatures favor crystallization kinetics.

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Structure development in highly oriented PET

Under some conditions, relaxation and crystallization are balanced. This is seen in Figure 11, which shows how both the relative fibre length (“shrinkage”) and optical birefringence change with treatment time at several temperatures under 2.1 MPa threadline stress [7]. Consider the curves for 120OC. At this temperature, the fibre initially shrinks, but shows later increases in length. WAXS results show that the elongation parallels the development of crystallinity. Thus chain re-coiling produces the initial shrinkage, but a slower crystallization process becomes dominant after some 150 ms. At 100°C crystallization never becomes effective. As the temperature is increased to 160 and 2OO0C,the crossover time becomes shorter and I00

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Figure 11. Isothermal ( a ) shrinkage and ( b ) birefringence curves [7] for P E T fibres heat-treated a t 2.1 MPa

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shorter. This behaviour is mirrored in the birefringence results. Shrinkage causes an initial decrease in the magnitude of the birefringence, indicating a decrease in chain orientation. At later times, the birefringence increases, due to a realignment of chains, induced by crystallization. At higher stresses, crystallization dominates over relaxation from the beginning. Figure 12 shows the change in fibre length at several temperatures under 10 MPa stress [49]. Here the time scale is considerably expanded, relative to Figure 11. In this case, the “shrinkage” is always negative; i. e., the fibre lengthens. For heat-treatment under constant length (no controlled applied stress) , relaxation dominates the transformation for very long times. This can be seen in the orientation of the crystallites, as measured by the azimuthal breadth of WAXS Bragg peaks along their Debye rings. This behaviour is shown in Figure 13 [48]. At very long times, the orientation improves, probably through an axial tension associated with the restraints of adjacent crystallites on the re-coiling of interlamellar tie chains. SAXS scans exhibit patterns of the types shows in Figure 3. Small angle maxima arise and grow with time. These maxima are elongated transverse to the fibre axis. The entities producing the maxima are thus narrow in the transverse direction. Intensity traces in the transverse direction, along channels such as indicated by the dashed line in Figure 3(b), can be obtained. Guinier analyses of such traces assign a value of approximately 3.0 nm to

Structure development in highly oriented PET

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Figure 13. Development of the azimuthal breadth of (110) WAXS peaks with time at four temperatures of isothermal heat-treatment [48]

the diameter of the structural entities [7]. This value does not vary with time of heat-treatment. hkO WAXS Bragg peaks are found to become increasingly narrow with time of heat-treatment [7]. The breadth of hkO peaks is determined by the transverse diameter of the diffracting entities (crystallites) and by the internal perfection of those entities. Both decreasing perfection and decreasing particle size act t o broaden Bragg peaks. In the present case, the SAXS results show that the crystallite diameter does not change. Thus the WAXS results show that the crystallites become increasingly perfect as the transformation progresses. The picture which has emerged to this point, from TEM observation and property measurements is as follows: (1) In the initial stages of transformation, rather imperfect] rodlike crystals with a diameter of some 3 0 A form. Either initially or soon after formation, the rods become periodically segmented, with axially alternating regions of high and low density (crystallike and noncrystalline regions)] as indicated by the appearance of an axial small-angle X-ray maximum. (2) Very soon after formation] the high density regions aggregate laterally, t o form lamellalike entities. The persistence of the original rodlike nature is evident in the unvarying transverse scattering shape of the SAXS peaks. Presumably the new lamelliform regions have not welded the seams between crystallites. Indeed, such a process would be very difficult, entailing a change of orientation of each crystallite as it adds to a growing lamella

[521.

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(3) The perfection of the crystalline regions improves continuously with time of heat-treatment. This picture is in qualitative agreement with what is expected because of difficulties in dissipation of the heat of fusion at the advancing growth front. The generic prediction was for the formation of imperfect, rodlike crystals. Since such moieties can be only metastable, because of the energy stored in surfaces and internal defects, further changes with treatment time would be expected] and are manifested in the continuous increase in perfection and the fibrillar t o lamellar transformation. 4.2. Kinetics

The kinetics of structure and property changes exhibit an intriguing duality. Examples are the kinetics of fibre elongation during treatment and density. These property isotherms for fibres treated under 10 MPa stress are shown in Figures 12 and 14 [49]. Consider, for example, a temperature of 140OC. At this temperature, the time t o attain one-half the final value is approximately 7 ms for elongation and approximately 17 ms for density. Other properties follow basically either the faster track demonstrated by elongation or the slower track demonstrated by density [49]. Fast changes are shown by shrinkage in 80°C water and by the onset of crystalline diffraction peaks. Slow changes are shown by the intensity growth of the SAXS maximum and the tensile modulus. The rapid change, as we have already seen, is associated with the formation of imperfect rodlike crystallites. These entities appear to immobilize

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Annealing Time (ms) Figure 14. Isothermal density evolution [49] for PET fibres heat-treated at 10 MPa

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the noncrystallized chains sufficiently to inhibit further shrinkage of the material above T,. The tensile modulus, on the other hand, depends more generally on the overall degree of crystallinity and develops at the slower rate associated with the density increase. 5. Low temperature transformation: radial distribution function studies In molecular kinetics, there is a general inverse correlation between time and temperature; what develops at very short times at high temperatures may develop after long times at low temperatures. Keeping this in mind, we consider now a study of low temperature transformations - cold cristallization - in P E T fibres. This work is best set in the context of scanning calorimetry (DSC) traces. In Figure 15 are shown DSC traces of an amorphous, unoriented P E T ribbon (curve 0) and of an as-spun fibre which had been spun at 3,000 m/min (curve 1) [53]. The amorphous ribbon exhibits a clearly marked glass transition centered at 70°C and a crystallization exotherm at 120'C. Curve 1 represents a fibre heated under fixed-end conditions during calorimetry. Here the glass transition is interrupted by a small exotherm whose peak is near 77OC. Two larger crystallization exotherms occur at higher temperatures. In further DSC results not shown here, as tension is applied to the fibre during calorimetry, the small 77OC exotherm persists and the onset and peak of the principal crystallization exotherm(s) move toward lower temperatures. 0.1

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Figure 16. Equatorial WAXS scans of PET fibre spun at 3,000 m/min and subsequently brought to a specified temperature, at constant length, and immediately cooled to room temperature [53]: 1 - as-spun, 2 - 77OC, 3 - 82"C, 4 - 87OC, 5

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In order to examine the structural changes, DSC scans under fixed-end constraints (curve 2) have been interrupted at various temperatures and the fibre rapidly cooled t o room temperature. The temperatures at which the temperature increase was interrupted were as follows: 77°C at the centre of the small endotherm; 82°C at the end of the small endotherm; 87°C at an early stage of the first major endotherm; 100°C at a late stage of the first major endotherm; 135'C after completion of all endothermic processes. Carefully controlled room temperature WAXS diffractometer scans of these specimens were made [53]. The axis of rotation in this case was the fibre axis; what is probed is the structure normal t o the fibre axis. The WAXS curves are collected in Figure 16. The most obvious comment is that no defined crystalline peaks occur until curve 5, which represents a fibre brought to 100°C before cooling. The information contained in curves 1 through 4 can be obtained only through Fourier inversion to obtain cylindrical distribution functions. Reduced cylindrical distributions (CDF's) derived from the curves of Figure 16 are shown in Figure 17 [53]. Here R is the transverse (normal to

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b LL

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Figure 17. Approximate cylindrical distribution functions obtained from the WAXS scans of Figure 16 [53]: 1 - asspun, 2 - 77OC, 3 - 82OC, 4 - 87OC, 5 - 100°C, 6 - 135OC

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!

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Figure 18. Cylindrical distribution functions to larger R-values [53]: 1 - 87OC, 2 - 1OO0C,3- 135OC

the fibre axis) distance from a carbon atom taken at R = 0. The magnitude of the CDF represents the average atomic density in a circular region R from the C atom. A CDF level of 0 denotes a local atomic density identical to the average for the fibre. It should be noted that the CDF's reported here were obtained using an approximation method [54] which is most accurate at larger R-levels. The CDF curves for all fibres are identical to R = 6A. Up t o that radial distance all CDF correlations are intrachain and should be identical for all fibres. Beyond 8.k the correlations are interchain and are of interest to us. We see a buildup in the level of interchain correlation as the maximum temperature attained by the fibre increases. Up to 87"C, this the interchain correlations damp completely by approximately 15 radius corresponding to a diameter of ca. 3 0 k Above this temperature, the correlations extend to approximately 35 corresponding to a diameter of ca. 70A. This is best seen in Figure 18, which extends the R-axis. The variation of the cylinder radius with temperature is shown in Figure 19. The portrait emerging from these results is that of the creation during the Tg-interrupting endothermic process of correlated, or crystallike, domains extending laterally to some 30 During the higher temperature endothermic process, the domains of correlation are extended laterally to some 70A, the dimension previously determined by SAXS in the interrupted heat-treatment studies outlined in the previous section. A simplified model of this behaviour is shown in Figure 20. The model depicts the increasing perfection and lateral growth of axially aligned crys-

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Figure 19. Transverse size of crystallites [53],as obtained from CDF curves. With respect to the DSC curves of Figure 15, the arrows indicate, from left to right, the onset of the glass transition, the centre of the small exotherm which interrupts the glass transition and the centre of the major exotherm

Figure 20. Model of stages of transformation: (a) formation of very narrow, defective crystalline or mesophasic microfibrils; (b) axial segmentation of those microfibrils into crystalline and amorphous blocks; (c) transverse growth of the crystallites, and (d) dissolution of remnants of the microfibrils

tallites. This behaviour is similar to or identical with what occurs at higher temperatures a n d very short treatment times, as described in t h e last section.

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6. T h e r m a l dendrite m o d e l

It is intended here to demonstrate that first-order predictions of the fibrillar dimensions agree with the experimental results given above. Approximate treatments of the shape and velocity of the growing entities have been given by Tiller and Schultz [46] for isothermal growth (free growth, in the terminology of crystal growth) and by Schultz [47,48] for a material passing at constant velocity through a temperature gradient containing the crystallization temperature (constrained growth). The constrained growth case is applicable t o high-speed spinning, as demonstrated in Figure 21. This figure depicts a fibre being spun into a room temperature environment at velocity V. As a volume element moves downstream, it loses temperature. A monitor on the spinline would show that crystallization occurs at a specific point in room space - i. e., at a specific temperature. It is as if a volume element were being forced through a temperature gradient at velocity V and chooses a specific temperature for growth at that velocity. We demonstrate now that imperfect crystals must be the result of the initial transformation in such a threadline. Quantities which are useful in this discussion are the mass and thermal diffusion lengths 6, and 6 t . These lengths are the approximate distances over which molecuIar or thermal diffusion occur in the material ahead of a growing interface [47,55]. We shall see that for processes occurring in the spinline the mass diffusion length is subatomic, forcing the conclusion that for transformation of any kind t o occur, it must occur with no change in the concentration of noncrystallizable chains or segments; the molecules cannot demix rapidly enough. The diffusion lengths are related to the mass and thermal diffusivities and the interface velocity via Sc = D,/V and 6, = Dt/V [47]. In the present case, the interface moves with the velocity of the fibre. The mass and thermal diffusivities can be estimated. While the mass self-diffusivities of P E T in P E T are not known, values for most molten polymers are in the range

v

Position

Figure 21. Schematic of fibre spinline

384

J.

M.Schultz

at lower temperatures to 10-"cm2/s at higher melt temperatures. Crystallization occurs in the spinline for velocities of some 4,000 m/min and above. Using this value for V and 10-"cm2/s for the interface velocity, the mass diffusion length is of the order of 10-'5cm! For lower diffusivities, the mass diffusion length is even smaller. Thus, demixing at the crystallization front is not possible; chains cannot disentangle themselves and diffuse away rapidly enough to keep up with the moving interface. The implication is that under spinning conditions normally nonincorporable chains and badly entangled nodes must be incorporated into the growing crystal. A corollary is that the driving force must be very high in order for crystals of such high internal energy t o form. If such conditions obtain, it would be only under very high molecular extension, where the entropy of the melt is much lower than it would be for a relaxed, random-coil melt. Consequently the melting point becomes very high and the effective undercooling is at least several tens, if not hundreds, of degrees [41,43,45]. Finally, since no chain migration takes place, there will be no effect of mass diffusion on the morphology of the interface. We examine now the effect of thermal diffusion. For unoriented PET, the thermal diffusivity at the temperatures of interest is approximately 0.6 x 10-3cm2/s [56]. We shall assume that this value is approximately valid for oriented PET also. This corresponds to a thermal diffusion length of the order of 100 nm. Such a diffusion length scale will constrain the growth front to lateral dimensions commensurate with a small escape range of the phonons. The situation in which the growth front is influenced by the ability of the system to.dissipate the heat of fusion is one which gives rise t o rodlike crystals, or thermal dendrites. There is, in fact, a large literature on thermal dendrite growth kinetics and morphology (see, e. g., [55,57591 for recent reviews). For us, however, it is the most basic treatment which is useful. In 1958, Ivantsov published a treatment of coupled steady state growth and heat flow for the growth of a rodlike, isothemal crystal of circular cross-section and a paraboloidal tip [60]. Solution of Fourier law for this moving boundary problem gives the following:

where Y = Vp/2Dt

(2)

and where &(y) is the exponential integral function, p the radius of the dendrite tip, ys the crystal-melt interfacial energy, cp the specific heat of the melt, T, the equilibrium melting point of a boundless crystal, L the heat of fusion, To (< T,) the temperature of the melt at a position remote from the interface, and 6T the meliting point increase due to chain extension. The square-bracketed term on the right of Eq. (1) is the difference in temperature of the melt at the interface and the far-field melt. This

385

Structure development in highly oriented PET

6000

u

s W

>

3000k 1500

UJ

I

30 f',

I

40

!O

nm

Figure 22. Solution of Eq. ( I ) , using parameters appropriate to PET [48] temperature would be T, were the system in equilibrium. However, in the present case, the energy stored in the surface reduces the melting point by an amount (2y,T,/L)/p (the capillarity term), and the chain extension in the melt increases the melting point by an amount 6T. Solution of Eq. (1) for any temperature T yields a relationship between the spinline velocity V and the radius p of the dendrite tip. A nest of such curves for several temperatures, computed using variables appropriate t o P E T , is shown in Figure 22 [48]. For these computations, 6T was set at zero; this is allowable since a 6T correction can be made post fucto. To understand what might happen, consider first the curve for 190OC. For spinline (and, hence, interface) velocities above ca. 2500 m/min there is no solution to Eq. (1); it is not possible to conduct heat away rapidly enough at those interface velocities. Below 2500 m/min, the process is viable. Now consider a volume element moving at 2500 m/min through the temperature gradient along the threadline. N o crystallization is possible until the temperature has been reduced to 190OC. At that temperature and for that spinline velocity only one solution to Eq. (1) is available, corresponding to the peak in the 190°C curve in Figure 22. The crystal-noncrystal interface therefore sets up at 190°C, with a tip radius of some 8A. This solution

J . M . Schultz

386

3 3

2

3

3 3 n

3 3 3

U

0 0

0 0 0

N

0 0

s

0

Structure development in highly oriented PET

n

\

\

\ \

\

\

\

\ \

\

\

1 \

\

387

388

J . M. Schultz

changes somewhat when account is taken later for the chain orientation effect (6T). Figure 23 shows the predictions of transformation temperature and dendrite tip radius for P E T fibres. As indicated in [48], there are several unjustified simplifications in the analysis. But the measurements with which the computed results may be compared are likewise crude and any broad agreement would indicate the potential validity of the model. In Figure 24 are shown experimental crystallite diameters [43,61,62], taken using Scherrer’s formula. Also shown are predicted diameters [48], using two sets of surface energy and thermal diffusivities for P ET, both sets lying within the uncertainties at which those quantities are known. The absolute agreement between experiment and prediction is reasonable. Likewise, Figure 25 shows experimentally determined crystallization temperatures in PET spinlines, compared to the range of predicted temperatures, using the possible range of ST (which, in turn, depends upon the relaxation characteristics of the melt). Again, the absolute agreement is reasonable. It is less easy t o predict the transformation characteristics for fibres transforming as in the interrupted heat-treatment investigations cited

220 Eq. (71, Including 6T

200

180 Eq.(7)

, Excluding

bT

c /

/

/

/ /

A

1

D

0 0

X0

140

I

3000

I

1

I

4000

5000

6000

SPIN ILINE VELOCITY

,m/rnin.

Figure 25. Comparison [48] of the predicted range of fibril diameter with measurements [43,61,62]

Structure development in highly oriented PET

389

above. This case is complicated for two reasons: (1) it is not certain whether the crystallites grow with the threadline velocity or at a slower speed and (2) the operating condition at the front is less easy t o infer. The first of these problems is exemplified by the two sketches of Figure 26. In case A of Figure 26, one envisions here existing crystalline microfibrils growing at the velocity of the growth front. In case B, many crystals nucleate and grow during the time in which they pass through the hot zone. Case A would constitute an upper bound for the growth front velocity; a lower bound would be associated with case B. For the interrupted heat-treatments described above, crystallinity is nearly always observed for threadline velocities of 20 cm/s. This velocity can then be taken crudely as the case A upper bound. For case B, a smallest possible axial crystallite length would be some 5 nm. For the lower bound case, the crystals have 20 ms in which t o grow this 5 nm, corresponding to a velocity of 2.5 x 10-5cm/s. Whether growth occurs according to case A or case B is speculative; but more on that below. The second uncertainty relates t o what optimization principle nature would employ to set absolute values of V and p in the solution of Eq. (1). Since in the interrupted heat-treatment, the temperature increases t o the hot zone, the argument for decreasing temperature given above for the spinline cannot be valid. It is likely that case A more nearly represents what happens in the interrupted heat-treatment case. This is seen as follows. First, consider why

V / A

Figure 26. Models of types A and B transformation for the case of a thread passing a narrow hot zone. In type A the crystals grow continuousiy a t the velocity of the threadline. In B, crystals nucleate profusely but grow to only some specified length as the fibre passes throgh the hot zone

390

J . M . Schultz

growth would be discontinuous. Discontinuous growth would be expected if either uncrystallizable chains or heat built up at the crystal melt interface and “choked” further growth. Since heat flow is rapid enough for case A or case B, this is not a consideration. The diffusion of uncrystallizable chains from the growth tips, could be, however, problematic. For such a problem, we examine the mass diffusion lengths. The mass diffusion length for case A is still subatomic. For case B, the range of diffusion lengths is from subatomic at relatively low temperatures to some 4 nm at relatively high temperatures. Thus, except for very high temperatures the chain segments are unable t o disentangle and diffuse away from the interface. This implies, again, that all matter is incorporated, except at high temperatures. And implied also is that once a crystal begins to grow, there is no reason for it to stop growing, since there is no buildup of nonincorporable chains at the front. For this reason, case A is the more probable model. The question of the operating condition at the interface is more difficult. Maximum velocity [63,64] and marginal interface stability [65,66] have been suggested as optimization operations (operating conditions). Crudely, the marginal stability condition predicts dendrite tip radii about ten times larger that maximum velocity prediction. Thus in our case the diameters expected can be bounded by the maximum velocity prediction and a number about ten times larger. Considering the several curves of Figure 22, the maximum velocity dendrite radii should be in the range of 1 to 3 nm. A range of values, based on the two possible operating conditions, is then 1 to 30 nm, a range which includes the observed values described earlier (ca. 3 nm). The large uncertainty in the prediction makes this a far from satisfactory conclusion and indicates that detailed molecular simulation may be in order to test the correctness of the approach.

7. Concluding remarks What has been described in the preceding sections is attempts to characterize and explain the developtment of structure in highly oriented PET. Post mortem and in situ investigations have pointed to a microfibrillar microstructure, in which the microfibrils could be either individual fibrillar crystals or lamellar stacks. Additionally, the presence of a highly oriented but weakly crystalline or noncrystalline mesophase has been postulated. Spinline measurments point to a critical stress or deformation level associated with crystallization in the spinline. Interrupted transformation experiments have enabled detailed characterization of fibres crystallized for short times under controlled temperature and stress conditions. These results show the rapid creation of very fine, defective microfibrils, probably the oriented mesophase suggested earlier. These microfibrils, and their rapid conversion to row structures, are seen directly, using transmission

Structure development in highly oriented P E T

391

electron microscopy. Under low stress conditions a competition between chain relaxation and fibril formation is observed in property measurements. At higher temperatures and/or stresses, chain relaxation cannot keep up with crystallization kinetics and defective microfibrils are always inferred. DSC mesaurements and the characterization of interrupted DSC treatments show that microfibrillar crystallization occurs as soon as sufficient chain mobility is available; this process is manifested as an interruption to the glass transition process. Upon higher temperature treatment] the lateral correlation of the microfibrils increases. Presumably the microfibrils now consist of the narrow, cylindrical row structures seen in electron micrographs. The kinetics of isothermal structure and property changes likewise show two stages of transformation. In the first stage the chains are immobilized against shrinkage in water at 8OOC. This stage runs parallel t o the onset of crystallization and the creation of the initial microfibrils. The axial stiffness increses more slowly and in general parallels the overall level of crystallinity. The creation of imperfect microfibrillar crystals is a result of problems of heat and material dissipation at the transformation interface. Sharply pointed, needlelike crystals must be created in order for the transformation to occur at the threadline velocity; only then can the heat flow be sufficiently three-dimensional to permit transformation at the required rate. Further, at typical spinline or heat-setting velocities it is not possible to disentangle and diffuse away poorly crystallizable material, such as imperfect or short chains or entanglements. These defects must be incorporated into the crystallites, a behaviour possible only at very high driving forces. This microfibrillar transformation has been modeled as the growth of thermal dendrites. This model predicts the correct range of microfibril diameter and of the transformation temperature in high-speed spinlines. References S. Fakirov, D. Stahl, Angew. Makromol. Chem. 102,117 (1982) S. R. Padibjo, I. M. Ward, Polymer 24, 1103 (1983) T. Kunugi, A. Suzuki, M. Hashimoto, J . A p p l . Polym. Sci. 26,213 (1981.) M. Evstatiev, S. Fakirov, A. Apostolov, H. Hristov, J. M. Schultz, Polym. Eng. S c i . 32,964 (1992) 5. D. C. Prevorsek, H. J. Oswald, in: Solid State Behavior of Linear Polyesters a n d Polyamides, edited by J. M. Schultz, S. Fakirov, Prentice-Hall, Englewood Cliffs, New Jersey 1990, p. 131 6. F. van Antwerpen, D. W. van Krevelen, J . Polym. Sci., Polym. Phys. Ed. 1. 2. 3. 4.

11, 2423 (1970) 7. Perla N. Peszkin, J. M. Schultz, J . S. Lin, J . Polym. Sci., Polym. Phys. Ed. 24,2591 (1986) 8. H. A. Hristov, J . M. Schultz, Polymer 29,1211 (1988) 9. A. Cobbold, R. d e P. Daubeny, K. Deutsch, P. Markey, Nature 172, 806 (1953)

392

J . M . Schultz

10. J . Sicorski, in: Fzbrt Structuve, edited by J . W . S. Hearle, R. H. Peters, Butterworths, London 1963 11. R. D. van Veld, G . Morris, H. R. Billica, J . Appl. Polym. Sci. 12, 2709 (1968) 12. W . 0. Statton, J.L Koenig, M. Hannon, J . Appl. Phys. 4 1 , 4290 (1970) 13. R. Murray, H. A. Davis, P. Tucker, J . Appl. Polym. Sci. 33, 177 (1978) 14. R. Haggege, %iber Diffraction Methods”, in: A CS Symposium Series 141, edited by A. D. French, K. H. Gardner, Amer. Chem. SOC.,Washington 1980 15. H. J. Biangardi, H. G. Zachmann, Prog. Colloid Polym. Sci. 62, 71 (1977) 16. T. Kawai, H . Sasano, in: Proc. Intern. Symp. Fiber Sci., Hakone, Japan, August 20-24, 1985, Elsevier Applied Science, Barking, Essex 1986, p. 62 17. H. J. Biangardi, H. G. Zachmann, Makromol. Chem. 177, 1173 (1976) 18. H. J. Biangardi, Makromol. Chem. 179, 2051 (1978) 19. H. J. Biangardi, H. G. Zachmann, J . Polym. Sci., Polym. Symp. Ed. 58, 169 (1977) 20. V. M. Nadkarni, J. M. Schultz, J . Polym. Sci., Polym. Phys. Ed. 15, 2151 (1977) 21. P. Predecki, W . 0. Statton, in: Proc. Conf. on Small-Angle Scattering, Syracuse, N . Y . , June 24-26, 1965, edited by H. Bromberger, Gordon & Breach, New York 1967 22. V. I. Gerasimov, Ya. V. Genin, A. I. Kitaigorodsky, D. Ya. Tsvankin, Kolloid Z. Z. Polym. 250, 518 (1972) 23. G. Harburn, J. W. Lewis, J. 0. Warwicker, Polymer 26, 469 (1985) 24. P. H. Hermans, A.Weidinger, Makromol. Chem. 39, 76 (1960) 25. P. F. Dismore, W . 0. Statton, J . Polym. Sci. C13, 133 (1966) 26. J. H. Dumbleton, J . Polym. Sci. 7A-2, 667 (1969) 27. R. J. Samuels, J . Polym. Sci. 10A-2, 781 (1972) 28. S. Fakirov, E. W . Fischer, R. Hoffmann, G. F. Schmidt, Polymer 18, 1121 (1977) 29. R. J. Matyi, B. Crist, Jr., Colloid Polym. Sci. B 1 6 , 15 (1979) 30. E. W. Fischer, S. Fakirov, J . Moter. Sci. 11, 1041 (1976) 31. G. Farrow, I. M. Ward, Brit. J . Appl. Phys. 11, 543 (1960) 32. U. Eichhoff, H. G. Zachmann, Makromol. Chem. 147, 41 (1971) 33. H. G. Zachmann, Polym. Eng. Sci. 19, 966 (1971) 34. K. Rosenke, H. G. Zachmann, Prog. Colloid Polym. Sci. 64, 245 (1978) 35. H. J. Biangardi, Prog. Colloid Polym. Sci. 69, 99 (1979) 36. G. Jellinek, W . Ringes, G. Heidemann, Ber. Bunsenges. Phys. Chem. 74, 924 (1970) 37. W. L. Lindner, Polymer 14, 9 (1973) 38. V. B. Gupta, S. Kumar, Polymer 1 9 , 953 (1978) 39. 0.Ishizuka, K. Katayama, in: Proc. Intern. Symp. Fiber Sci., Hakone, Japan, August 20-24, 1985, Elsevier Applied Science, Barking, Essex 1986 40. H. H. George, A. Hole, A. Buckley, Polym. Eng. Sci. 23, 95 (1983). 41. G. Bragato, G . Gianotti, Eur. Polym. J . 19, 795 (1983) 42. J . Cheng, X. Guan, R. Wei, H. Ma, Internat. Polym. Processing3, 95 (1988) 43. J . Shimizu, T. Kikutani, A. Takaku, in: Proc. Intern. Symp. Fiber Sci., Hakone, Japan, August 20-24, 1985, Elsevier Applied Science, Barking, Essex 1986, p. 62 44. A. Ziabicki, L. Jarecki, in: High-speed Fiber Spinning, edited by A. Ziabicki, H. Kawai, John Wiley, New York 1985, p. 225

Structure development in highly oriented P E T

393

45. H. H . George, in: High-speed f‘zber Spinnzng, edited by A . Ziabicki, H. Kawai, John Wiley, New York 1985, p. 271 46. W. A. Tiller, J. M. Schultz, J. Polym. Sci., Polym. Phys. Ed. 22,143 (1984) 47. J. M. Schultz, Polymer 32,3268 (1991) 48. J. M. Schultz, Polym. Eng. Sci. 31,661 (1991) 49. K.-G. Lee, J . M. Schultz, Polymer, in press 50. H. Chang, K.-G. Lee, J. M. Schultz, J. Macromol. Sci., Phys., in press. 51. K. M. Gupte, Heike Motz, J. M. Schultz, J. Polym. Sci., Polym. Phys. Ed. 21, 1927 (1983) 52. J. M. Schultz, J. Petermann, Colloid Polyrn. Sci. 262,294 (1984) 53. H. A. Hristov, J.M. Schultz, J . Polyrn. Sci., Polym. Phys. Ed. 28 1647 (1990) 54. H. A. Hristov, R. Barton, Jr., J. M. Schultz, J . Polymer Sci., Polym. Phys. Ed. 29,883 (1991) 55. J. S. Langer, Rev. Mod. Phys. 52, 1 (1980) 56. D. W. van Krevelen, “Properties of Polymers”, Elsevier, Amsterdam 1976 57. D. P. Woodruff, “The Solid-Liquid Interface”, Cambridge Univ. Press 1973 58. W . Kurz, D.J. Fisher, “Fundamentals of Solidification”, Trans Tech, Aedermannsdorf (Switzerland) 1984 59. W . A. Tiller, “The Science of Crystallization. Macroscopic Phenomena and Defect Generation”, Cambridge Univ. Press 1991 60. G. P. Ivantsov, “Growth of Crystals”, Consultants Bureau, New York 1958. 61. H. M. Heuvel, R. Huisrnan, in: High Speed Spinning, edited by A. Ziabicki, H. Kawai, John Wiley, New York 1985, p. 295 62. G. Perez, in: High Speed Spinning, edited by A. Ziabicki, H. Kawai, John Wiley, New York 1985, p. 333 63. D. E. Temkin, Dokl. Akad. Nauk SSSR 132, 1307 (1960) 64. G. F. Bolling, W . A. Tiller, J . A p p l . Phys. 32,2587 (1961) 65. J. S. Langer, H. Muller-Krumbhaar, J . Cryst. Growth 42, 11 (1977) 66. J. S. Langer, H. Muller-Krumbhaar, Acta Met. 26, 1681,1689,1697 (1978)

Oriented Polymer Material> Stoyko Fakirov Copyright 0 2002 Wiley-VCH Verlag GmbH & Co. KGaP

Chapter 13

Preparation of highly oriented fibres or films with excellent mechanical properties by the zone-drawing/zone-annealing met hod

T. Kunugi

1. Basics of the zone-drawing/zone-annealing method

The zone-drawinglzone-annealing method is one of the routes to highmodulus and high-strength fibres or films. This method was invented by the author in 1979. Since then it has been gradually improved and applied to various semicrystalline polymers. The principle has been varied depending on the superstructure of the samples under consideration. The main principles are described below. 1.1. Original zone-drawing/zone-annealing method

Although the ideal structure of an ultra-high strength fibre is extendedchain single crystal, it is desired at least that the crystalline regions are constituted only of extended-chain crystals, and the amorphous regions contain a large number of tie chains which pass through many crystals and have a similar extent of stresses and lengths (see Chapter 15). The zone-drawinglzone-annealing method was tried in view of producing such a structure. Since it is difficult to convert directly an unoriented original fibre into the extended-chain texture, the procedure was divided

Highly oriented fibres or films by the zone-drawing/zone-annealing method 395

Original Highly oriented amorphous fibre fibre

Highly oriented crystalline fibre

--Tensile

tester

- - Band heater - -Thermocouple

Zone-annealing

.-

Crosshead

Figure 1. Principle of the original zonedrawing/zone-annealing method

Figure 2. Schematic diagram of the apparatus used by the zonedrawing/zone-annealing method

into two stages; zone-drawing and zone-annealing. Zone-drawing was applied to as-spun fibres in order t o produce a fibre with as high an orientation and as low a crystallinity as possible, whereas the zone-annealing was subsequently carried out to impart high orientation and crystallinity to the zone-drawn fibre (Figure 1). The apparatus was the usual tensile tester partially reconstructed as seen in Figure 2. A band heater 2 m m wide was attached to the crosshead, moving a t an optimum speed. The upper end of the fibre was fixed a t a frame, and a desired tension was applied to the lower end by weighting. The fibre was drawn easily and quickly, producing necking by zone-drawing carried out a t a temperature above T, . The zone-drawn fibre was crystallized from one end of the fibre by zone-annealing carried out under a high tension a t an optimum temperature for crystallization. 1.2. Multistep zone-drawing/zone-annealing method

In the case of a semicrystalline polymer, the as-spun fibre consists of a large number of lamellar blocks and amorphous regions containing loop chains, tie chains and chain ends. Therefore, it is difficult to withdraw amorphous chains from such a complex structure or to achieve the extended chain crystal structure by one-step zone-drawing or zone-annealing. Thus the multistep method w a s proposed and carried out with increasing tension and temperature.

T. Kuiiugi

396 1.3. High -t e mpe rat ure t o n e -drawing method

As mentioned above, the as-spun fibres or as-extruded films consist of lamellar blocks and amorphous regions. The lamellar blocks are distributed at random, and their size is varying. Further, the amorphous chains are at random in orientation, length and tension degree, and represent loop chains, tie chains and chain ends. If such an inhomogeneous structure is stretched, the force concentrates at weak points, resulting in the breakage of the fibre. In order to avoid this difficulty, the high-temperature zone-drawing method was proposed. The method was carried out at a very high temperature close t o or above the conventional melting points of crystalline or semicrystalline polymers. The principle is shown schematically in Figure 3. The crystallites in the fibres are almost melted in the narrow heating zone, and the molecuHeater Original fibre

I

n Figure 3. Principle of the high-temperature zone-drawing method

lar chains are easily withdrawn, with unfolding of chains. Usually, after the first high-temperature zone-drawing, the molecular chains are still relaxed and are not fully stretched; the zone-drawing and zone-annealing must be repeated further. According to this method, the alignment and/or quantity of crystallites in the original materials, i.e. the initial morphology and thermal history of the starting materials are not under consideration. 1.4. Vertical two-step zone-drawing method

The principle of this method is shown in Figure 4. The as-extruded films contain randomly scattered lamellar blocks. However, such crystallites can be easily and highly aligned by drawing at a relatively low draw ratio. After the first drawing this structure can be regarded as a lamellar-stacking structure in the direction perpendicular to the first drawing direction. If zonedrawing is carried out in this direction, the lamellae will unfold easily since van der Waals forces are very weak. The first drawing and the second zonedrawing are termed “transverse drawing” and “longitudinal zone-drawing” ,

Highly oriented fibres or films by t h e zone-drawinglzone-annealing method 397

Randomly scattered lamellar structures

1

Oriented and extended chain structure

Transverse drawing

1

Zone-annealing

Stacked lamellar structure

Figure 4. Principle of the vertical two-step zone-drawing method

respectively. After the longitudinal drawing, the usual zone-drawing and zone-annealing are performed on the films. By this method, films with very high modulus and strength can be obtained. Zone-drawing and zone-annealing methods have the following common characteristics and advantages: (1) Since the fibre (or film) is locally heated only in a narrow heating zone, the quantity of heat required for drawing or annealing can be decreased to a great extent. (2) Thermal degradation can be prevented because of the short heating time. This is a great advantage in the case of heat-irresistant polymers. (3) Thermal effects before drawing can be avoided, since the fibre is subjected to the first thermal effect in the heating zone. Compared to the hot-drawings in oven or in bath, thickening of lamellae and crystallization which inhibit the full extension of molecular chains can be fairly decreased. (4)Very high tensions and temperatures can be applied to the fibres or films because the heating zone is very narrow. (5) Since the tension is maintained constant throughout an experiment, the fibre superstructure does not fluctuate along the fibre axis. In the case of films, the width remains constant and the molecular orientation is constant over the width.

T. Kunugi

398 2. Application to p o l y m e r fibres or films

2.1. Polyethylene The initial morphology of the original materials is very important, especially in superdrawing. As it is well known, single crystal mats consist of regular stackings of lamellae. Surface of the mat

Heater

w

-

Tension

Figure 5 . Principle of the zone-drawing of high molecular weight PE single crystal mat

Zone-drawing seems to be the most suitable method for superdrawing of single crystal mats, as seen in Figure 5. In order to decrease molecular chain-end deffects, ultra-high molecular weight (UHMW) polyethylene, Hizex Million 340 M powder (MW = 4.5 x lo6) of Mitsui Petrochemical Industries, Ltd. was used [1,2]. The powder was dissolved in boiling pxylene at a concentration of 0.1%. The dilute solution was cooled at a cooling rate of 0.5OC/min from 14OOC to 12OOC and then allowed to cool t o room temperature. The crystals were deposited as a gel-like precipitate. The solution was filtered and the precipitate was squeezed between filter papers. The mat thus prepared was pressed and then dried and cut into strips 2 m m wide and about 100 mm long. The strips were zone-drawn and then zone-annealed under the conditions shown in Table 1. Each stage was repeated 4 times at increasing tension. These steps are denoted as ZD-1, -2, -3, -4 and ZA-1, -2, -3, -4. The birefringence at each step is shown in

Table 1. Conditions of zone-drawing/zone-annealing of high molecular weight PE single crystal mats Step

Heater temperature ("C)

Tension (kg/mm2)

Heater speed (mm/min)

ZD-1 ZD-2

125 115 115 115 135 135 135 135

0.3 6 12 20 10 20 30 40

5 10

ZD-3 ZD-4

ZA-1 ZA-2 ZA-3 Z A-4

10 10 75 75 75 75

Highly oriented fibres or films by t h e zone-drawinglzone-annealing method 399

Z A-4 film

ZD-1 film Figure 6. Change in birefringence with the processing of PE

Original mat

101 -

0 0

I

50

100 150 Draw ratio

200

Figure 7. Birefringence vs. draw ratio drawing in hot for zone-drawing (a), water (- - -), and coextrusion (. . . ) of

1

,

I

1500 1300 Wave number (cm-')

Figure 8. Change in a fragment of the infrared spectrum resulting from zonedrawing and zone-annealing of PE

PE

Figure 6 while the dependence between the draw ratio and birefringence is shown in Figure 7 . The maximum values of the draw ratio and birefringence are 170 and 0.072, respectively. It is seen that the dependence is linear in the draw ratio range from 50 t o 170. On the contrary, in the cases of coextrusion and drawing in hot water, the birefringence increases rapidly up to 0.062 and then remains constant. Zone-drawing involves a very sharp necking boundary. It is expected that a fairly regular unfolding of the lamellae takes place. Figure 8 shows chainges in a part of the IR spectrum with zone-drawing and zone-annealing. Although three gauche bands can be observed at 1303, 1350 and 1359 cm-' in the IR spectrum of the original mat, these bands almost disappear even after the first zone-drawing. They are not detected at all in the spectrum of the ZA-4 film. As the bands belong to the amorphous region and are assigned to gtg (1303 cm-l), gg (1353 cm-l) and gtg or gttg (1359 cm-l), respectively, their disappearance

T. K u n u g i

400

a

10

30

20

40

b

10

20

30 29

40

(O)

Figure 9. Equatorial X-ray diffraction patterns of the ZD-1 P E film: (a) through pattern; (b) edge pattern

suggests an increase in crystallinity or trans conformation of molecular chains. The crystallinity of the ZA-4 film was estimated t o be 0.90 from the WAXS pattern. The zonedrawn and zoneannealed films indicate a double orientation, as seen in Figure 9. The b-axis is almost perfectly oriented parallel to the film surface.

Highly oriented fibres or films by the zone-drawing/zone-annealing method 401

250

Birefringence x lo3 50- 60 70

30

40

1

1

1

80

I

250 '

200

200 ' n

-du

150 150.

100

dc7

50

'q

-

'q

0

0

20

60 80 100 120 140 Temperature (' C)

100 50

40

Figure 10. Temperature dependence of the dynamic modulus (E') for the zonedrawn and zone-annealed PE films: (V) ZD-1; (m) ZD-2; (A) ZD-3; ( 0 )ZD-4; (V)ZA-1; (0) ZA-2; (A) ZA-3; (a) ZA4; - - - maximum values

0

50

100 150 Draw ratio

200

Figure 11. Dynamic modulus vs. draw ratio or birefringence in PE sampkes

Figure 10 shows the temperature dependence of the dynamic modulus (E') for each step of zone-drawing and zone-annealing. E' increases stepwise with the processing. The highest modulus is 232 GPa at room temperature, and 127 GPa even at 100OC. The tensile strength of the ZA-4 film is 6 GPa. The relationship between E' and the draw ratio or birefringence are shown in Figure 11. It is obvious that zone-drawing/zone-annealing is a quite effective method for drawing of UHMW PE mats (see also Chapter 2). 2.2. Polypropylene

Since as-spun fibres or as-extruded films of isotactic polypropylene have a relatively high crystallinity (from 35 to SO%), the high-temperature zoneTable 2. Conditions of zone-drawingfzone-annealingof isotactic polypropylene films Step HT-ZD-1 HT-ZD-2 HT-ZD-3 HT-ZD-4 HT-ZD-5 ZA-1 ZA-2

ZA-3 ZA-4

Heater temperature ("C) 150 150 150 150 150 170 170 170 170

Tension (kg/mm2) Heater speed (mm/min) 0.2 3 6 9 12 12 15 18 21

10 10 10

10 10 50

50 50

50

T. Kunugi

402

drawing method wits utilized [3,4]. The original film with crystallinity of 38 %, birefringence of 0.0024 and thickness of 80 p m was supplied by Toray Co. Ltd. The conditions of zone-drawing are shown in Table 2. The drawing temperature of 15OOC at the first stage is close to the melting of the original film, 161OC. The high-temperature zone-drawing was repeated five times, and the tension was gradually increased from 0.2 to 12 kg/mm2. Further, the zone-annealing was carried out at 17OOC four times at increasing tension from 12 to 21 kg/mm2. The moving speed of the heater was 10 mm/min for zone-drawing and 50 mm/min for zone-annealing. The maximum values of the draw ratio and birefringence reached 25.6 and 0.044,respectively. Figure 12 shows the birefringence at each step; the maximum value is very high, and corresponds to 94 % of the crystal

01

'

1

8

I

I

'

I

I

'

HT-ZD1 -2 -3 -4 -5ZA-1-2 -3 -4

c

1.0

-

0.8

-

0.6

-

0.4

-

2

v

I

1

1

w

w

0

0

.o

0.-

-9- - - 0- -

0-0.2

0

I

I

I

I

I

I

Highly oriented fibres or films by the zone-drawing/zone-annealing method 403

intrinsic birefringence of 0.0468.The crystallinity remained almost constant (74%) after ZD-2. Figure 13 shows the almost linear relationship between the birefringence and draw ratio, suggesting that the drawing is performed effectively. Figure 14 shows the orientation factors of crystallites and amorphous chains at each step. The former easily reached 0.99 by ZD-1 and did not change over the processing, whereas the latter gradually increased with the processing. The maximumvalue of fa was 0.77. In Figures 15 and 16, the temperature dependances of E‘ and E” are shown. The El value is increased stepwise by the processing. The E’ of the ZA-4 fibre is 27 GPa at room temperature, i.e. it is 79 % of the crystal modulus along molecular chains, 34 GPa. Also, the ZA-4 fibre exhibits high El values at elevated temperatures, for example, 19 GPa at 100°C and 13 GPa even at 150’C. Since 15OOC is the temperature of the beginning of crystal melting in the DSC curve, it is found that such a high modulus is observed immediately before melting. Two dispersion peaks can be seen in the El’-temperature curve. The lower temperature peak corresponds to the a,-dispersion, whereas the highest temperature peak represents the a,-dispersion. The former peak decreased in intensity with the processing, but the latter one increased rapidly in intensity and shifted t o higher temperatures (Figure 16). It can be suggested that the crystallites increase in quantity and improve in quality. This suggestion is also supported by the results of DSC measurements. Thus the melting peak becomes steeper and shifts to higher temperatures. It can be assumed from the change in the cr,-dispersion in Figure 16 that the movement or relaxation of amorphous chains is strongly prevented by the connected crystallites in the higher temperature range. In addition, 1.5

1 .o h

du

v

N 0.5

0 0

50

100

150

Temperature ( O C)

Figure 15. Temperature dependence of the dynamic modulus ( E l )for the zonedrawn and zone-annealed PP films

Temperature (“C)

Figure 16. Temperature dependence of the loss modulus (E”) for the zonedrawn and zone-annealed PP films

404

7'. Kunugi

the increase of fa contributes greatly to the improvement in mechanical properties, because fa is almost proportional to the E' value.

2.3. Polyvinyl alcohol Although the crystal modulus of polyvinyl alcohol is very high, 250 GPa, the attained maximum moduli of fibres or films could not exceed 40-60 GP a for a long time, probably due to the existence of OH groups and hardness of the crystals [4]. The OH groups cause steric hindrance and prevent slippage and alignment of molecular chains during drawing. In addition, hydrogen bonds are formed between adjacent OH groups. The intra- or intermolecular hydrogen bonds are very numerous and random in orientation. On the other hand, the crystals of polyvinyl alcohol have a higher melting point of 228-250°C and are harder in plastic deformation than those of PE. The crystallites act as points that bundle the molecular chains and inhibit the free movement of the amorphous chains. Unless the hydrogen bonds and crystals are eliminated by dissolution or softening, a superdrawing comparable to that of PE would be impossible. The relationships between the drawing temperature and the superstructure or mechanical properties are discussed below. The original material was gel-spun fibres with a polymerization degree of 11 800, crystallinity of 44 %, and diameter of 184 pm, supplied by Kurare Co.,Ltd. The fibres were predrawn in draft up to about three-fold on gelspinning. Zone-drawing was carried out at temperatures (Td)varying from 80 to 26OOC under a constant tension of 1.7 kg/mm2. In the case of zonedrawing or zone-annealing, the drawing and annealing temperatures are in fact those of the heater, because the real temperature of the samples cannot be measured during the experiments.

Drawing temperature ("C) Drawing temperature ("C)

Figure 17. Draw ratio vs. drawing ternperature of PVA fibres

Figure 18. Birefrigence vs. drawing temperature of PVA fibres

Highly oriented fibres or films by the zone-drawing/zone-annealing method 405

Figure 17 shows the relationship between T d and the draw ratio. The latter increases discontinuously around 90°C, corresponding to Tg of this polymer. The draw ratio increases rapidly above 2OOOC and reaches 15 times. Figure 18 shows the change in birefringence with T d ; it increases gradually in the T d range of 100-260OC. Figure 19 shows E' as a function of T d : with increasing T d , E' increases over the entire temperature range measured. Particularly above 22OoC, the increments of E' become larger with increasing T d . Figure 20 shows the temperature dependence of tan 5 for fibres zone-drawn at various T d . The a,-dispersion peak occurs at a constant temperature of 6OoC, but decreases gradually in intensity with increasing T d . However, the a,-dispersion peak shifts from 16OOC to higher temperatures, suggesting that the crystal structure becomes more rigid with the rise of T d . The crystallinity is estimated to be 80 % from an X-ray diffraction pattern. It is found that when zone-drawing is carried out at a temperature close to the melting point, high drawability and excellent mechanical properties could be attained. Table 3 shows the conditions of repeated high-temperature zonedrawings with increasing T d and tension. Figure 21 shows the increase of E' with the repetition. After the third high-temperature zone-drawing, the fibre was subjected to a vibrating heat-treatment. The maximum E'

01

0

Temperature ( " C )

Figure 19. Temperature dependence of the dynamic modulus ( E ' ) for PVA fibres zone-drawn at various drawing temperatures under a constant tension of 1.7 kg/mm2: 1 - zone-drawn at 100OC; 2 - 1 2 O O C ; 3 - 14OOC; 4 - 160OC; 5 - 18OOC; 6 - 2OOOC; 7 - 2 2 O O C ; 8 - 24OOC; 9 - 26OOC

I

I

I

50 100 150 Temperature ( " C )

I

200

Figure 20. Temperature dependence of tan6 for PVA fibres zone-drawn at various drawing temperatures under a constant tension of 1.7 kg/mm2

406

T. Kunugi

Table 3. Conditions of zone-drawing/zone-annealing of polyvinyl alcohol fibres Step

Heater temperature ("C)

Tension (kg/mm2)

ZD-1 ZD-2 ZD-3

255 210 220 20~230

1.7 25 30 - (at 110 Hz)

Heat treatment

t

0*01 0 0

50

100

150

200

Temperature ("C) Figure 21. Temperature dependence of the dynamic modulus ( E ' ) of PVA fibre at each step: 4 ZD-1; W ZD-2; A ZD-3; Vibrating heat treatment

0

50

100

150

200

Temperature ("C) Figure 22. Temperature dependence of tan 6 of the PVA fibre at each step

value was 115 GPa at room temperature and 40 GPa even at 200OC. From Figure 22 showing the temperature dependences of tan 6, it is clear that the a,-dispersion peak decreases considerably in intensity and shifts to higher temperatures, while the a,-dispersion peak shifts to still higher temperatures and cannot be observed within the temperature range measured. 2.4. Poly( ethylene terephthalate)

Poly(ethy1ene terephthalate) (PET) is suitable for the application of the original zone-drawing/zone-annealing method, because as-spun fibres are almost amorphous [5-81. The purpose of zone-drawing is to produce a fibre with as high an orientation as possible, preventing crystallization. Therefore the zone-drawing was carried out at a temperature above Tg(6OOC) and below the cold-crystallization temperature (12OOC). In the case of PET fibre, the maximum values of modulus, tensile strength, birefringence and crystallinity were 21 GPa, 1.1 GPa, 0.249, and 60 %, respectively. In this section, the application of the zone-drawing/zone-annealing method to PET films is described. This method can be applied to films by means of a slit-shaped heater. The heater used was 2 mm wide, 3 mm thick,

Highly oriented fibres or films by the zone-drawing/zone-annealing method 407

(iio)

-2 I

I

I

i

10

20

b

30

28

40

("1

Figure 23. Equatorial X-ray diffraction patterns of the zone-drawn and zoneannealed PET film: (a) through pattern; (b) edge pattern and 80 mm long. The original material was an unstretched film produced by a T-die extrusion method, supplied by Dia Hoil Co., Ltd. (crystallinity of 1.8 % and thickness of 60 pm). The film used for zone-drawing was 40 mm wide and 300 mm long, cut out of the original material in the mold direction. The conditions of zone-drawing and zone-annealing are shown in Table 4. The film was zone-drawn easily to four times the initial length; then the zone-drawn film was zone-annealed six times at the optimum temperature for crystallization under a tension as high as possible.

T. Kunugi

408

Temperature ("C) Figure 24. Temperature dependence-of the dynamic modulus (E') and loss mod0 ) the zone-annealed ulus (E") for P E T films cut in two vertical directions; (4, m) films which were cut out parallel and perpendicular to the draw direction, (0, a biaxial-stretched commercial P E T film cut out parallel and perpendicular to the machine direction Table 4. Conditions of zone-drawing/zone-annealing of poly(ethy1ene terephthalate) films Step ZD ZA-1-6

Heater temperature ("C)

Tension (kg/mm2)

Heater speed (mm/min)

90

0.78 15 16

40 20

190-200

-

Table 5 shows the changes in birefringence and crystallinity with the processing. It was also found from infrared spectral data that the trans con-

Highly oriented fibres or films by the zone-drawing/zone-annealing method 409

E;,

+5

Figure 25. Polar plots of the dynamic moduli (E’) at various temperatures for the zone-drawn PET film: ( 0 )measured at 25°C; ( 0 ) at 60°C; (m) at 100°C; (0) at 140°C; ( A ) at 180°C; (A) at 220°C; (-) calculated theoretically

Figure 26. Polar plots of the dynamic moduli (E’) at various temperatures for the zone-annealed PET film: (0) measured at 25°C; (0) at 60°C; (m) at 100°C; (0)at 140°C; ( A ) at 180°C; (A) at 220°C; (-) calculated theoretically

formation content increased and the gauche one decreased rapidly by zonedrawing and zone-annealing. Further, a difference in the X-ray diffraction patterns taken in the through- and edge-directions was detected (Figure 23), indicating a double orientation, i.e. in addition to the orientation of molecular chains in the stretching direction, phenylene rings are arranged

410

T. Kunugi Table 5. Orientation and crystallinity of PET films at each step Step

Crystallinity (%)

Birefringence

Original film

-

ZD film ZA film

1.8 21.4 45.5

0.142 0.217

in parallel to the film surface. Table 6 shows the tensile properties of the film at each step. Young's modulus and tensile strength of the zone-annealed fibre reach 14.5 GP a and 0.869 GPa, respectively. Figure 24 shows the temperature dependences of Et and El', compared to El and E" anisotropies of the zone-annealed film and with those of a commercially available biaxial-stretched film. E' at room temperature of the zone-annealed film is about 4.7 times that of the biaxial-stretched film. The a-dispersion peak of the zone-annealed film appeares at 12OoC, which is much higher than that (8OOC) of the commercially available material. In addition, the anisotropy of E' within the film faces for the zone-drawn and zone-annealed films are shown as polar plots at various temperatures in Figures 25 and 26. Although the anisotropy of E' of the zone-drawn film decreases with increasing temperature, that of the zone-annealed one remains unaltered even at 220OC. Table 6. Tensile properties of PET film at each step Step

Young's modulus (GPa)

Original film

ZD film ZA film

1.4 7.0 14.5

Tensile strength

(k.3/mm2) 26.0 86.9

Elongation at break (%)

23.8 7.4

2.5. Nylon 6 and 66

Nylon 6 and 66, as well as PET, are important fibre forming materials, which can be economically mass produced and have a variety of excellent physical properties. However, the mechanical properties are very low compared to theoretical values. For instance, the modulus of commercial high tenacity fibres is about 5 GPa, which is only 3% of the crystal modulus along the molecular chains, 165 GPa. This seems to be caused by insufficient unfolding of lamellae contained in the as-spun fibres. Although the ideal structure of an ultrahigh strength fibre is the extended-chain single crystal, it is desired at least to extend and align all the molecular chains under the same tension to induce cooperation in competition with the force. The crystalline regions are constituted only of extended-chain crystals, while the amorphous regions contain a number of tie chains which pass through

Highly oriented fibres or films by the zone-drawing/zone-annealing method 41 1

Table 7. Conditions of zone-drawing/zone-annealing of Nylon 6 fibres Step

Heater temperature ("C)

Tension ( k g / n d )

Heater speed (mm/min)

ZD-1

80 80 80 80 180

0.9 3.17 11.8 18.4 21.5

40 40 40 40 300

ZD-2 ZD-3 ZD-4 ZA-1-

6

Table 8. Orientation and crystallinity of Nylon 6 fibres at each step Step

Birefringence x lo3

fc

f.3

Crystallinity (%)

51.5 62.7

0.856 0.880

0.590 0.824

41.4 49.5

ZD-4 fibre ZA-6 fibre

Table 9. Tensile properties of Nylon 6 fibres at each step Step

Young's modulus

ZD-4 fibre ZA-6 fibre

(GW

Tensile strength (kg/mmZ)

Elongation at break (%)

3.54 11.10

41.4 96.5

49.0 10.6

many crystals and have similar extents of stresses and length. The multistep zone-drawing/zone-annealing method was applied to Nylon 6 fibres in order to achieve such a structure [9-131. The original material was as-spun fibre of 0.41 mm in diameter, birefringence of 9.5 x

X

- 1

LI

1

50

100

150 Temperature ("C)

I

Figure 27. Temperature dependence of the dynamic modulus (E') for Nylon 6 fibres at each step: (- - -) original fibre; (A) ZD-2; (A) ZD-3; ZD-4; (4)ZA-6 fibre

0 0

0 Temperature ("C)

Figure 28. Temperature dependence of the loss modulus (E") for Nylon 6 fibres at each step: (- - -) original fibre; (A) ZD-2; (A) ZD-3; 0 ZD-4; (4) ZA-6 fibre

412

T. Kunugi

and a crystallinity of 29.4 % supplied by Toray Research Center, Inc. The conditions of zone-drawing and zone-annealing are shown in Table 7. Table 8 shows the birefringence, f, and fa, and crystallinity at each step. Although the crystallinity does not exceed 50 %, the birefringence reaches a high value of 0.0627, corresponding to 80 % of the intrinsic crystal birefringence. Table 9 shows the change in tensile properties with the processing. Further, the temperature dependences of E' and E" at each step are shown in Figures 27 and 28. Although the El value increases stepwise with the repetitions of zone-drawing, the attainable value is still low. However, the E' value increases drastically by zone-annealing over the temperature range, and reaches 15.7 GPa at room temperature, which is 9 % of the crystal modulus. The a-dispersion peak observed at 90°C in Figure 28 is ascribed to micro-Brownian motion of large amorphous molecular segments caused by a break down of hydrogen bonds. The peak increases in height and shifts gradually to higher temperatures with the processing. Since the increase of the E" peak height implies an increase in intermolecular friction, this fact suggests that the amorphous molecular chains are densely packed. The high-temperature zone-drawing method was applied to Nylon 66 15

10

-

-.

dc3

v

Q 5-

0 0

50

100

150

200

Temperature ("C) Figure 29. Temperature dependence of the dynamic modulus E' for Nylon 66 fibres at each step; ( 0 )original fibre, (m) HT-ZD-I, (A) HT-ZD-2, ( 0 )HT-ZD-3 fibre

Highly oriented fibres or films by the zone-drawing/zone-annealing method 4 13

Table 10. Conditions of high-temperature zone-drawing of Nylon 66 fibres Step

Heater temperature ( ' C )

HT-ZD-I HT-ZD-2 HT-ZD-3

Tension (kg/mm2) Heater speed (mm/mh) 0.3 2.8 4.1

210 220 230

50 50 50

Table 31. Orientation and crystallinity of Nylon 66 fibres at each step Step HT-ZD-1 fibre HT-ZD-2 fibre HT-ZD-3 fibre

Birefringence x lo3

fc

fa

Crystallinity (%)

64.6 71.4 74.4

0.980 0.981 0.987

0.672 0.774 0.826

33.1 37.3 37.7

fibres as well. The conditions of zone-drawing, and the orientation factors and crystallinity of the obtained fibres are shown in Tables 10 and 11, respectively. Although the crystallinity is relatively low, the orientation, particularly fa increases substantially. Figure 29 shows the change in E' value with the processing. In spite of zone-drawing of only three times, the E' value reaches 13.6 GPa at room temperature and 5.8 GPa at 240OC. 2.6. Poly(ether-ether-ketone)

Poly(ether-ether-ketone) (PEEK) is an outstanding thermoplastic polymer with useful properties including excellent resistances to heat, chemicals and radiation. PEEK can also be used as a high-temperature fibre or film. Since zone-drawing/zone-annealing makes use of a narrow heating zone, this method is quite appropriate for polymers with high Tgand high crystallization temperature, such as PEEK [14-171 and polyimides. The original material was an as-extruded, amorphous PEEK film 110 p m thick, with birefringence of 0.0175 and density of 1.26 g/cm3, supplied by Mitsui Toatsu Chemical Co., Ltd. Strips 2 mm wide and 280 mm long were cut out from the original film. Table 12 shows the conditions of two routes of zone-drawinglzoneannealing. In Route 1, zone-drawing was carried out at 14OoC,i.e. close t o T, (143OC), whereas in Route 2, it was carried out at 17OoC,i.e. close t o the crystallization temperature (173OC). Zone-annealing was performed at temperatures from 2OOOC to 280OC. Figures 30 and 31 show the changes in birefringence and crystallinity with the processing. It was found that the crystallization which occured during zone-drawing at 17OOC depressed the orientation of molecular chains. Furthermore, the crystallites which generated on zone-drawing interfere the crystallization on the subsequent zoneannealing. Consequently, Route 1 is better than Route 2. Namely, zonedrawing results in stretching and alignment of molecular chains, whereas zone-annealing leads to extended-chain crystal structures.

414

T. Kunugi Table 12. Conditions of zone-drawing/zone-annealing of PEEK films Heater temperature (“C)

Tension (kg/mm2)

Heater speed (mm/min)

Route 1 ZD-1 ZD-2 ZD-3 Z A-1 ZA-2 Z A-3 ZA-4

140 140 140 200 240 260 280

1.6 6 9 12 14 15 17

57 57 57 57 57 57 57

Route 2 ZD-1 ZD-2 ZD-3 ZA-1 ZA-2 Z A-3 Z A-4 Z A-5

170 170 170 200 220 240 260 280

1.6 6 9 12 14 16 18 20

57 57 57 57 57 57 57 57

Step

Figure 30. Change in birefringence with Figure 31. Change in crystallinity with the processing of PEEK films: (9) the processing of PEEK films: (4) Route 1, ( 0 )Route 2 Route 1, ( 0 )Route 2

The maximum values of the draw ratio and birefringence are 4.4 and 0.298, respectively. The latter is close to the intrinsic crystal birefringence of 0.321. Figures 32 and 33 show the temperature dependences of E’ and tan 6 for the original film, the zone-drawn films and the zone-annealed ones. The E’ value increases with the processing, reaching 13.3 GPa at room temperature, for the ZA-4 film finally obtained this value being however only 21% of the crystal modulus along the molecular chains. Nevertheless E’ remains high at elevated temperatures, for example 12 GPa at 100°C, 7 GPa at 2OO0C,and 5 GPa even at 300°C. The a-dispersion peak observed in Figure 33 decreases in intensity and shifts to higher temperatures with the processing. In Table 13 the tensile properties at each step are listed. It is found that Young’s modulus and tensile strength reach 11.8 GPa and

Highly oriented fibres or films by the zone-drawing/zone-annealing method 415

21

12

10 h

2W 8

0.10

Y

'q6 4 2 --wm, 0.

I

I

I

1

I

L

1.17 GPa, respectively. The application of zone-annealing to PEEK fibres is illustrated on a commercially available fibre, which is already drawn up to 3 times and has a birefringence of 0.234 and a crystallinity of 28 %. The conditions of zone-annealing are given in Table 14. Zone-annealing is repeated five Table 13. Tensile properties of polyether ether ketone film (Route 1) at each step Step

Young's modulus (GPa)

Tensile strength (kg/-2)

2.39 5.42 8.52 10.16 10.72 11.50 11.69 11.78

-

-

0.32 0.52 0.82 0.85 0.88 0.89 1.17

17.5 15.0 14.3 13.3 11.0 10.8

Original film ZD-1 film ZD-2 film ZD-3 film ZA-1 film ZA-2 film ZA-3 film ZA-4 film

Elongation at break (%)

13.0

Table 14. Conditions of zone-drawing/zone-annealing of commercially available PEEK fibres Step

Heater temperature ("C)

Tension (kg/mm2)

Heater speed (mm/min)

ZA-1 ZA-2 ZA-3 ZA-4 ZA-5

200 220 240 260 280

20 25 30 32 33

50 50 50

50 50

416

T. Kunugi

Table 15. Draw ratio and birefringence of commercially available PEEK fibres zone-annealed at each step Step

Birefringence x lo3

Draw ratio

-

Commercial fibre ZA-1 fibre ZA-2 fibre Z A-3 fibre ZA-4 fibre ZA-5 fibre

0.234 0.278 0.287 0.298 0.301 0.316

1.3 1.4 1.5 1.6 1.7

Table 16. Tensile properties of commercially available PEEK fibres zone-annealed at each step Step Commercial fibre ZA-1 fibre ZA-2 fibre ZA-3 fibre ZA-4 fibre ZA-5 fibre

Young's modulus (GPa)

Tensile strength (kg/mm2)

Elongation at break (%)

6.93 8.50 9.46 10.15 10.50 11.71

0.66 0.77 0.84 0.94 1.03 1.11

23.9 14.9 11.0 10.2 9.5 8.2

Temperature ("C) Figure 34. Temperature dependence of the dynamic modulus (E') for commercial PEEK fibre and zone-annealed PEEK fibre: ( 0 )commercial PEEK fibre, (A) ZA1, (0) ZA-2, (0)ZA-3, ( A ) ZA-4, (m) ZA-5

Highly oriented fibres or films by the zone-drawing/zone-annealing method 417

times with increasing the heater temperature and the applied tension. The final conditions for ZA-5, 28OOC and 33 kg/mm2 are very severe. Table 15 shows the draw ratio and the birefringence at each step. Despite the low draw ratio of 1.7, the attained maximum birefringence is quite high, 0.316. Table 16 shows the change in tensile properties with the processing. Young's modulus and tensile strength reach 11.7.GPa and 1.11 GPa, respectively. Figure 34 shows the temperature dependence of E' for the fibre at each step. These mechanical properties are almost identical to those obtained by zone-drawing/zone-annealing of the amorphous film mentioned above, and are higher by about two times than those of commercial PEEK films. Recently a high modulus of about 20 GPa is obtained with PEEK fibres.

2.7. Polyirnide In the general case of polyimide, a film of the respective polyacid is drawn and then transformed into polyimide by thermal or chemical procedures. Drawing and imidation of the precursor film are often carried out at the same time. The polyimide film has a two-phase superstructure, which consists of ordered and disordered phases. However, the difference in electron density between the two phases is small. Consequently, the polyimide film has a slight drawability and excellent toughness. The zone-annealing method was applied to Kapton H, a typical polyimide film [18,19]. Kapton H film (thickness of 26 pm and density of 1.411 g/cm3) was supplied by Toray-du Pont Co., Ltd. and strips 2 mm wide and 17 mm long were cut out. The conditions of zone-annealing are shown in Table 17. By five repetitions of the zone-annealing, the draw ratio, density, and birefringence increased to 2.4, 1.420 g/cm3, and 0.481, respectively. Table 18 shows the tensile properties of the film at each step. Young's modulus and tensile strength reached 24.0 GPa and 1.06 GPa, and correspond to 7.5 and 2.8 times those of the commercial Kapton H film, respectively. Figure 35 shows the temperature dependences of E' and tan 5 for the fibre at each step. Although the El value is almost unchanged by ZA1-ZA-3, the increments of E' by ZA-4 and ZA-5 are strikingly large. The E' value of the ZA-5 film is 22 GPa at room temperature and 8 GPa even at 4OO0C, which is twice that of Kapton H film at room temperature. Two dispersion peaks appear in the vicinity of 5OoC and 360OC. The first one is the /3-dispersion and the second peak is the a-dispersion. The a-dispersion peak decreases in height and shifts to lower temperatures with the processing. Compared to the results for other polymers, this reverse behaviour is related to the slippages of molecular chains along phenylene rings, because the slippages increase with the parallel orientation of phenylene rings.

418

T. Kunugi

Table 17. Conditions of zone-drawing/zone-annealing of Kapton H films Step

Heater temperature ("C)

Tension (kg/mm2)

Heater speed (mm/min)

ZD-1 ZD-2 ZD-3 ZD-4 ZD-5

300 320 340 360 380

8 15 18 20 25

60 60 60 60 60

Table 18. Tensile properties of Kapton H film zone-drawn at each step Step

Young's modulus

Tensile strength (kg/mm2)

Elongationat break (%)

3.23 10.18 10.28 12.19 15.27 24.01

0.38 0.65 0.75 0.83 0.93 1.06

75.2 11.0 8.2 7.0 6.1 4.3

Kapton H film ZD-1 film ZD-2 film ZD-3 film ZD-4 film ZD-5 film

n nc V.VV

0.05 0.04 '9

c

0.03

e

* 0.02 0.01 01 0

I

I

I

I

I

200 300 400 500 Temperature ("C) Figure 35. Temperature dependence of the dynamic modulus ( E ' ) and tan 6 for zone-drawn Kapton H films

100

Highly oriented fibres or films by the zone-drawing/zone-annealing method 4 19

3. A recent d ev elo p men t of the zone-drawing/zone-annealing method In order to produce more effectively high modulus and high strength fibres, a novel zone-drawing method is recently developed, the so-called “vibrating zone-drawing method” [20]. Vibration parallel to the fibre axis is applied during zone-drawing. The vibration, heat and tension are presumed to cooperate for withdrawing molecular chains from complicated and entangled superstructures. The aparatus is schematically shown in Figure 36. It consists of an amplifier, vibrator equipped with an accelerometer, and zone-heater.

Weight Figure 36. Schematic representation of the apparatus used for the vibrating zonedrawing/zone-annealing method

The original material is an amorphous as-spun P E T fibre, diameter of 248 pm , supplied by Toray Co., Ltd. The most suitable conditions determined after a number of preliminary experiments are listed in Table 19. Table 19. Conditions of vibrating zone-drawing of poly(ethy1ene terephthalate) fibres Step

Heater temperature

Applied tension (k13/mm2)

(“C) VZD-1 VZD-2 VZD-3 VZD-4

0.7 19 30 41

90 120 210 210

Heater speed

Frequency

Amplitude

(Hz)

(w)

(-/mi4 50 50 50 50

100 10 100 100

50 50 50 50

Table 20. Draw ratio, birefringence, f, and fa of PET fibres obtained by the vibrating zone-drawing (VZD) method Step Original fibre VZD-1 fibre VZD-2 fibre VZD-3 fibre VZD-4 fibre

Draw ratio

Birefringence x lo3

fc

fa

-

-

-

-

3.80 6.45 7.65 7.70

0.161 0.240 0.255 0.259

0.982 0.989 0.991 0.991

0.394 0.744 0.753 0.783

T. Kunugi

420 -."

o ,VZd-4 o 0.20 A

,VZd-4 ,VZd-3 ,VZd-2 .VZD-1

'c 0.10 0.05 0

0

50

100

150

200 250

Temperature ( " C )

Figure 37. Temperature dependence of the dynamic modulus (E') for the vibrating zone-drawn PET fibre at each step

0

50

100

150

200

2 0

Temperature ( " C )

Figure 38. Temperature dependence of tan 6 for the vibrating zone-drawn PET fibre at each step

The vibrating zone-drawing is repeated four times by increasing the tension. Table 20 shows the changes in draw ratio, birefringence, f, and fa, and crystallinity with the processing. Although the draw ratio is 7.7, the maximum birefringence reaches 0.259, which corresponds to 83 % of the intrinsic crystal birefringence of 0.310. The maximum fa value, 0.783, is fairly high. Figures 37 and 38 show the temperature dependences of E' and tan 6, respectively. The E' of the fibre finally obtained is 37 GPa at room temperature. The E' value mainatains its high level at elevated temperatures; 29 GPa at 100°C, 19 GPa even at 200OC. From Figure 38 it is found that the a-dispersion peak decreases in height and shifts to higher temperatures with the processing. It is assumed that the amorphous molecular chains are fully extended by the combined action of vibration, heating and tension. 4. Conclusion

As described above, the zone-drawinglzone-annealing method can be applied to a variety of crystalline polymers and improves quite considerably the mechanical properties of fibres or films by means of a simple apparatus and easy procedure [21-281. It is obvious from the linear relation between the draw ratio and birefringence or draw ratio and mechanical properties that the method has an excellent effect on the molecular orientation and formation of extended-chain structures. It is an important characteristic of this method that the resulting fibres or films show high moduli a t el-

Highly oriented fibres or films by the zone-drawing/zone-annealing method 421

evated temperatures. The vertical two-step zone-drawing method is also very useful for producing high strength polymer films or tapes. At present, the study of a high-speed and continuous zonedrawing/zone-annealing method is carried out in our laboratory.

References

T. Kunugi, T. Kunugi, T. Kunugi, T. Kunugi, 5. T. Kunugi,

1. 2. 3. 4. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

17. 18.

19. 20. 21. 22. 23. 24. 25. 26. 27. 28.

I. Aoki, M. Hashimoto, Kobunshi Ronbunshu 38,301 (1981) S. Oomori, S. Mikami, Polymer 29, 814 (1988) T. Ito, M. Hashimoto, J. Appl. Polym. Sci. 28, 179 (1983) T. Suzuki, Polym. Prepr., Japan 36, 1115 (1987) T. Kawasumi, T. Ito, J. Appl. Polym. Sci. 40, 2101 (1990) A. Suzuki, M. Hashimoto, J. Appl. Polym. Sci. 26, 213 (1981) A. Suzuki, M. Hashimoto, J . Appl. Polym. Sci. 26, 1951 (1981) C. Ichinose, A. Suzuki, J. Appl. Polym. Sci. 31,429 (1986) A. Suzuki, C. Ichinose, Kubunshi Ronbunshu 49, 69 (1992)

T. Kunugi, T. Kunugi, T. Kunugi, T. Kunugi, T. Kunugi, I. Akiyama, M. Hashimoto, Polymer 23, 1193 (1982) T. Kunugi, I. Akiyama, M. Hashimoto, Polymer 23, 1199 (1982) T. Kunugi, T. Ikuta, M. Hashimoto, K. Matsuzaki, Polymer 23, 1983 (1982) A. Suzuki, T. Kunugi, S. Maruyama, Konbunshi Ronbunshu 49, 741 (1992) T. Kunugi, T. Hayakawa, A. Mizushima, Polymer 32,808 (1991) T. Kunugi, A. Suzuki, J. Itoda, Kubunshi Ronbunshu 47, 961 (1990) T. Kunugi, Pacific Polymer Prepr., Pacific Polymer Federation (Hawaii) Vol. 1,95 (1989) T. Kunugi, Proc. of the MRS International Meeting on Advanced Materials Vol. 1, 201 (1989) T. Kunugi, Progr. and Abstr., Polymer Processing SOC.,3/7 (1988) (Florida) T. Kunugi, Japan Pat, Kokai Sho 63-197628 (1988) T. Kunugi, 34th IUPAC Intern. Symp. Macrom., Prague 1992, Abstr., 2-P89 T. Kunugi, Japan Pat., 1343924 Showa 54 (1979) T. Kunugi, Japan Pat., 1461970 Showa 54 (1979) T. Kunugi, Japan Pat., 1499541 Showa 56 (1981) T. Kunugi, Japan Pat., Kokai Sho 61-244834 (1986) T. Kunugi, Japan Pat., Kokai Sho 61-255833 (1986) T. Kunugi et al., Japan Pat., Kokai Sho 63-293035 (1988) T. Kunugi et al., Japan Pat., Shutu. Sho 63-105834 (1988) T. Kunugi et al., Japan Pat., Shutu. Hei 2-138001 (1990)

Oriented Polymer Material> Stoyko Fakirov Copyright 0 2002 Wiley-VCH Verlag GmbH & Co. KGaP

Chapter 14

Alternative approaches to highly oriented polyesters and polyamides with improved mechanical properties

S. Fakirov

1. General considerations

The development of high performance polymer materials is one of the main subjects in contemporary materials science. Such polymers are distinguished by a structure usually involving (i) maximal orientation of macromolecules, (ii) perfect crystallites built up of extended chains and (iii) a relatively high molecular weight of the polymer. There are two principal and basically different approaches to the realization of high modulus and high stregth polymer materials: synthesis of new polymers with “tailored” properties and structural modification of known and widely applied polymers. Liquid crystalline (lyotropic and thermotropic) polymers represent a good illustration of the successful synthesis of new types of materials. Despite their excellent mechanical properties, this new class of polymers still has limited practical application, mainly due to high production costs [l] (see Chapter 17). The methods based on structural modification of commercial polymers are much more accessible. They can be classified as cold or hot drawing [1,2], solid state extrusion [l-31, zone drawing [4,5] (see Chapter 13) and rapid drawing from melts or solutions [1,6,7]. These mechanical and/or thermal treatments result in transformation of the isotropic structure into

Alternative approaches to highly oriented polyesters and polyamides

423

a fibrillar one [1,2]. The models of microfibrillar morphology proposed by Peterlin (for polyolefins [2]) and Prevorsek (for polyesters and polyamides [8]) provide a very good explanation of some properties, particularly the mechanical properties. The concept that the mechanical properties of the fibrillar material are determined to the greatest extent by the number of molecules under stress is generally accepted. Because tie molecules represent about 1-3% [2] or about 10-20% [9] of the total number of chains in the crystallites, it is quite natural that the achieved maximal values of the tensile strength (u)and the elasticity modulus ( E ) are considerably lower (by orders of magnitude) than those calculated theoretically or observed with liquid crystalline polymers. The high mechanical parameters in the latter case result from the supermolecular organization of liquid crystalline polymers: maximal alignment of parallel chains in the absence of chain folding. Unfortunately, such a fibrillar morphology has not been obtained in polyolefins and particularly in polycondensates. The lower ability of condensation polymers to form such a structure as compared to polyolefins is related to their peculiarities - larger crosssection of the macromolecules, more irregular chain structure, lower molecular weights (see also Chapter 11). The desired supermolecular structure is usually achieved by thermal and mechanical (orientation) treatment. During thermal treatment at elevated temperature, together with structural changes (crystallization and relaxation) , condensation polymers could undergo chemical interactions, e.g. additional condensation, destruction, exchange reactions, due to the presence of reactive groups in these polymers (-CONH-, -COOHI -NH2, -OH, -COO-) in contrast to polyolefins where only destruction could take place [lo]: Additional condensation (AC):

4 O O H

+ HO-

-Ha0

4 0 0 -

Trans- (or ezchange) reactions (TR):

HN-

-CcO

-NH

I

+ I

+

-CONH-

+-NHCO-

OC-

Both types of reactions are studied quite well because of their commercial importance [11,12]. The solid state additional condensation is the common way for manufacturing of polyester or polyamide based engineering

424

S. Fakirov

plastics destinguished by increased molecular weights [11,12]. The higher molecular weight enhances not only the processing but also improves considerably the mechanical parameters of these plastics. Such materials are characterized by very high deformation ability even at ambient temperature (up to 15 times [14]) as demonstrated on fibres and films of polyethylene ter aphthalate [10 ,13 ,141. Solid state reactions affect not only the processing conditions and mechanical behaviour of linear polycondensates. Additional condensation and trans (exchange) reactions can be used to eliminate defects in the fibrils, originating from chain ends, entanglements and chain folds, as shown schematically in Figure 1. It should be added here, that besides the molecular weight increase, additional solid state condensation results in the rise of the number of tie molecules. In contrast to the chemical aspects of solid state reactions, their role in the creation of the physical structure in condensation polymers is rather underestimated, as emphasized by Wunderlich [15]. Before discussing some results suggesting a possibility of considerable improvement of the mechanical properties of condensation polymers by means of solid state rections, let us try to answer a very essential question:

-CO NH-CO~NH-

-COOH -NY

TR,

NH-% (CO-

AC

Figure 1. Schematic representation of elimination of defects through solid state reactions in linear polycondensates: AC - additional condensation, T R - trans reactions

Alternative approaches to highly oriented polyesters and polyamides

425

what is the most favourable initial state of the polymer - completely amorphous, maximally crystalline or semicrystalline one, for the obtaining of highly oriented macromolecular systems with perfectly alligned chains. 2. Improvement of the mechanical properties of polycondensates by ultraquenching of their melts

2.1. Creation of optimal initial structure for preparing highly oriented polycondenaates According to Peterlin, a highly oriented system can be obtained only by starting from highly crystalline polymers, at least in the case of polyethylene [2]. It has been established, however, that polyethylene with very low crystallinity, obtained by rapid cooling, exhibits a drawability higher by an order of magnitude as compared to that of the maximally crystalline polymer [16]. The amorphous state seems to be more appropriate for drawing and orientation in the case of polymers with low chain flexibility. This assumption is checked first. In order to obtain samples with as low crystallinity as possible (or completely amorphous ones) a technique for ultraquenching was developed [17,18]. The facilities for ultraquenching are similar to those used in the production of glassy metals. Ultraquenching has been carried out as follows [18]. Commercial powdery dried polymer was molten in the barrel of an Instron capillary rheometer and after a retention for 10-20 min a t a temperature higher by 20-40°C than the melting point, the melt was extruded (at a rate of 5-10 mm/min) trough a nozzle on metal rolls rotating at about 30-80 rpm immerced in a cooling bath (-20 down to -15OOC). The distance between the rolls and the nozzle was kept as small as possible in order to achieve rapid quenching of the polymer melt. In this way a continuous film (4-6 mm wide and 0.08-0.12 mm thick, depending on the roll-to-roll distance and extrusion rate) was obtained and tested with or without additional treatment. In some cases the samples were stored under ambient conditions (designated further as “stored samples”) and thereafter mechanical and thermal treatments were carried out, followed by static mechanical tests. Drawing and testing were performed at room temperature at a cross-head speed of 5 mm/min. In general, drawing of the ultraquenched samples was carried out to the maximal achievable degree. Annealing was carried out in a vacuum oven (40 mbar) for 6 h, the drawn samples being always with fixed ends. For the sake of comparison, commercial films of Nylon 6 (PA 6) and poly(buty1ene terephthalate) (PBT) were subjected to the same treatment (except for ultraquenching) and tested. The first conclusion based on these studies [17-191 is that the mechanical properties of the starting commercial and ultraquenched undrawn

426

S. Fakirov

(stored) samples are almost the same, except for their drawability. The ultraquenched samples have A = 7.0 (PA 6 ) and A = 8.0 (PBT) against A = 4.0 and 4.5, respectively, for the commercial materials. At the maximum draw ratio (A = 7-8) the tensile strength u and the elasticity modulus E double their values for both polymers subjected to ultraquenching, the elongation at break, 6, being in the same time reduced by three times. After thermal treatment at 12OOC for 6 h of the drawn samples, the observed relationships are preserved in general. Taking into account that the E-values of the starting materials are of the same order of magnitude (ca. 1 GPa), it should be pointed out that drawing and subsequent annealing at 12OOC of the commercial samples lead only to twice higher values while a drastic increase of E is observed with the ultraquenched samples - by 6 times for PA and by 5 times for PBT [18]. Considering the fact that both types of materials - commercial and ultraquenched undrawn ones - have undergone the same thermal treatment, the observed strong increase of the elasticity modulus can be attributed only to the better orientation due to the enhanced drawability at room temperature (A = 7-8) which, by the way, is not observed with as-quenched samples (the maximal draw ratio achieved is of about 3-3.5 ~71). Coming back to the basic question - what should be the starting polymer structure in order to achieve maximum orientation - one has to recall the existence of numerous reports on the poor drawability of amorphous polymers [20-241. The commercial samples have higher crystallinity than those subjected to ultraquenching and storage as revealed by calorimetric and X-ray measurements [18].If drawing is enhanced by higher crystallinity, one should expect higher draw ratios for the commercial samples but just the opposite situation is actually observed. The results lead to the following assumption: the most favourable structure for the achievement of high orientation is the crystalline but imperfect one. Ultraquenching of the polymer melt, particularly after thermal treatment above the melting temperature, creates an almost amorphous or slightly crystalline structure. Subsequent storage at room temperature preserves this structure or causes additional crystallization under very unThus, the crystalline phase should confavourable conditions (close to Tg). sist of a large number of small and imperfect crystallites. Another characteristic feature of this imperfect structure is the lack of large, spatially well defined regions, differing substantially in their electron densities (i.e. crystalline and amorphous regions), as demonstrated by small angle X-ray scattering (SAXS) curves [18]. It can be concluded that for the preparation of highly oriented polyesters and nylons (resulting further in high-strength and high-modulus fibres), one has to start with a disordered polymer, the amorphous matrix of which embeds a large number of small crystallites. Such a structure can be created by ultraquenching of a polymer melt in the shape of thin films or fibres.

Alternative approaches to highly oriented polyesters and polyamides

427

Another peculiarity of the ultraquenched samples is their lower concentration of chain folds in crystallites, as compared to commercial ones. It is well known [25] that the IR-spectral band at 988 cm-' in the case of PBT (and PET) is assigned to chain folding in the crystallites. The IR spectra of films of both types of samples are shown in Figure2. It is seen that annealing of drawn commercial samples results in a strong increase of the band at 988 cm-l (Figure2A, curve (c)) which is not observed with ultraquenched samples (Figure 2B, curve (c)). Further, unlike commercial samples, the higher draw ratio of the ultraquenched ones (A = 8 against X = 4.5)destroys drastically the chain folds.

L

1100

I

I

1003

9@

I

I

800 NOD

I

1

I

1OcK)

9W

8cx)

cmA

Cm'

8

Figure 2. IR spectra of commercial (A) and ultraquenched stored (B) films of PBT undergone additional treatments as follows: (A) commercial: (a) untreated; (b) drawn (A = 4.5); (c) drawn and annealed at 21OOC for 6 h; (B) ultraquenched and stored: (a) untreated; (b) drawn (A = 8); (c) drawn and annealed at 210°C for 6 h

428

S. Fakirov

2.2. Ultraquenching with previous melt annealing

Except for PET, polymers crystallize very fast from their melts and their obtaining in the glassy state is rather difficult. This is also valid for PA 6 regardless of how rapidly the melt has been cooled down [26]. In the same time the crystallization kinetics of PA 6 strongly depends on the thermal history of the melt [27,28]. As reported recently [27], the melt memory effect has a cumulative +aracter, e.g. the erazing of the memory depends on the annealing temperature and duration. A critical tempearture of Ta = 28OOC was found, above which the memory disappears completely. It turned out that this temperature value coincides with the equilibrium melting tempearture of PA 6 which was determined independently [29]. It can be concluded that annealing of PA 6 melts above 28OOC results in the removal of all crystalline residues playing the role of nuclei in subsequent crystallization. Taking into account these observations and using the ultraquenching technique described above, an attempt was made to obtain completely amorphous PA 6 [30,31]. The as-quenched sample showed just an amorphous halo on wide angle X-ray scattering (WAXS) diffractograms, a glass transition temperature Tg as well as a crystallization peak on the traces of the differential scanning calorimeter (DSC), in contrast to the other samples subjected to annealing after ultraquenching [32]. These results are supported by the data on structural relaxation in the glass transition region [32]. In this way the cooling rate was determined to amount to 470°C/min [32], i.e. it is close to that of ultraquenched PET (400°C/min [33]). The preparation of the ultraquenched films was carried out as described above, without or with annealing of the melt for 20 min a t 3OOOC before extrusion. These films and commercial ones were cold drawn up to the maximum values (A = 3-5) and thereafter annealed (the drawn ones at constant strain) for 6 h at 190OC. The results of static mechanical measurements are summarized in Table 1 [32]. It is seen that regardless of the sample history, both drawing and thermal treatment lead to an improvement of the mechanical properties which is in agreement with numerous reports [1,10,34]. However the most striking observation is that the ultraquenched samples with previous annealing of the melt show almost three times higher tensile strength, two times higher modulus and lower elongation than the commercial samples (Table 1,I). Similarly to the situation with glassy metals [35], these results demonstrate the peculiarity of amorphous solids - higher tensile strength than that of the crystalline ones with the same chemical composition. The same trend is observed with the drawn samples (Table 1,II). The ultraquenched samples obtained from a previously annealed melt show two times higher tensile strength and modulus, retaining the same elongation at break. The same magnitudes are even higher (up to three times at a twice lower elongation at break) for the samples annealed at 17OOC for 3 h and

Alternative approaches to highly oriented polyesters and polyamides

4%

Table 1. Static mechanical data of commercial Nylon 6 , ultraquenched Nylon 6, and ultraquenched Nylon 6 with previous annealing of the melt [32] Treatment and parameters followed

Commercial Ultraquenched Ultraquenched Nylon 6 Nylon 6 with Nylon 6 (DuPont) previous melt annealing (20 min at 300' C)

I. Before drawing 1. Elasticity modulus, GPa 2. Tensile strength, MPa 3. Relative elongation at break, %

0.5 40 300

0.2 55 90

0.8 110 200

1.1 110 20

0.4

55 20

2.5 250 25

1.3 150 20

0.8 120 25

4.5 360 9

11. After cold drawing 1. Elasticity modulus, GPa 2. Tensile strength, MPa 3. Relative elongation at break, %

111. After cold drawing and annealing for 3 h at 170'C 1. Elasticity modulus, GPa 2. Tensile strength, MPa 3. Relative elongation at break, %

obtained by ultraquenching of a previously annealed melt (Table 1,111). These results lead to another important assumption. Under the conditions chosen, ultraquenching itself would hardly produce completely amorphous PA 6. Only the thermal treatment of the melt at a higher temperature, aiming at the destruction of the existing crystallization nuclei can prevent subsequent crystallization during the rapid cooling and results in the obtaining of more or less completely amorphous PA 6 [31]. It is worth noting another peculiarity of amorphous PA 6 - its lower drawability at room temperature as compared to that of commercial films ( E = 200% agianst E = 300%, Table 1,I). As far as the ultraquenched (with melt annealing) sample is the most amorphous one, this observation confirms the above conclusion that the most appropriate starting structure for optimal orientation - the completely amorphous state is hardly the best one. 2.3. Ultraquenching of polymer blends Blending of crystallizable polymers is another approach to the suppression of crystallization from melts. This technique was also used for the preparation of amorphous polyesters by means of ultraquenching [36]. The ultraquenched polymer blends of various ratios were prepared in the same way as the homopolymers. Because of the low crystallization rate, particularly

S. Fakirov

430

of PET, melt annealing was not applied. The melt at 31OOC was quenched at a rate of 400°C/min [33]. According to WAXS and DSC measurements, the strips obtained were amorphous [33,37]. The results of mechanical tests of the PBT/PET blend (1:l by wt.) are shown in Table 2 together with data of commercial PET and PBT processed in the same manner (but not subjected to ultraquenching) presented for the sake of comparison. Table 2. Static mechanical data of commercial PET and PBT films as well as of ultraquenched PET/PBT blend (1:l by wt.) [36] Treatment and parameters followed

Commercial Commercial Ultraquenched PET film PBT film PET/PBT blend

I. Before drawing 1. Elasticity modulus, GPa 2. Tensile strength, MPa 3. Relative elongation at break, %

1.1 55 320

1.0 40 430

160 400

1.4 230 320

3.5 165 80

1.2 260 30

5.5 250 20

1.0

11. After cold drawing 1. Elasticity modulus, GPa 2. Tensile strength, MPa 3. Relative elongation at break, %

111. After cold drawing and annealing for 6 h at 190°C 1. Elasticity modulus, GPa 2. Tensile strength, MPa 3. Relative elongation at break, %

2.3 220 40

The data presented in Table 2 show that similar to the case of homopolymers (Table l), ultraquenching of polymer blends is a technique improving the mechanical properties. The as-quenched samples show much higher tensile strength and subsequent drawing and annealing lead to materials with improved modulus, compared to the commercial ones subjected to the same mechanical and thermal treatment. 3. Improvement of the mechanical properties of oriented polycondensates by drawing and thermal treatment 3.1. Contribution of solid state reactions to the improvement of the mechanical properties of polyesthers and polyamides

As pointed out in the introduction to this chapter, the ideal structure resulting in optimal mechanical parameters should be characterized by as much as possible stretched chains, of the highest molecular weight, perfectly aligned to each other. Solid state reactions are expected to contribute to the fulfillment of these requirements by achievement of maximum molecular

Alternative approaches to highly oriented polyesters and polyamides

43 1

weight values and creation of a perfect structure by elimination of defects (Figure 1). Starting by the experience available [11,34],it seemed that such a structure can be realized by two-stage cold drawing, each stage followed by high tempearture annealing [38]. The structural and chemical changes in oriented polycondensates taking place during these thermal and mechanical treatments are outlined in Figure3. After the first cold drawing (up to A = 5 ) the polymers are subjected t o annealing in vacuum at a temperature close to but below the melting one (T, = 26OOC in the case of PET, FigureS(a). In addition to crystallization and relaxation, chemical reactions take place during this treatment, resulting in the elimination of defects (Figure 1) and increase of the molecular weight and hence to improved drawability [10,13,34]. These changes occurring during annealing are presented schematically in Figure 3(a,b).

I

I

C

d

AC

-

h

T

(260“C1

I

(6-20)

TR‘

I

..

I a

b

Figure 3. Models illustrating the physical and chemical changes in oriented partially crystalline PET subjected to additional drawing and annealing with fixed ends: (a) structure of the sample after cold drawing (A = 4.5); (b) structure of the same sample after annealing (T, = 26OOC); (c) structure of the same sample after a second cold drawing (A = 15-20); (d) structure of the same sample after a second annealing (T, = 250-270OC). AC - additional condensation; TR trans (exchange) reactions; the dashed line denotes two separate microfibrils [38]

432

S. Fakirov

When an oriented and annealed partially crystalline high molecular weight material (Figure 3(b)) is subjected to a second drawing, conformational changes related to the complete extension (at moderate stresses) of the macrochains in the amorphous regions are effected along the direction of the external strain. Further drawing could result in the destruction of the crystallites by chain defolding and alignment in the draw direction. Such a conformational transition has already been proved for PET [39], PA 6 [40], and PBT [41]. The structure created as a result of such mechanical treatment is shown schematically in Figure3(c) (see also Chapter 13). All these changes in highly oriented linear polycondensates lead to further perfection of the crystallites of extended macrochains and correspondingly to a small increase of the density of the crystalline regions ( p c ) and the density difference ( A p ) between the crystalline and amorphous regions. For this reason a slight rise of the overall scattering power of SAXS is quite probable in comparison to that of unannealed highly oriented (A = 15-20) samples. The final morphological structure of highly oriented polycondensates illustrated in Figure 3(d) is simillar to that of polymers obtained from liquid crystalline mesophases (parallel alignment of the chains along the fibril axis). It is quite natural to expect that a polymer with such supermolecular structure should be characterized by very good mechanical properties due to the great number of chains bearing the external mechanical strain and to the presence of strong molecular interactions. In view of the practical application of polycondensates with improved mechanical properties, evidence should be provided about the extent to which the above discussed processes actually occur. SAXS curves of samples with different draw ratios (A = 5 and X = 20) are shown in Figire4. It is seen that five-fold drawing (Figure4, curve (a)) does not lead to the appearance of a SAXS maximum. This is an experimental indication of the absence of alternating regions with a substantial density difference in the structure of these samples. It can be concluded from this observation that the material consists of more or less extended chains, building up a predominantly amorphous phase embedding a large number (but small in size) of defective crystallites (Figure 3(a)). WAXS studies of the same samples confirm this conclusion [38]. Thermal treatment of this material (T, = 260OC) leads to considerable structural changes, as indicated by the change in the trend of the curve (b) shown in Figure4. This experimental evidence of the structural changes is presented in Figure 3(b). The simultaneous crystallization and relaxation processes during thermal treatment leads to formation of alternating crystalline and amorphous regions; perfection of the crystallites resulting in a significant rise of pc and subsequently of Ap and appearance of a long spacing, L. The much more perfect crystalline structure of these samples is confirmed by their WAXS patterns [38]. The absence of a SAXS maximum in the samples with X = 20 (Figure4,

Alternative approaches to highly oriented polyesters and polyamides

2 '-

433

1600-

E

\

._ 2 1200-

L

4"

800 -

400 -

Figure 4. SAXS curves of a drawn PET bristle: (a) X = 5, unannealed; (b) X = 5, annealed at 26OoC for 6 h; (c) X = 20, unannealed; (d) X = 20, an-

curve (c)) is an indication of the disappearance of the alternating structure caused by the second drawing at room temperature as well as of partial destruction of the crystallites through defolding and extension of the chains in the draw direction, as shown in Figure 3(c). The slight shift of the SAXS curve to higher intensities suggests a more perfect structure of the crystallites comprising mainly extended chains as compared to the small and more defective ones built up of folded chains in the case of samples with X = 5 (FigureS(a)). Figure4, curve (d) shows the SAXS of the sample with X = 20 annealed at 26OOC. In this case, too, a SAXS maximum is not registered. This fact is an experimental confirmation of the assumption, that due to the extremely low molecular mobility in a highly oriented polymer system with very strong intermolecular bonds, the occurrence of physical (crystallization and mostly relaxation) processes is strongly hampered. The insolubility of this material (in a phenol-tetrachloroethane mixture, 1:l by wt., at 14OOC [42]) is an indirect proof of the creation of a dense packing with strong molecular interactions. The slight shift toward higher intensities of the SAXS curve (without the appearance of a maximum) of the twenty-fold drawn samples annealed at 26OOC (Figure4, curve (d)) is an indication of the increase of the sample density as a result of perfection of the structures, mostly of the crystallites. The results of the mechanical tests of samples with different draw ratios (A = 5 or 20) are presented in Table 3. They are a further experimental proof of the difference in the morphological structures of both materials. It is seen that the samples with X = 5 annealed at 260°C for 6 h show an extremely high deformation ability ( E = 320%, Table 3, Sample 3). The latter is an indication that, under these conditions, the chemical reactions presented in Figure3(b) have taken place with a subsequent rise in the molecular weight. Taking into account that the five-fold drawn samples are subjected to a second drawing at room temperature (after annealing a t 26OoC), the total draw ratio amounts to X = 20. It is seen in Table 3 that

434

S. Fakirov

the tensile strength and elasticity modulus of the samples with X = 20 are almost twice as high as those of the samples with X = 5 (u = 0.51 GPa and E = 13.8 GPa against u = 0.22 GPa and E = 9.3 GPa, Table 3, Samples 1). After annealing at 200°C the samples with X = 20 have E = 18.6 GP a and u = 0.6 GPa. These parameters become slightly lower when annealing is carried out at 26OOC but their values are three times ( E ) and four times (u)higher than those of the samples with X = 5 annealed at the same temperature (Table 3, Samples 3). Table 3. Mechanical tests of drawn PET bristles annealed under constant strain [38] X = 5, annealed for 6 h

Sample No.

T, ("C)

1 2 3

unannealed 200 260

X = 20, annealed for 2 h

(GPa)

E (GPa)

(%)

0.51 0.60 0.57

13.8 18.6 16.7

17 16 18

E

U

(GPa)

E (GPa)

(%)

0.22 0.26 0.14

9.3 11.5 6.5

61 38 320

U

E

These substantial differences in the mechanical properties of both materials are mainly due to the relatively greater number of chains under stress bearing the external strain as well as to the strong molecular interactions in the highly oriented material. This statement is also supported by the fact that the samples with X = 20 show a rather low and constant elongation a t break (16-18%) regardless of the annealing temperature, in contrast to the case of X = 5 (38-320%). An attempt was made to evaluate the amount j? of the taut tie molecules (TTM) [43]. Depending on the model used for these calculations, one differentiates between the case when all TTM are concentrated on the outer boundary of the microfibril (intermicrofibrillar TTM, p') and the case when the TTM are almost uniformly distributed over the entire cross section of the microfibril (intramicrofibrillar TTM, p") [44]. Under the restriction E, >> E,, where E, is the axial elastic modulus of a single crystal (for P E T it amounts to 107.8 GPa [45]), and E, is that of the completely amorphous sample, one obtains P' = E / E , and P" = (1 - w c ) E / E c ,where E is the experimentally measured value of the axial elastic modulus [44]. In the first case (P'), the elastic modulus is strictly proportional to the fraction of TTM per layer; in the second case (PI'), the elastic modulus is always higher than in the first one. Further, the proportionality of the elastic modulus to the fraction of TTM (intramicrofibrillar, intermicrofibrillar and interfibrillar) yields an almost linear increase in the axial elastic modulus E with the draw ratio X since the fraction of intermicrofibrillar and interfibrillar TTM is almost proportional to the draw ratio of the fibrous structure [44]. It turned out that for both series of P E T samples (with X = 5 and X = 20) the two magnitudes p' and pll increase in a broad annealing

Alternative approaches

t.0

highly oriented polyesters and polyamides

435

temperature range up to 220-240°C and thereafter they drop. What is more striking, the values of both p’ and pl’ are almost doubly higher for samples with X = 20 than those for samples with X = 5 [43]. These experimental data represent a convincing proof of the conformational transitions and chemical changes illustrated in Figure l for polycondensates subjected to mechanical (orientational) and thermal treatment. All these processes contribute to the formation as well as to the perfection of the structure of highly oriented polycondensation materials. Such a structure results in improved mechanical properties as compared to those of commercial polymers with the same chemical composition [46]. 3.2. I m p r o v e m e n t of mechanical properties of polyesters a n d polyamides by zone annealing u n d e r stress

The zone drawing and zone annealing method proposed by Kunugi and co-workers is frequently used for the preparation of highly oriented fibres or films with improved mechanical properties (see Chapter 13). Taking advantage of our previous observation (see Section 2.2) that rapid cooling after extrusion results in better drawability, PET pellets were extruded in a cooling ice-water bath [47]. The resulting amorphous (according to the X-ray tests) filaments (diameter of 0.15 mm) were drawn at ambient temperature at 50 mm/min to X = 7 and thereafter blown with warm air (about 6OOC) for 5 min, followed by a second drawing up to total X = 9 and then blown again (5 min, 60-70OC). In this way the starting Sample 1 was prepared (diameter of 0.065 mm and crystallinity wc(p) = 0.24, Table4). A bunch of such filaments was subjected to zone annealing under stress using a 2 mm wide heater. By varying the applied stress, temperature and number of passages of the heater along the filaments with X = 9, four types of samples (2-5, Table 4) were prepared. Samples 6 and 7 (Table 4) were obtained from Sample 1 by annealing with fixed ends for 1 h at 15OOC and 2OOOC respectively, i.e. by non-zone annealing. The results of the structural characterization and mechanical tests are presented in Table 4. SAXS measurements show that the starting material (Sample 1, Table 4) has no scattering maximum, indicating the absence of sufficiently large regions of different density. The structure of this sample can be described by the model in Figure 3(a). All samples subjected to zone annealing (Samples 2-5, Table 4) show a well expressed maximum (similar to curve (b) in Figure4) in contrast to the non-zone annealed ones (Samples 6 and 7, Table 4) since a maximum is not observed for T, = 15OOC while that for T, = 2OOOC is quite weak [47]. Comparison of the two types of annealing suggests that during zone annealing for a much shorter time (several minutes against 60 minutes) a t lower temperature (14O-16O0C against 150 and 2OOOC) a more regular structure is created due to the mechanical tension. It is interesting to compare the mechanical parameters of the samples presented in Table 4. The zone annealed Sample 3 is characterized by the

100 100 100 150 150 150 100 150 200 100 150 200

150 200

Ta("C)

-

140 150 160 140 150 160 150 150 150 140 150 160

-

2 4 5 2 4 5 2 2 4 2 4 5

-

1 1

ta (h)

' Annealed with fixed ends

6' 7'

5

4

3

1 2

Sam- Applied Tza Number of ple stress ("C) heater's No. (MPa) passages

Zone ann. conditions

234 234

238

-

235

-

230

265 262

262

-

262

-

260

0.51 0.49

0.43

-

0.45

-

0.30

T& T: wc ("C) ("C) (DSC)

DSC

121

-

154

141

144

141

-

(A)

L

0.36 0.32

0.37

0.38

0.41

0.39

0.24

wC(p)

0.240 0.275

0.330

0.275

0.250

0.230

0.220

An

Structural parameters

0.69 0.72

0.92

0.89

0.96

0.83

0.66

17.2 17.8

20.3

19.2

19.4

19.1

15.4

p'

p"

0.1880 0.1186

0.1782 0.1062

0.1803 0.1062

0.1774 0.1081

14.0 0.1596 0.1021 14.0 0.1651 0.1123

6.4

6.8

7.2

9.3

15.2 0.1429 0.1086

U E E (GPa) (GPa) (%)

Mechanical parameters

Table 4. Zone (Tza) and non zone (T,) annealing conditions, calorimetric data (Tm),long spacing (L), degree of crystallinity ( w c ) , birefringence coefficient (An), mechanical parameters (a,E, E ) , total number of tie molecules ( E / E c ) and taut tie molecules fraction (1 - w , ) E / E , of drawn (A = 9) PE T filaments [47]

w

4

s

7

v,

0,

Alternative approaches to highly oriented polyesters and polyamides

437

highest tensile strength value u = 0.96 GPa which is higher by 30% than that of the starting Sample 1. In the same time the elasticity modulus is rather high ( E = 19-20 GPa) for all zone annealed samples (Samples 2-5, Table 4) and exceeds by 25% that of the starting material. The mechanical characteristics of the non-zone annealed Samples 6 and 7 are inbetween those of the starting sample and the zone annealed ones. The observed considerable improvement of the mechanical properties of zone annealed filaments is related to the increased amount of interfibrillar TTM p', as it can be seen in Table 4. The fraction of intrafibrillar T T M p" remains, however, almost unchanged in accordance with the considerations of Peterlin [44]. The same approach to the improvement of the mechanical properties was applied to P E T films (with almost the same results [48]) and to PA 6 filaments [49]. In the latter case cold drawing resulted in X = 7.6 and the mechanical characteristics doubled their values as compared to the starting material, reaching u = 0.91 GPa, E = 8.7 GPa and E = 15%, respectively [491f Finally, it should be noted that, taking into account the relatively low temperatures of zone annealing and its short duration, it is hard to expect the occurrence of solid state reactions. For this reason, the observed improvement in the mechanical properties should be attributed solely to physical processes creating a supermolecular structure that leads to optimal mechanical behaviour. 4. Attempts to overcome the mechanical anisotropy of highly drawn polymer films

4.1. Cross-plied laminates bonded through physical healing of highly drawn polyolefin films A generality pertaining to oriented films is that the greater the degree of orientation in one direction to impart high levels of mechanical properties, such as tensile strength, the lower the level of properties in the transverse direction. In uniaxially oriented films both tensile strength and elongation at break in the direction transverse to orientation can be so low that during ordinary processing or manipulation the film fibrillates, becoming useless for some applications which could otherwise employ the high tensile strength. Biaxially oriented films of good balance of properties can also be produced but in an effort to make biaxially oriented films of very high tensile strengths by segmental drawing, the high strength attained in the first direction draw is diminished by the second direction draw. Thus, attempts have been made to fabricate cross-lapped, interfacially bonded laminar structures with the direction of orientation at an angle to each other in successive laminae or layers to capitalize on the very high tensile strength of uniaxial films. In the common methods of bonding, adhesives have been

438

S. Fakirov

less than totally suitable and fusion bonding destroys or excessively diminishes orientation, defeating the purpose of orientation to produce a high level of mechanical properties [50]. Interfacially bonded structures or laminates fabricated from hundreds cross-plied extremely high oriented polypropylene films display unique properties. Because of the very high impact strength and transparency to microwaves, they are used as armor for protection of radar antennas from balistic objects. The bonding of the layers is a result of mutual diffusion of macromolecules through the interface boundary during the pressing of the laminates at elevated temperature (close but below the melting one). As far as in this case one deals with physical healing, the higher the processing temperature, the better the interfacial bonding is but in the same time a loss of orientation is observed. For this reason, attempts have been made [50-521 to the improvement of the bonding of polypropylene films even at lower temperature, using two approaches. According to the first one [50,51] a very thin layer of polyethylene has been deposited (from solution) on the polypropylene surface prior to lamination. The processing is carried out slightly above T, of polyethylene but far below T, of polypropylene so that the polyethylene molecules could penetrate into the contacting surfaces of polypropylene films, thus ensuring a good welding of the interfaces. The second approach [52]aims a t the creation of chemical linkage between polypropylene molecules belonging to two adjacent layers. This is achieved by interspersing catalysts for crosslinking (dicumyl peroxide and benzoyl peroxide) between two contacting laminae or sheets, urging the sheets into intimate contact by application of pressure and heating the laminate to a temperature effective to activate crosslinking of the polymer chains in the presence of the catalyst but considerably below the melting point of the laminae. 4.2. Laminates bonded through chemical healing of highly drawn

polycondensate films

Physical healing representing a mutual self-diffusion across the interface boundary supposes high chain mobility, i.e. only the chains from amorphous phases can be involved as far as the process is carried out below the melting point [ll,121.Condensation polymers being usually crystalline and distinguished by higher chain rigidity are less inclined t o physical healing than polyolefins. However, due to their ability to undergo solid state reactions (Figure l), they show a new type of healing - chemical healing in addition to the physical one [11,12,53-581.A serious advantage of chemical healing as a welding technique resides in the fact, that chemical interaction resulting in joining two pieces being in contact is possible even between chains incorporated in the crystallites. Further, since solid state reactions are observed between species differing in chemical composition, a heterochemical healing has been reported [55].The existence of chemical healing

Alternative approaches to highly oriented polyesters and polyarnides

439

has been proved by experiments excluding or strongly suppressing physical diffusion using crosslinked polyamides as partners in the welding [56] or polymers distinguished by very rigid molecules (native cellulose [SS]). Chemical healing can be accelerated by spreading of catalysts of transreactions or additional condensation on the contact surfaces [59]. Lamination through chemical healing allows to overcome a peculiarity of liquid crystalline polymers - their molecular orientation strongly depends on the article thickness. For this reason, the thickness increase leads to a loss of the unique mechanical properties of this class of polymers. Thicker articles can be obtained using thin (15-200 microns) highly oriented foils by lamination (parallel or crossplied) and bonding through chemical healing [601. Chemical healing is not limited to the bonding of films; other structures with surfaces suitable for the required contact can also be subjected to healing. The method is applicable to strips, bands, billets, tubes, rods and pipes. Pipe structures and cable wraps with cross-lapped bonded strip windings of uniaxially oriented film are greatly resistant to bursting; this is a major application of the method. Another interesting aspect is the welding of composite sheets and rods, including fibre reinforced, crosslink polyester fishing rods. Chemical healing can be put to good use in the production of rib-reinforced panels, pairs of adherent sheets, with ribs on one of them for beam-like strength. Such a structure is achieved by positioning the sheets between two heated platens, one at least with cavities for the formation of ribs by air pressure through the sheet interface. After the ribs are formed, the sheets are pressed together and bonded. Adhesives present problems such as premature sticking. Chemical bonding by the present method obviates this and permits the use of oriented sheets [59,60]. 4.3. Laminates bonded through chemical healing with a coupling agent of highly drawn polycondensate films

In addition to the application of a catalyst for condensation or exchange reactions [59], the welding can be enhanced by means of a coupling agent capable t o interact with groups of the polymeric chain of each partner [57,59]. Multifunctional organic compounds, such as pyromellitic acid, benzophenone tetracarboxylic acid and others, can be used as coupling agents dispersed on at least one of the surfaces to be bonded. Then the contacting surfaces should be brought to a temperature effective to initiate an interaction of the coupling agents and the polymeric chains. Lamination based on diffusional self-bonding or chemical interactions in the solid state as described above is carried out at elevated temperatures, in vacuum or inert atmosphere. Recently a technique was developed for welding under very mild conditions through chemical healing using appropriate agents [61-631. Use is made of the well known reaction of methoxymethylation at ambient temperature [64].

440

S. Fakirov

+

-CONH-

CH30H

+ +

acid

(CHZO), -CON-

3OoC

I

CHzOCH3 -CON-

+

-

I

CH2OCH3 CONH-

-CONacid

I FH2

+CH30H

-CON-

As seen in the reaction scheme, welding or lamination of polymers containing amide groups consists in the creation of methylene bridges between the nitrogen atoms of two closely situated amide groups. In the present case the methoxymethylation reaction occurs between the contacting surfaces of two physically independent, separate bodies or substrates. The amides of the substrate can be the same or different, synthetic (nylons, polypeptides) or natural (proteins, polyamides). At a working temperature of 30°C a measurable effect can be observed even after 30 min while after 30 h the welding is so strong that when subjected to a shear test the material breaks outside the welded area [62,63]. The most important advantage of the proposed method is that the process can be carried out at ambient temperature. In contrast to lamination at elevated temperatures, the loss of orientation is avoided and the procedure can be applied to temperture sensitive materials. 5 . Conclusion

The demand for new polymer materials distinguished by combinations of properties which are sometimes unknown in traditional materials steadily increases. A special role is played by high-strength, high-modulus materials. A mile-stone in this respect was the introduction of liquid crystalline polymers. However, for many reasons (complex monomers and synthesis, expensive processing) the case of Kevlar can be considered as a happy exception rather than a guiding rule. Again attention was directed t o “classical” polymers and the best example is the gel-spinning of polyethylene with ultrahigh molecular weight. Condensation polymers were outside this scope of interest because of their peculiarities in molecular structure, flexibility, molecular weights, etc. (see Chapter 11). In the present chapter an attempt is made to poit out alternative approaches to the improvement of the mechanical properties of polyesters and polyamides by taking advantage of their specificity related to chemical composition and higher reactivity as compared to polyolefins.

Alternative approaches to highly oriented polyesters and polyamides

44 1

Looking for an answer to the question concerning the most appropriate starting structure for the obtaining of highly oriented polyesters and polyamides, it was found that it is the slightly crystalline but imperfect one. Ultraquenching of films from polyesters, polyamides and their blends resulted in the obtaining of almost completely amorphous species which, similarly to glassy metals, show tensile strength up to 3 times higher than that of semicrystalline samples. Special attention is paid to solid state reactions (trans reactions and additional condensation) as a successful approach to the creation of a desired supermolecular structure mainly through the elimination of deffects and increase in molecular weight. By means of two-stage cold drawing, each stage followed by high temperature annealing, in addition to the very high draw ratio achieved at room temperature (up to X = 20), doubly higher tensile strength (0.60 GPa) and elasticity modulus (18.6 GPa) are observed. Finally, techiques for overcoming the mechanical anisotropy in highly oriented films are described. They are based on the recently discovered phenomenon of chemical healing, i.e. joining of two or more polymer bodies as a result of chemical interactions at the interfaces. The approaches described allow the obtaining of articles with unique mechanical properties. References 1. A. Ciferri, I. M. Ward, “Ultra High Modulus Polymers”, Applied Science Publications, London 1979 2. A. Peterlin, Colloid Polym. Sci. 265, 357 (1987) 3. A. E. Zachariades, R. S. Porter, “Solid State Extrusion of Thermoplastics”, in: The Strenght a n d Stiflness of Polymers, edited by A. E. Zachariades, R. S. Porter, Marcel Dekker Inc., New York, Basel 1983 4. T. Kunugi, Ch. Ichinose, A. Suzuki, J. Appl. Polym. Sci. 31, 426 (1986) 5. U. Goeschel, K. Nitzsche, Acta Polymerica 36, 580 (1985) 6. J. Peterman, R. M. Gohil, J. Mater. Sci. 14, 2260 (1979) 7. H. Brody, J. Macromol. Sci., Phys. B22, 19 (1983) 8. D. C. Prevorsek, Y. D. Kwor, R. K. Sharma, J. Mater. Sci. 12, 2310 (1977) 9. K. E. Perepelkin, “Structure and Properties of Fibres”, Khimia, Moskow 1985, p. 44 (in Russian) 10. S. Fakirov, “Structures and Properties of Polymers”, Sofia Press, Sofia 1985

11. S. Fakirov, “Polycondensation Polymers a n d Solid State Reactions”, Nauka i Izkustwo, Sofia 1989 (in Bulgarian) 12. S. Fakirov, “Solid State Reactions in Linear Polycondensates”, in: Solid State Behavior of Linear Polyesters and Polyamides, edited by J. M. Schultz, S. Fakirov, Prentice Hall, Englewood Cliffs, New Jersey 1990 13. S. Fakirov, D. Stahl, Angew. Makromol. Chem. 102, 117 (1982) 14. K. Slusallek, H. G. Zachmann, Kolloid Z. Z. Polym. 251, 865 (1973) 15. B. Wunderlich, Macromolecular Physics, Academic Press, New York, San Francisco, London 1973, vol. 1 16. J. P. Bell, J. H. Dumbleton, J. Polym. Sci. A-2, 1033 (1969)

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S. Fakirov

17. S. Fakirov, N. Avramova, M. Evstatiev, Proceedings of the 2nd Dresden Polymer Discussion, Technical University of Dresden, Academy of Sciences of the GDR, March 1989, Part 2, p. 85 18. S. Fakirov, M. Evstatiev, J. M. Schultz, J. Appl. Polym. Sci. 42,575 (1991) 19. M. Evstatiev, Ph. D. Thesis, Sofia University, 1988, Sofia, Bulgaria 20. A. S. Argon, M. M. Salama, Mater. Sci. Eng. 23, 219 (1976) 21. P. Smith, R.R. Mateson, Jr., P. A. Irvine Polymer 21,1095 (1984) 22. F. De Candia, R. Gennaro, V. Vittoria, Makromol. Chem. 175,2983 (1974) 23. R. E. Lion, R. J. Farris, W. J. Mac Knight, J. Polym. Sci., Polym. Phys. Ed. 21,329 (1983) 24. G. S. Y. Yeh, P. H. Geil, J. Macromol. Sci. B1 235, 351 (1967) 25. J. L. Koenig, M. J. Hannon, “Infrared Studies of Chain Folding in Polymers. II Poly(ethy1ene terephthalate)”, in: Cryogenic Properties of Polymers, edited by T. T. Serafini, J. L. Koenig, Marcel Dekker Inc., New York 1968, p. 171 26. A. Reichle, A. Frietzsche, Angew. Chem. 74,562 (1962) 27. N. Avramova, S. Fakirov, I. Avramov, J. Polym. Sci., Polym. Phys. Ed. 22, 311 (1984) 28. N. Avramova, S. Fakirov, J. Polym. Sci., Polym. Phys. Ed. 24, 761 (1986) 29. S. Fakirov, N. Avramova, J. Polym. Sci., Polym. Lett. Ed. 20,635 (1982) 30. S. Fakirov, S. Petrovich, N. Avramova, J. M. Schultz, Compt. Rend. Acad. Bulg. Sci. 42, 33 (1989) 31. US 4,915,885 (1990), University of Delaware, Inv.: N. Avramova, I. Avramov, S. Fakirov, J. M. Schultz 32. I. Avramov, N. Avramova, S. Fakirov, Makromol. Chem., Rapid Commun. 11, 135 (1990) 33. I. Avramov, N. Avramova, S. Fakirov, J. Polym. Sci., Polym. Phys. Ed. 27, 2419 (1989) 34. S. Fakirov, E. W. Fischer, IUPAC Intern. Symp. on Macromolecules, Aberdeen, 1974, Abstr. book, p. 85 35. P. Chandari, D. Turnbull, Science 199,11 (1978) 36. I. Avramov, N. Avramova, J. Macromol. Sci., Phys. B30,335 (1991) 37. M. Evstatiev, S. Fakirov, Ann. Uniu. Sofia, Faculte de Chimie 82,111 (1992) 38. S. Fakirov, M. Evstatiev, Polymer 31,431 (1990) 39. S. Fakirov, Colloid Polym. Sci. 256, 115 (1978) 40. S. Fakirov, I. Seganov, Vysokomol. Soedin. A23, 766 (1981) 41. M. Evstatiev, I. Seganov, S. Fakirov, Acta Polymerica 39, 191 (1988) 42. A. B. Pakshver, A. A. Konkina, “‘Control in the Production of Chemical Fibres”, Khimia, Moscow 1967 (in Russian) 43. M. G. Evstatiev, S. C. Fakirov, Vysokomol. Soedin. A32, 1697 (1990) 44. A. Peterlin, “Mechanical and Transport Properties of Drawn Semicrystalline Polymers”, in: The Strenght a n d Stiffness of Polymers, edited by A. E. Zachariades, R. S. Porter, Marcel Dekker Inc., New York, Basel, 1983 45. I. Sakurada, K. Kaji, Kobunshi Kagaku 26,817 (1969) 46. US 4,842,789 (1989), University of Delaware, Inv.: M. Evstatiev, S. Fakirov, J. M. Schultz 47. M. Evstatiev, M. Sarkissova, S. Petrovich, S. Fakirov, Acta Polymerica43, 143 (1992) 48. M. Evstatiev, S. Fakirov, A. Apostolov, H. Hristov, J. M. Schultz, Polym. Eng. Sci. 32,964 (1992)

Alternative approaches to highly oriented polyesters and polyamides 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60.

61. 62. 63. 64.

443

M. Evstatiev, M. Sarkissova, Vysokomol. Soedin., in press I-Hwa Lee, P h . D. Thesis, 1987, University of Delaware, USA J. M. Schultz, I-Hwa Lee, J. Muter. Sci. 23, 4237 (1988) US 4,575,470 (1986), University of Delaware, Inv.: S. Fakirov, I-Hwa Lee, J. M. Schultz; Chem. Abstr. 107, 226005h (1986) S. Fakirov, J. Polym. Sci. 22, 2095 (1984) S.Fakirov, Makromol. Chem. 185, 1607 (1984) S.Fakirov, Polymer Commun. 27, 137 (1985) S. Fakirov, N. Avramova, J. Polym. Sci., Polym. Phys. Ed. 25, 1331 (1987) S.Fakirov, Vysokomol. Soedin. B27, 653 (1985) N. Avramova, S. Fakirov, Makromol. Chem., Rapid Commun. 11,135 (1990) US 4,715,919 (1987), University of Delaware, Inv.: S. Fakirov, J. M. Schultz; Chem. Abstr. 108, 1 6 8 8 0 5 ~(1988) US 4,902,369 (1990), University of Delaware, Inv.: N. Avramova, S. Fakirov; Chem. Abstr. 112, 2 1 8 4 0 5 ~(1990) N. Avramova, S. Fakirov, Angew. Makromol. Chem. 179, 1 (1990) US 4,895,612 (1990), University of Delaware, Inv.: N. Avramova, S. Fakirov, J. M. Schultz; Chem. Abstr. 111, 59131g (1989) US 4,980,237 (1990), University of Delaware, Inv.: N. Avramova, S. Fakirov, J. M. Schultz T. Arakawa, F. Nagatoshi, N. Arai, J. Polym. Sci. A-2, 1461 (1969)

Oriented Polymer Material> Stoyko Fakirov Copyright 0 2002 Wiley-VCH Verlag GmbH & Co. KGaP

Chapter 15

Structural aspects of the damage tolerance of Spectra fibres and composites

D. C. Prevorsek

1. Introduction Liquid crystalline solutions, liquid crystalline melts, and solutions of flexible high molecular weight polymers can be converted into products of exceptionally high strength and modulus. This remarkable technological achievement in fibre technology renewed interest in the theoretical limits of strength of uniaxial polymers. These limits are necessary to assess the potential for improvements in fibre strength beyond the levels currently achieved. It has been known since the early work of H. Mark that the maximum theoretical tensile strength of uniaxially oriented polymers is almost two orders of magnitude higher than that of the corresponding fibres. Although a great deal has been written about the maximum achievable strength, the question of how this limit in strength should be estimated is still not settled (see also Chapters 1, 2, 10, 11). At present, one of the most relevant questions of fibre science is whether the strength of current high performance fibres is sufficiently close to the theoretical limits to consider the current processes as the last step in ultrastrong fibre technology, or whether the gap between current strength and theoretical potential is so large that new processes should be developed allowing another quantum jump in strength.

Structural aspects of damage tolerance of Spectra fibres and composites

445

The same question was addressed in 1972 [l] with regard to the strength of polyethylene fibres: Maximum achievable strength, GPa Theoretical [2] Experimental [l] 18.6-19.6

19.5-22.9

1/3-1/6 Theoretical maximum strength [l],GPa 2.9 -4.4

These data are frequently quoted and are still accepted as a yardstick to estaimate the quality of fibres. With the ultrastrong polyethylene fibres, now commercially available, the maximum attainable strength of about 4.0 GPa (45 g/den) has already been achieved. In the original work [l] the technologically achievable fibre strength was realistically placed at ca. one-fifth of the theoretical fibre strength. 1.1. Theoretical limits i n modulus and strength The theoretical limits in modulus are calculated from the stretching, bending, and torsional force constants. The low temperature, high rate of deformation modulus of ultrastrong polyethylene fibres of the Spectra type is so close to the theoretical limits that extensive research to further increase the modulus is not warranted. The measured crystalline modulus is also within the limits predicted by theories, indicating that the structure of a large volume fraction ( w 75%) of the fibre is nearly perfect. This conclusion is confirmed by the crystalline orientation function, crystalline density, and the very high melting point of the fibre (see Chapters 10, 11). However, it must be realized that even with a modulus close to the theoretical limit, a fibre does not necessarily exhibit the strength that approaches the theoretical limit. Modulus is a volume property where contributions of all domains are averaged according to the schemes that depend on the structural arrangements of these domains. Conversely, strength is governed by the weakest element of the structure. The strengths of heterogeneous structures such as fibres therefore fall far below the theoretical limit despite nearly theoretical modulus. All synthetic fibres consist of at least three distinct types of domains: the amorphous and crystalline domains of the microfibril, and the interfibrillar matter. The microfibril is an essential element of the structure with well-defined lateral dimension that usually falls in the range of 6.0-20.0 nm. Very little is known, however, about the length of the microfibril and the structure and size of the flaw surrounding the end. In high performance fibres, the microfibril appears to be an endless structural element. A structural model illustrating these domains for conventional melt-spun fibres is shown in Figure 1. The weakest element is the disordered domain labeled A. Microfibrils of finite length have been proposed for fibres prepared from spherulitic precursors. In this case, the structural discontinuity at the microfibril end should be even weaker than the disordered domains of the

D. C . Prevorsek

446 MicrofibriIs

t

c

Crystallites

Extended noncrystalline molecules

Disordered domains A

Figure 1. Structure of melt-spun fibres microfibril. Therefore, the processes that produce considerable increases in strength must eliminate the microfibril ends, and strengthen or eliminate the weak disordered domains (see also Chapters 2, 11 and 12).

1.2. The ultrastrong polyethylene fibres The realization that very strong fibres can be made from flexible polyethylene represents a major scientific discovery. Until then, it was believed that substantial molecular rigidity and the existence of a nematic phase are essential for producing very strong fibre as implemented by the well documented and successful technology of aramid fibres (Kevlar) developed by DuPont company [3]. The high performance polyethylene (PE) fibres available to date are made by a solution spinning process that evolved from the Couette flow surface growth experiments of Pennings [4]. By studying the mechanisms of fibre formation in the Couette flow experiments, Pennings and his students, Smith, Lemstra and Kalb [5] developed the principles for solution spinning of ultra-high molecular weight PE as well as a process disclosed in patents which represents the foundation of DSM technology for producing Dyneema fibres [ 6 ] . Some of the fibres used in our studies are made by an Allied-

Structural aspects of damage tolerance of Spectra fibres and composites

3.50

f2 %

Gel SpunPE

2.50

-

2.00

-

3.00

447

Kevlar 49

'HighCarbon Strength

Rigid Rod PBX LCPs

Ultrahigh Modulus Carbon

0.00

0.50

1.00

1.50

2.00

Specific Tensile Modulus

2.50

3.00

3.50

18 N.mflrg

Figure 2. Specific tensile strength vs. specific modulus showing gel spun PE fibre with other fibres Signal solution spinning process developed by Kavesh and Prevorsek [7]. These fibres are commercially available under the trade names of Spectra@ 900 and Spectra@ 1000. It should be noted that the solution spinning used to produce ultrastrong PE fibres using high molecular weight P E is frequently referred to as gel spinning. This term is misleading. The process as it is practiced t o date involves spinning a solution that is, on cooling to ambient temperature, transformed into gels that have sufficient strength and integrity to be handled by conventional fibre processing equipment. The commercially available solution spun PE fibres exhibit outstanding mechanical properties. Nevertheless, it is not just their specific modulus and strength illustrated in Figure 2 that contribute to their rapid acceptance in a variety of applications. Their commercial success must also be attributed to their unmatched damage tolerance and fatigue resistance. The ability of these fibres to fail in shear and/or compression without losing a great deal of tensile strength is a unique characteristic of PE and represents a distinct advantage over other reinforcing materials. This is particularly important when the products are used in the technology of survival, where the primary function of a part is to protect structures, people or equipment from the blasts of explosions and impact of fast moving projectiles, etc. The scope of this report is to identify the properties or combination of properties that make PE fibres particularly suitable for the applications that represent the foundation for their successful commercialization. Focussing, therefore, on

D. C. Prevorsek

448

their unique damage tolerance, fatigue and abrasion resistance, and the capability of delayed recovery after an apparently plastic deformation, we will identify the molecular and morphological origins of these properties and review the fundamental differences between PE and other high performance fibres. 2. Creep

2.1. Structural parameters affecting creep Creep can be controlled in thermoplastic fibres such as PE,polypropylene (PP),poly(ethy1ene terephtalate) (PET),etc. by processing as well as by chemical modifications. Because of their inherent dimensional instability under load, and availability of processes that convert PE through melt or solution spinning into ultra strong and ultrahigh-modulus fibres, PE fibres have been the subject of numerous investigations that have both technological and scientific relevance. Since it has been shown that drawing decreases chain folding by forming extended chain tie molecules, the plots of creep vs. draw ratio reflect the role of chain extension and chain folding on creep. The magnitude of this effect for loads of 0.10, 0.15 and 0.20 GPa is illustrated in Figure 3

Time. s

Figure 3. Creep compliance

(eo/uo) of

ultrahigh modulus polyethylene fibres.

fin = 6180; f i w = 101,450; effect of draw ratio: A = lox and B = 3 0 x ; effect of load: 0 = 0.1 GPa, A = 0.15 GPa, and V = 0.2 GPa [8].Courtesy of Butterworth & Co. (Publishers)

Structural aspects of damage tolerance of Spectra fibres and composites

449

for PE fibres having a draw ratio of 10 and 30. The molecular weight dependence of creep, on the other hand, reflects the role of chain ends and chain length on the ability of molecules to slip one past another. Therefore, the creep resistance or dimensional stability under load increases with increasing molecular weight (see Figure 4). This effect has been observed with many fibres but is particularly important for ultrastrong polyethylene of Spectra type, where the combination of very high draw ratio with exceptionally high molecular weight results in dimensionally stable fibres suitable for numerous industrial applications. For comparison with the lower molecular weight and lower draw ratio fibres studied, we also show in Figure 4 the creep data of fibres spun from dilute solutions and drawn to draw ratios exceeding 75. With linear high density P E of M , = 1.7 x 106-3.2 x lo6 and M , = 220,000-430,000, it was possible to prepare fibres showing 0.04% or less creep in one month at 23OC and 0.1 GPa. It has been shown that a mechanical model consisting of two parallel Maxwell elements represents well the creep and recovery behaviour of PE and PP fibres [10,11]. Based on this model, an equation has been derived [12] allowing the analysis of creep data in terms of the two thermally activated processes postulated by the model. This analysis has been particularly useful for the interpretation of the effects of draw ratio, molecular weight, and the short pendant groups as well as radiation cross-linking on the activation volumes and the preexponential factors reflecting the amount of potential sites for molecular rearrangements that lead to the microscopic creep [12]. An illustration of the analysis that makes use of the constant “plateau” creep rates observed when creep rates are plotted as a function of total creep strain is presented in Figure 5. By fitting the equation to curves of log(p1ateau creep rate) versus applied stress, values of actiavation parameters of the two processes have been obtained [12].

3-

.‘2*’

8

11 Month

-

10

107

ioJ

lo4

105

106

IC

Time. s

Figure 4. Creep of ultrahigh modulus polyethylene fibres (draw ratio = 20 and load = 0.1 GPa). Effect of molecular weight: A, Mn= 6180; A?,,, = 101,450; B, M , = 33,000; M,,, = 312,000; C , Mn = 290,000; M,,, = 2,200,000, extendedchain polyethylene fibres [8,9]

D. C. Prevorsek

450

10-8

-

0

1

2

3

4

5

6

7

8

(n,,

Figure 5. Ultrahigh modulus polyethylene = 33,000; &fw= 312,000; draw ratio: X = 20). Creep rate i , vs. % strain ( e c ) at various stresses [ I l l . To convert GPa to psi, multiply by 145,000 The small activation volume process has been attributed to the movement of chains in the crystalline regions. Its activation volume v 2 decreases with the draw ratio, suggesting this process is more localized with increasing orientation and improved molecular alignment and crystallinity. Radiation cross-linking and introductions of pendent groups by copolymerization have no significant effect on 02 [ 111. Melt spun and very high molecular weight solution spun fibres [13] show different creep behaviour. The latter fibre, the preparation of which involves an intermediate porous structure [13], exhibits a very low plateau creep rate at high stresses. This is reflected in a very low value of the activation volume v 2 = 0.015 (nm)3, indicating a highly localized process for slip in the crystalline phase. This, in turn, indicates a perfect order of the crystalline phase in solution spun fibre. At low stresses, however, the plateau creep rate of solution spun fibre is much higher than that of melt spun fibres. This dimensional instability at low stresses must, according t o the analysis, be attributed to the high population of potential creep sites in the oriented amorphous domains. The size of the activation volume, which could also contribute to the high creep rate, is not a factor [ll]. Solution spun extended-chain Spectra 900 fibres, the preparation of which proceeds via nonporous fibrous intermediates [14], compared with the former solution spun fibres of similar molecular weight [13], show a further reduction in the activation volume v 1 to 0.28-0.25 (nm)3. This reflects tighter disordered domains with fewer potential sites for molecular

Structural aspects of damage tolerance of Spectra fibres and composites

451

rearrangements that lead to microscopical creep. Since 02 is also reduced, crystalline order in Spectra 900 fibres is also improved above that of the other solution spun fibres. This is reflected in a high melting point and dimensional stability at high loads. For technological purposes it is therefore important to note that creep can be reduced by increasing draw ratio and molecular weight, cross-linking and copolymerization. 2.2. Deformation in creep versus plastic deformation in drawing

Since the unrecoverable creep extension is much less than the deformation during drawing, less is known about the details of creep mechanism than is known about the mechanism of drawing because present techniques cannot resolve very small structural changes occurring during creep. Nevertheless, it was shown that in uniaxially oriented low density PE, the most likely creep mechanism is interfibrillar slip coupled with chain slippage, a mechanism occurring also during drawing of fibre between intermediate and high draw ratios [15]. Since the mechanism of unrecoverable creep resembles the mechanism of the drawing process, unrecoverable creep should result in property changes similar to those observed during drawing. Increases in draw ratio lead to an increase in modulus, reduction in elongation at break, and increases in tensile strengths; therefore, similar trends can be expected in creep experiments. This w a s confirmed by measuring fibre properties before, during and after cyclic loading in tension for PE, PET and PAN fibres [16]. Permanent deformation in tension (creep) can be regarded as an extension of the drawing process. It diminishes with increasing draw ratio and should approach a minimum for a given polymer when all molecules are fully extended. This is demonstrated with extended-chain fibres produced from ultrahigh PE. Their dimensional stability in creep is noteworthy and greatly exceeds that of P E fibres produced by melt spinning. The similarity between draw ratio and creep extension decreases during the creep experiment. At some point, fibres must start losing strength, leading to creep rupture. Measurements of fibre strength during fatigue experiments using fibres with the morphology shown in Figure 1 demonstrate that this process appears to be limited to a very short time. The decrease in strength is very fast during the period preceding fibre rupture [17]. This is unlikely to be the case with extended-chain fibres, where creep and draw ratio do not proceed via similar mechanisms. 3. Strain rate effects in ultrastrong polyethylene fibres and composites

Polyethylene fibres of Spectra type are on a weight basis the strongest and almost the stiffest commercially available materials (Figure 2). It has

452

D. C . Prevorsek

also been established that uniaxial PEs become even stronger, stiffer and tougher with increasing rate of deformation. Theoretical work relative to strain rate dependence of uniaxial PE has been carried out by Termonia et al. [18]. These authors predicted that an increase in the deformation rate from lo-' to l o 2 min-' should lead to a sixfold increase in fibre strength. Testing at strain rates achievable by standard laboratory equipment indicates large modulus increases with increasing rate of deformation. These increases were particularly large at elevated temperatures (10013OOC). Because of this favourable strain-rate sensitivity, Spectra fibres are rapidly gaining acceptance in applications concerned with the survivability of equipments, apparatus and people. In these applications, the protecting material can encounter rates of deformations which can be 6 orders of magnitude or more higher than those of standard laboratory testing. To develop the background and develop data base for design of damage tolerance structure, it is necessary to study the behaviour of fibres and composites under these extreme conditions. This section summarizes the progress we have made in this experimentally and analytically demanding field. Materials studied include commercially available Spectra 1000 fibres and their unidirectional composites [19]. Spectra composite samples were prepared by laminating unidirectional Spectra 1000 prepregs of commercially available Spectra Shield type using [0/90] fibre angle stacking sequence. The matrix polymer of the Spectra prepreg was Kraton D1107, a triblock copolymer of polystyrene, polyisoprene and polystyrene produced by Shell Chemical Company. The fibre content was 70% by weight. High speed photography was used for the determination of both the transversely impacted fibres and the projectile target interaction. 3.1. Ballistic impact on fibres

The impact velocity V and the velocity of the transverse wave, C,, which is relative to the laboratory coordinate system, can be determined from the high speed photographic records. The C, values measured from the sequences have an accuracy of f4%. As expected [19], the values for rubber are very low and very dependent on the preload. The corresponding velocities for Kevlar and Spectra are very much higher, and those for Spectra the highest of all [19]. Figure 6 expresses this graphically. Note that there is almost linear increase with the initial tension but with Spectra having the greatest slope. The value of E is a dynamic modulus for the strain rate of 1.2 x 10' s-l (i.e., 7.2 x lo3 min-'). The dynamic value of E = 320 GPa for Spectra is very high, approaching the theoretical limit. This can be compared with the value for steel of 210 GPa and diamond 1050 GPa. Since Spectra has a low density, the velocity of longitudinal stress wave is very high. The value of ca. 18,000 m.s-' is much higher than that of steel (i.e., ca. 5500 m.s-') and is comparable with that of diamond (also about 18,000 m s - ' depending on the crystallographic direction).

S t r u c t u r a l aspects of damage tolerance of

0

10

20

Spectra fibres and composites

30

40

50

453

60

lnltlrlknrion (N)

Figure 6. Transverse wave velocity vs. initial tension 3.2. Ballistic impact on Spectra composites

It should be noted that numerical simulations of high speed impact phenomena in two dimensions have been done rather routinely [20]. For a more realistic simulation, a three-dimensional analysis is required. However, most of the three-dimensional computer codes are for isotropic materials, such as metals. Therefore, a new approach had to be developed to treat Spectra composites that are highly anisotropic and viscoelastic. In addition, the properties of Spectra fibres are highly strain rate dependent as shown in Figure 7. To take these factors into consideration, we used a general finite element code, Marc, developed by Marc Analysis Research Corp. Marc is capable of handling three-dimensional dynamic problems, as well as anisotropic materials. Strain rate dependence of properties was handled in a stepwise manner [19]. Parallel to the theoretical analysis, experimental observations were also performed [15]. The phenomena of high speed impact on Spectra composites during a ballistic impact were analyzed by examining the Spectra composite panels subjected to the ballistic impact. It was observed that the failure process of Spectra composites could be divided into four stages. The Spectra composite target was first locally compressed upon contact of the projectile. Then several layers of Spectra fibre were broken at the impact point by high stresses developed at the contact area with the projectile (bullet). Then the projectile penetrated through several layers causing interfacial delamination. While penetrating the Spectra composite, the projectile was severely deformed into a mushroom shape, which reduced the stress at the contact area and finally the projectile came to a stop. Fig-

D. C. Prevorsek

454

1:

0 Gauge Length 2.5

cm

7.5 cm

2Scm

I

I 0

.

A

A A A D

A 0

o

m 0

I

10

102

*

-

9

* .-**

r’o3

.-

* ...-I 10 4

Strain Rate (Min”)

Figure 7. Effect of strain rate on tensile modulus of Spectra 1000 fibre

ure 8 illustrates the bullet deformation and partial penetration of Spectra composite as observed by high speed photography. These experimental observations were compared with analytical results [19]. In Figure 9 the experimentally observed deflection of the Spectra panel during the ballistic impact was compared with theoretically predicted deflection by the simulation. As can be seen, the prediction is in very good agreement with the experimental observation up to 70 ps. After 70 ps, the prediction deviates slightly from the experimental observation. The prediction of bullet velocity during ballistic impact also agrees well with the experimental observation [19]. The projectile velocity decreases rapidly a t the initial stage of impact. Within 20 ps, the original velocity has been ULTRASTRONG POLYETHYLENE

Panel Compreased

Delamination Initiated

Panel Delaminated

Bullet Stopped

Figure 8. Experimentally observed penetration of projectile through Spectra composite panel

Structural aspects of damage tolerance of Spectra fibres and composites 40

455

Experimentally Observed Front Surface Deflection

-

Predicted

30 E E

Rear of Projectile

-*

EE

-s

20 Bullet and Panel Damage Completed

is

VZ of Panel Thickness Penetrated

(D

10

Deformed Bullet 40

80 lime (pS)

120

Figure 9. Comparison of experimentally observed deflection of Spectra composite panel and theoretically predicted deflection reduced by approximately 30%, indicating that approximately 50% of the bullet kinetic energy has been absorbed. This may be attributed t o the strain-rate-dependent characteristic of Spectra fibre. 4. Damage tolerance in penetration

Until the introduction of Spectra composites in armour technology, the structural composites made of Kevlar and S-2 glass have been and are still used also as armour or components of armour. Neither technical nor patent literature relative to aramid or glass fibre armour indicates that there are fundamental differences between the damage tolerance of structural composite and that of armour. In structural composites, the measure of the damage tolerance is frequently the retention of compressive strength after impact (CAI). In armour, on the other hand, the damage tolerance is expressed in terms of penetration resistance. When a carbon fibre-epoxy resin composite (as a representative of structural composite family) is impacted perpendicularly t o its surface, the test panel exhibits, under the impact point, “damage” that involves (a) intralaminar failure, (b) delamination, and (c) fibre failure. As illustrated in Figure 10, the mechanisms (a) and (b) involve matrix

456

D. C . Prevorsek

Figure 10. Damage mechanism in rigid composites; (a) intrLaminar delamination, (c) fibre failure

ilure, (b)

cracking. The fibre failure, on the other hand, occurs only at very severe conditions. This must be avoided. Hence, it is the practice that the composite design and the choice of fibres and matrix is such that the fibre failure never occurs in use. The typical specifications for structural composites require that after the most severe impact expected in use, the composite maintains X% of the original compressive strength. The typical range for X is from 30 to 60%. With regard to the issue of damage, it should be noted that placing of the structural composite panel on a firm support and then impacting the panel under the specified conditions eliminates or greatly reduces the damage, because the support eliminates deflection that is the primary cause of matrix failure.

4.1. Mechanisms of penetration and analysis of penetration resistance In contrast to structural composites where damage takes place in the matrix or fibre matrix interface, in penetration, the fibre breakage is unavoidable. Considering that current high performance fibres have outstanding tensile properties but are relatively weak in compression and shear, it follows that enhancement in penetration resistance whould be achieved by designing structures where penetration involves as much as possible straining and breaking of fibres in tension. To identify desirable and required matrix and fibre characteristics t o maximize the penetration resistance of a flat panel, it is necessary t o determine the principal mechanisms that are involved in penetration. In the

Structural aspects of damage tolerance of Spectra fibres and composites

cutting

amoli dlometer pointed pro~ect~ios

b'ade'ngmnt*

457

\

breaking in tension

Figure 11. Principal mechanism of failure in penetration author's analysis the following three mechanisms were distinguished (Figure 11): - lateral displacements of fibres (matrix and interfacial failures); - breaking of fibres in shear or compression (cutting); and - breaking of fibres in tension.

The relative importance of these mechanisms in the specific case depends on materials characteristics (fibres and matrix), composite design and the characteristics of penetrator geometry, velocity, mass, hardness, etc. High speed instrumented testing equipment using probes of various shapes, i.e. needles, blades, cylindrical and spherical shapes of various diameters, etc., is used to obtain the penetration resistance of various composites with respect to these three modes of failure. Various comparisons of P E, aramid fibre and composites were also made [21]. These studies produced the relative values shown in Figure 12. The data suggest that against very small diameter projectiles, aramid structures are advantageous because of high coefficient of friction. With respect to cutting, the high speed photography of transverse im30% higher cut resistance of pact of blade-like projectiles indicates a Spectra (PE) versus Kevlar [22] and with very large diameter projectiles and composite thicknesses exceeding 2.5 cm, penetration resistances were frequently recorded that were 2.5-4 times higher with P E than with aramid fibre composites [23]. This 2.5 - 4-fold advantage of PE over aramid was attributed to strain rate dependence of PE fibres, specifically tensile modulus and strength [18,24]. At ballistic rate of deformation the specific properties of P E fibres shift much more to the higher values than those of any other reinforcing fibres because of their unique morphological composite structure. With regard to the fundamental difference between the damage in penetration and damage in structural composites, it should be noted that the

-

D. C. Prevorsek

458 1.00 I

PROJECTILE DIAMETER

Figure 12. Failure mechanism of composite armour

damage in penetration is primarily reflected by the fibre breakage and that the role of the matrix is significant only in case of small diameter penetrators (of less than 0.5 cm). Consider the case in Figure 13 where are shown the results of the defor-

Figure 13. Projectile penetration analysis of composite panel

Structural aspects of damage tolerance of Spectra fibres and composites

459

mation analysis of the impact of a deformable projectile against a Spectra fibre uniaxial composite at the moment when the projectile is stopped. In this particular case, the projectile was stopped between 15-20 p s after the impact. The energy balance calculation shows that the observed damage, breakage of fibres in shear, represents approximately 10% of the total energy absorbed by the target [21]. The rest of the kinetic energy of the projectile is converted into the strain energy of the fibres. After the projectile is stopped, a large portion of the deformation is recovered almost instantly, although the recovery process continues for a long time. This analytical approach, assuming three principal modes of penetration complemented with high speed testing of composites using probes of various shapes and sizes conforming to these three mechanisms, proved to be very useful. Typical applications include the design of armour for specific uses, analysis of the effects of fibre and matrix properties, studies of the effects of interface and fibre surface treatments. However, upon analysis of the performances of various composites on repeated impact, a need of revision arose; this problem is discussed in the next section. 4.2. Repeated impact and additional energy absorption mecha-

nism of PE fibre To broaden the data base and develop design criteria for penetration in damage-tolerant composites, it was necessary to consider also the behaviour of these composites on repeated impact. When those studies were undertaken, the original goal was to establish some empirical rules of accumulative damage that could be used to design structures that must survive repeated impact without penetration. To develop such cumulative damage rules, approximately equivalent composites were constructed using Spectra 900, S-2 glass, Kevlar 49 and carbon fibre fabrics impregnated with the epoxy matrix (Araldite 6010) and hardener (HY956). These composites were subjected to the instrumented impact test and the approximate levels of impact energies were established at which S-2 glass, Kevlar 49 and carbon fibre composites failed but the Spectra composite survived the impact (Table 1). The failure of Kevlar composite at a 6.6 times lower impact energy than that which Spectra 900 composite was able to withstand without penetration, was originally attributed to some peculiarity of sample penetration or testing that could not readily be identified. Note that the respective calculations indicated that under optimal conditions the penetration resistance of Spectra composites could approach only a four-fold advantage in energy absorption over an “equivalent” Kevlar composite. Despite this concern, the plan to develop the rules of cumulative damage was followed. To accomplish this, the Spectra 900 panel was subjected to the same impact conditions (e.g. 6.6 times energy to penetrate Kevlar 49 panel) five times and the Spectra panel survived all five impacts without

460

D. C . Prevorsek

Table 1. Comparison of repetitive impact results for various fibre reinforced composites Laminate

No. of Impact Max. Energy (ft-lb) repetitive energy load impacts (ft-lb) (lb) Maximum load Total Actual 31.0 36.9 45.3 48.7 52.7 57.8 58.6

Observations

Actual Actual %Absa Actual %Absa 89 31.3 100 No penetration 1691 27.7 100 No penetration 32.7 89 36.9 2063 100 No penetration 40.6 90 45.5 2545 100 No penetration 88 48.7 2917 42.8 100 No penetration 44.9 85 52.6 3297 100 No penetration 78 57.6 3701 45.4 100 No penetration 74 58.3 3916 43.0

Spectra900 Spectra900 Spectra900 Spectra900 Spectra900 Spectra900 Spectra900

1 2 3 4 5 6 7

s-2 glass Kelvar 49

1 1

11.6 8.8

356 245

1.8 1.3

16 15

10.3 9.9

100 100

Penetration Penetration

s-2 glass Kelvar 49

1 1

52.0 52.0

370 254

1.8 1.3

3 2

8.0 6.7

15 13

Penetration Penetration

"%Abs = per cent of the initial energy absorbed by the composite

failure [21]. Knowing that a 6.6 time impact energy required to penetrate the Kevlar panel must be very close to the energy required to penetrate the Spectra 900 panel, it was concluded that these panels can survive, without an apparent weakening, repeated impact at levels that are close to the energy required for their penetration. To determine what happens in these composites on such severe impact, a series of experiments were then conducted in which the impact energy was progressively increased from 6.6 to 9.6, and the force recorded during the impact. The peak force in four repeated impacts is plotted in Figure 14, which shows that the panel rigidity increased on impact, indicating some structural changes. These data clearly show that up to a critical level of impact, the damage in Spectra fibres does not accumulate and the structural changes, if they occur, involve minimal or no chain scission and therefore only insignificant loss of properties in tension. Some of these structural changes are recoverable. This brings us to another fundamental difference between damage tolerance in structural composites and penetration resistance. In rigid structural composites the damage is additive and on repeated impact the CAI progressively decreases and the damage area (matrix cracking) increases. In penetration of viscoelastic composites such as PE fibre composites, the damage is frequently recoverable. This situation exists when the energy levels of impact are lower than those causing fibre breakage. Under these conditions, the fibre damage consists of massive shear and compressive failures that do not involve chain breakage. With deformable armour, the recovery can be accomplished in the latter stage of impact when the fibres

Structural aspects of damage tolerance of Spectra fibres and composites

rn

6 0-

3.5-

3.0-

Spectra

2.0 2.5

1

461

.s

0s t.0

0.0

Glass Kevl8r

+

Figure

14.

Maximum load during repetitive impact cycle

are strained in tension. This process follows the initial stage of impact in which the fibres are exposed primarilly to compressive and shear stresses. Finally, it should be stressed again that the damage tolerance in structural composites and penetration resistance involve entirely different mechanisms and principles. In structural composites the fibres protect the matrix that is the locus of damage while the fibres are in most cases unaffected by the impact. In penetration the fibres are the primary bearer of damage and the primary function of the matrix is to provide sufficient integrity for the sample while allowing large deformations without failure or disintegration of samples on impact. The observed damage in structural composites correlates with the energy absorbed on impact. The observed damage in penetration resistance reflects only a small fraction of the absorbed energy. Penetration dynamics assuming three principal modes of deformation - lateral displacement of fibres, breaking of fibres in shear or compression, and straining and breaking of fibres in tension - explains a great deal provided that data of the energies associated with these penetration modes are determined in specifically designed high speed experiments with the mechanical properties of Spectra fibres at high strain rates. This approach, however, fails t o explain the outstanding performance of Spectra composites on repeated impact where the role of additional energy absorption mechanisms involving massive compression and shear failure had to be invoked to explain the data. The uniqueness of the damage tolerance and recovery of P E is attributed to the composite structure of Spectra fibres and the capability of P E crystalline phase to undergo, without chain breakage, large plastic deformations as well as compression and shear failure.

462

D. C. Prevorsek

5 . Morphology of ultrastrong P E fibres

In the design of the damage-tolerant-impact-resistantstructures, armour, etc., the modulus of the composite and the strain propagation rate (where E is the modulus and p is density) are just as important as strength and energy at break. We have therefore been investigating the strain-rate dependence of Spectra fibre properties using high speed photography and also high speed tensile testing equipment. Because of fibre clamping problems, the strength data exhibit very large scatter. The modulus data are, however, accurate. The plots of modulus change as function of strain rate in Figure 7 show a three-fold increase in modulus when the deformation rate increases from 10' to lo4 min-'. By combining these data with the moduli obtained by transverse impact, we can extend this curve to the strain rates of l o 5 min-l. These data show that a t ambient temperature the modulus of Spectra 1000 becomes insensitive to strain rate increases beyond lo4 min-'. It should be noted that, at this deformation rate, the modulus approaches the theoretical modulus of the perfectly aligned PE. It is also gratifying that the deflection analysis of composite subjected to projectile impact yielded modulus data which are in excellent agreement with the data of yarns. Considering the importance of strain-rate dependence of mechanical properties of ultrastrong PE fibres and the magnitude of this effect, it is desirable to review the morphological data of these fibres and discuss the possible origins of these effects. Spectra fibres are produced by spinning a solution of very high molecular weight PE. Typically, these molecules contain in the order of lo5 CH2 groups in the linear chain. During this conversion of the solution into a fully drawn fibre, the coiled molecules in the solution are converted into nearly perfectly oriented highly crystalline fibres. Based of the high modulus and strengths and wide angle X-ray diffraction, it has been inferred that a large volume fraction of 75% can be represented reasonably well by an idealized fibre structure that is typical for all organic fibrous materials. Spectra as well as other PE fibres exhibit a well defined aggregate structure on a macro (50 nm) as well as microfibrillar level (5 nm). Fundamental differences that may exist between PE and other high performance organic fibres, such as polyaramids, rigid rod and thermoplastic liquid crystalline fibres, must therefore originate in the longitudinal characteristics of these fibres and especially in the microfibril and interfibrillar matter. A generalized structural model representing the key characteristics of fibrous materials is shown in Figure 15. Small angle X-ray diffraction studies of Grubb [25], electron microscopy of Kramer [26] and especially the studies of Schaper et al. [27] provide a great deal of information relative to dimensional characteristics of the microfibrils. We consider PE fibre a composite consisting of nearly perfect needle-like

-

-

Struct.ura1 aspects of damage tolerance of Spectra fibres and composites

463

Spectra

PET Fibre

/ Kevlar

Kevlar

\

Figure 15. All man-made fibres consist of a multitude of structural elements. Their arrangements in fibre super-structure, and their dimensions are well defined and d o not vary a great deal from fibre to fibre. In general, all fibres consists of cylindrical macrofibrils having a diameter between 100-150 nm. Each macrofibril consists of cylindrical macrofibrils having a diameter between 5-10 nm. T h e microfibrils consist of crystalline and amorphous domains that are held together by intrafibrillar tie molecules while the microfibrils are held together by interfibrillar extended tie molecules. It is believed that the mechanical properties of fibres are to a large degree controlled by the structure of the microfibrils. T h e cross-section of the microfibrils contains about 75-100 molecules

4 64

D. C. Prevorsek

L/D= 50

Amorphous Domains

Figure 16. Idealized structural model of Spectra fibre crystals and disordered amorphous domains which are in a rubbery state at ambient temperature. The needlelike crystals are linked axially by small disordered domains, forming so-called microfibrils and these microfibrils are embedded in an amorphous domain (matrix). Since many molecules traverse the interface between the crystallites and the adjacent amorphous rubbery phase, the two phases are covalently bonded, thus producing a most effective impact-absorbing composite structure [21]. The amount of “amorphous” rubbery matter is 25% [28] and the ratio of length to diameter (L/D) of the crystals is about 40 [20]. Based on the work of Schaper et al. [27], Kip et al. [29] and our own morphological investigations, the structural model shown in Figure 16 is currently used by us for the ultrastrong PE fibres. It has been established by these techniques that high strength high modulus PE consists of microfibrils whose lateral dimension is well defined 4 nm. The studies of Schaper [27] indicate that the and amounts to microfibrils have a finite length of about 1000 to 2000 nm. This yields a microfibril aspect ratio L/D of 250-500. In addition, the small angle X-ray diffraction work of Grubb [25] indicates the presence of a long period of 200 nm. This means that the structure of the microfibril is not uniform in density but contains areas of different density that could be attributed to domains containing a high concentration of crystal defects. These findings are supported by the electron microscopy work of Kramer 1261. Based on the analysis of mechanical properties and degrees of crystallinity measured by WAXS, we propose that these disordered domains whose longitudinal dimensions appear to be 4-5 nm are “amorphous” domains that may contain a substantial amount of chain ends (see Chapter 7). A microfibrillar structure consistent with morphology, solid state mechanics and process mechanics is shown in Figure 17. Note that almost perfect crystals are linked by a small disordered domain. This disordered domain is in a rubbery state and covalently bonded to the solid state crystalline whisker. It should be noted that the dispersion of rubbery particles in a glassy

-

-

-

Structural aspects of damage tolerance of Spectra fibres and composites

465

Crystalline Length = 2000 - 4000 A Microfibril Diameter = 50

d

Figure 17. Proposed structure of microfibril of Spectra fibre matrix has played a key role in converting brittle plastics into an impact resistant plastic, as is the case of polystyrene toughened with rubber. This modification is still one of the most exploited technological schemes to improve the toughness and impact resistance of a variety of brittle materials, and the concept works despite poor bonding between the rubbery and glassy phases and the two phases exhibit distinct phase boundaries. Consider now the structure of PE microfibril illustrated by the composite model shown in Fig. 17. Note also that the long PE whiskers of L/D about 50 are tightly joined by tiny rubbery domains of like molecules. The only difference between the solid crystalline and amorphous domains is in the 3-dimensional order of the crystal that is absent in the rubbery junction of two adjacent crystals in the microfibril. This brings us to a challenging question: Is it possible t o conceive a more effective structure for combining modulus, strength, and impact resistance and propose such a structure regardless whether it can be made or not? We have been thinking about this fascinating problem for some time and arrived at the conclusion that Spectra fibre morphology is very close to the conceptual as well as technologically achievable optimum. References 1. K. E. Perepelkin, Angew. Makromol. Chem. 2 2 , 181 (1972) 2. P. Morse, Phys. Rev. 34, 57 (1929) 3. J. R. Schaefgen, T. I. Bair, J. W. Ballou, S. K. Kowlek, P. W. Morgan, M. Panar, J. Zimmermann, in: Ultra High Modulus Polymers, edited by A. Ciferri and I. M. Ward, Applied Science Publishers, London 1979, p. 173 4. A. J. Pennings, K. E. Menninger, ibid., p. 117 5 . P. Smith, P. J. Lemstra, B. Kalb, A.J. Pennings, Polymer Bull. 1,733 (1979) 6. P. Smith, P. J. Lemstra, US Patents Nos. 4,344,908, 4,422,993, 4,430,383 7. S. Kavesh, D. C. Prevorsek, US Patents Nos. 4,413,100. 4,536,536, 4,663,101 8. M . A. Wilding, I. M . Ward, Polymer 19, 969 (1978) 9. Spectra-900, Allied Corporation, Morristown, N. J.

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10. M. A. Wilding, I. M. Ward, Polymer22, 870 (1981) 11. I. M. Ward, M. A. Wilding, J. Polym. Sci. Phys. 22, 561 (1984) 12. D. C. Prevorsek, in: Encyclopedia of Polymer Science a n d Engineering, edited

13. 14.

15. 16. 17. 18. 19. 20.

21.

by H. Mark, N. M. Bikales, C. Overberger, G. Menges, Supplement Volume, 2nd edition, John Wiley & Sons, Inc. 1989, p. 803 A. J. Pennings et al., Pure Appl. Chem. 55, 777 (1983) D. C. Prevorsek, “Recent Advantages in Mechanical Properties of Fibers”, in: Proc. International Symp. on Fiber Science a n d Technology, Hakone, Japan, August 1985. The Society of Fiber Science and Technology, Japan, 1985 A. Cowking, J. Mater. Sci. 10, 1751 (1975) D. C. Prevorsek, Y. D. Kwon, J. Macromol. Sc:. Phys. 12, 447 (1976) D. C. Prevorsek, W. J. Lyons, J. Appl. Phys. 35, 3152 (1964) Y. Termonia, P. Meakin, P. Smith, Macromolecules 18, 2246 (1985) D. C. Prevorsek, H. B. Chin, Y. D. Kwon, J. E. Field, J. Appl. Polym. Sci., Appl. Polym. Symp. 47, 45 (1991) J. A. Zukas, T. Nicholas, H. F. Swift, L. B. Greszczuk, D. R. Curran, “Impact Dynamics”, Wiley, New York 1982, p. 367 D. C. Prevorsek, H . B. Chin, A. Bhatnager, Composite Structure 23, 137

(1993) 22. J. E. Field, unpublished results 23. D. C. Prevorsek, L‘lJltrahighModulus/Strength Polyethylene Composites”, in: Reference Book for Composites Technology, edited by S.M. Lee, Technomic Publishing Co., Lancaster , PA, USA 1989, p. 167 24. D. C. Prevorsek, H. B. Chin , Y. D. Kwon, “Strain Rate Eflects in Spectra Armour”, in: High Performance Composites for the 19909, edited by S. K. Das,C. P. Ballard and F. Marikar, The Minerals, Metals & Materials Society, Warrendale, PA, USA 1991, p. 451 25. D. T. Grubb, Macromolecules (in press) 26. V. Kramer, Allied-Signal Inc. unpublished data 27. A. Schaper, D. Zenke, E. Schultz, A. Hirte, M. Taege, Phys. Stat. Sol. (a) 116, 179 (1989) 28. W. R. Busing, Macromolecules 23,4608 (1990) 29. B. J. Kip, M. C. P. van Eijk and R. J. Meier, J . Polym. Sci., Polym. Phys. Ed. 29, 99 (1991)

Oriented Polymer Material> Stoyko Fakirov Copyright 0 2002 Wiley-VCH Verlag GmbH & Co. KGaP

Chapter 16

Segmental orientation in deformed rubbery networks

I. Bahar, B. Erman

1. Introduction

A rubbery network consists of linear polymer chains joined into a threedimensional structure by permanent cross-links or junctions. The polymer molecule between two junctions is referred to as the network chain. The macroscopic deformation of the network results in the displacement of the junction points, and hence in the transformation of the e n d - b e n d vectors 1: of the network chains. Rubbery networks are, in general, employed at temperatures well above the glass transition temperatures of the constituent chains. At these temperatures the chains between two junctions may take all possible configurations, subject to the constraints imposed by the connectivity of the network structure. Two molecular models, referred to as the u f i n e network, and phantom network models, have found widespread use in the analysis and interpretation of elasticity of rubbery networks. In the former [1,2], the junctions are assumed to be securely embedded in the network, and transform affinely with macroscopic deformation. On the other hand, in the phantom network model, the junctions are allowed to fluctuate about their mean positions, and the amplitude of these fluctuations is assumed to be independent of the macroscopic strain [3-51. According to both models, however, the network chains themselves are phantom-like, going freely from one configuration into another, in close conformity with the high temperature behaviour pointed out above. The configurational statistics of a network chain may only be

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I. Bahar, B. Erman

altered through the displacement of the two junctions at its extremities, i.e. by changing the magnitude of the end-to-end vector T , and is otherwise independent of intermolecular interactions along the chain contour. This picture forms the basis of the classical theories of rubber elasticity [ 6 ] ,and will be adopted in discussing segmental orientation in the present chapter. Segmental orientation or molecular orientation refers to the anisotropic distribution of chain segment orientations in space, due to the orienting effect of some external agent. In the case of uniaxially stretched rubbery networks, which will be the focus of the present chapter, segmental orientation results from the distortion of the configurations of network chains when the network is microscopically deformed. In the undistorted state, the orientations of chain segments are random, and hence the network is isotropic, inasmuch as the chain may undertake all possible configurations, without any bias. In the other extreme case of infinite degree of stretching of the network, segments tend to align exclusively along the direction of stretch. The mathematical description of segmental orientation at all levels of macroscopic deformation forms the object of the present chapter. It should be stated at the outset that the nature of segmental orientation in rubbery networks differs clearly from that in crystalline or glassy polymers. While the chains in the glassy or crystalline solids are fully or partly frozen, those in an elastomeric network have the full freedom of going from one configuration to another, subject to the constraints imposed by the network connectivity. The orientation at segmental level in glassy or crystalline networks is mostly induced by intermolecular coupling between closely packed neighboring molecules, while in the rubbery network intramolecular conformational distributions predominantly determine the degree of segmental orientation. The chapter is organized as follows: In Section 2, the network structure is defined for the discussion of segmental orientation. The relationship between the macroscopic state of deformation of the network and the microscopic or molecular deformationof network chains is presented. In Section 3, the characterization of segmental orientation in terms of molecular parameters and microscopic deformation is outlined. In Section 4, the expression for the orientation function in higher order approximation is described. In Section 5 , experimental techniques for determining segmental orientation are mentioned, emphasizing the characterization of segmental orientation by Fourier transform infrared dichroism measurements, in particular. Theoretical interpretation of infrared measurements and predictions based on the rotational isomeric state formalism of equilibrium statistics are presented and discussed in Section 6 .

Segmental orientation in deformed rubbery networks

469

2. Relationships b e t w e e n macroscopic and molecular deformation

and n e t w o r k structure

The network consists of v chains joined by random cross-linking or endlinking depending on the functionality of chain ends and/or the type of chemical reactions involved in network formation. The functionality, (6, of a junction is the number of chains meeting at that junction. Only perfect networks are considered in this chapter, in the sense that each chain terminates at two distinct junction points and there are no loops or dangling chains in the network. Insofar as the distribution of molecular weights between cross-links is concerned, network chains may be monodisperse, polydisperse, unimodal, bimodal, etc. The chains in a typical network comprise about 500 repeat units, and therefore, their end-to-end separations closely obey Gaussian distributions. These distributions are centered about a single value in unimodal, and two distinct values in bimodal networks. Unimodal networks will be considered in the present work. The state of microscopic deformation is defined by the displacement gradient tensor, A. In the present chapter, only uniaxial homogeneous deformation will be considered. In this case, assuming incompressibility of the network, A takes the form

where A is the ratio of the stretched length of the rubbery sample to its undeformed reference length. A-'I2 represents the deformation in the lateral direction. Thus, the first element along the diagonal of the matrix represents the extension ratio along the direction of stretch, which may be conveniently identified as the X-axis of a laboratory-fixed frame XYZ. The other two elements refer to the deformation along two lateral directions, Y and Z. The product of the three extension ratios equates to unity ensuring the incompressibility of the network. The homogeneous macroscopic deformation of a network results in the deformation of the network chains, described by the microscopic deformation tensor A2, as 0

(y2)

(Y2h 0

Here As, A, and A, denote the components of the microscopic deformation tensor along the X,Y and Z directions, respectively. ( x 2 ) denotes the

470

I. Bahar, B. Erman

mean-square x-component of chain end-to-end vectors in the deformed network. The angular brackets refer to the ensemble averages over all chains, either in the deformed state or in the undeformed reference state. The latter is indicated by the subscript zero appended to the angular brackets. Network chains in the reference state will be assumed to have the so-called unperturbed dimensions, characteristic of theta conditions, unless the network is isotropically swollen prior to deformation. Similar definitions apply to the other two directions. In the affine network model, since chain ends transform affinely, Eq. (2) takes the following form

"

For the phantom network model [7], the mean chain dimensions transform affinely but fluctuations are independent of the macroscopic deformation, and therefore the deformation at the molecular level is less than that given by Eq. (3). In this case Eq. (2) is replaced by

A2

=

1 -2/4!2

+2/4

0 (1 -2/4)X-'+2/4 0

0 0 (1 -2/4)X-'

+2/4

3

(4)

In real networks, the state of microscopic deformation is accepted to be intermediate between those given by Eqs. (3) and (4), as also evidenced by experimental findings [6]. 3. Segmental orientation in network chains

Segmental orientation in chains of a deformed network is characterized by the orientation of a given vector, u , rigidly affixed to one or more bonds along the network chain, as shown in Figure 1. For example, transition moment vectors u , rigidly attached to each repeat unit along the chain, are considered in Fourier transform infrared dichroism measurements, provided that the dipole moment change implied by a given infrared-active normal vibration may be ascribed to the reorientation of u.The broken solid line going from junction A to junction B, in Figure 1, represents a network chain. The dashed lines meeting at the two tetrafunctional junctions are bonds of other chains terminating at these junctions. The laboratory-fixed coordinate system is identified by the axes XYZ. The X-axis makes an angle x with u . 0 denotes the angle between the chain vector T and the X-axis. In uniaxial deformation, the X-axis is conveniently identified with the direction of the applied load which may be tensile or compressive. The

Segmental orientation in deformed rubbery networks

47 1

Figure 1. Schematic representation of a network chain between two junction points A and B. T is the network chain vector, also referred to as the end-toend separation vector, making an angle of 0 with the X-axis of the laboratory fixed frame OXYZ. u represents a vectorial quantity rigidly affixed to the chain, making an angle x with the X-axis. In FTIR experiments of uniaxially stretched networks, the X-axis is chosen along the stretch direction, and the vector U , which is generally appended to each repeat unit, stands for the transition moment vector associated with the observed absorption band

orientation of u with respect to the X-axis is expressed in terms of the orientation function S(x),which is given by the second Legendre polynomial pz(c0Sx) as

S(X)= ( ~ ~ ( c o s x=) (1/2)(3(cosZ ) X) - 1)

(5)

The overbar refers to ensemble averaging over all configurations of the chain, subject t o the conditions imposed on the positions of the junctions A and B. For the simplest case of the affine network model, for example, the junctions are assumed to be fixed in space. This model forms the starting point of the formulation of the present chapter. The average (-) results from two successive averages: First, the average over all configurations of a given chain with fixed ends is performed, which is designated by the overbar. Second, the averaging over all the chains of the network, subject t o different molecular extension ratios compatible with the imposed macroscopic deformation is performed, this being indicated by the angular brackets. The average cos2 x, appearing in the righthand side of Eq. ( 5 ) , was first derived by Nagai [8], and subsequently in more complete form by Flory [9]. The first order approximation for cos2 x is

A{ +

cos2x = 3 1 2Do

[& f (&+}I)-

(6)

472

I. Bahar, B. Erman

where DOis the configurational factor for segmental orientation given by

Do =

3(r2 cos' (P)o/(r2)o- 1 10

(7)

The angle (P in Eq. (7) represents the angle between u and T . For a given chain structure, the second order moments (r2)oand (r2cos2 0 ) o appearing in the front factor DO may be calculated by various theoretical schemes, among which is the rotational isomeric state formalism [9,6,15] and by Monte Carlo simulations [10,11]. The configurational factor has been shown to be inversely proportional to chain length, which is conveniently expressed as DO 1/n where n is the number of bonds in the network chain. For a freely jointed chain with N bonds, or for a real chain approximated by a freely jointed chain of N equivalent bonds (N 5 n),the front factor equates to 1/5N, as was originally shown by Kuhn and Griin [12] and later elaborated by Roe and Krigbaum [13] and Jarry and Monnerie [14]. Accordingly, the front factor of 1/5N may be interpreted as the orientation modulus of a Kuhn chain. This interpretation has been adopted indiscriminately, in the literature for the last fourty years. Departures of real network behaviour from the simple Kuhn formulation have been discussed by Erman and Bahar [15]. The ensemble average of Eq. (6) over all network chains in the deformed state leads to

-

where the definition for molecular deformation given by Eq. (2) has been employed. Substitution of Eq. (8) into Eq. (5) leads to the segmental orientation function

For uniaxial deformation, Equation (9) may be expressed in terms of macroscopic deformation tensor by substituting from Eq. (3) for the affine network model and from Eq. (4) for the phantom network model as

Segmental orientation is thus conveniently separated into two factors, a front factor DOwhich is purely a function of the chain structure, and a deformation dependent term which is a function of junction functionality and macroscopic deformation.

473

Segmental orientation in deformed rubbery networks

In the case of networks swollen prior to deformation and/or cross-linked in solution, Eq. (10) is replaced by

-

(mine)

~ o ( v 2 ~ / v 2 ) ~ /a ~ -(l a ) ~

(11)

~ ~ ( 21 / 4 ) (-v z c / v z > 2 / 3 ( a 2 - a-1) ( ~ h a n t o m )

where vac is the volume fraction of polymer during cross-linking, v2 is its volume fraction during stretching experiment and a is the extension ratio relative to the intermediate swollen but undistorted state. For dry networks, crosslinked in the bulk state, Eq. (11) reduces to Eq. (10). 4. Higher order approximation for segmental orientation

Equation (6) represents a suitable first approximation for segmental orientation in relatively long chains. In a strict sense, this expression and the resulting relationship of S ( x )to deformation, given by Eq. (10) or Eq. (ll), are valid for networks with relatively long chains obeying Gaussian statistics and subject to small strains. Eq. (10) is the first term of a series expansion in powers of l / n , whose higher order terms are to be included for representing segmental orientation on shorter chains and at higher deformations. The higher order approximation was first given by Nagai [8]. An improved version of the expression containing up to third order terms in 1/n has been recently obtained by Erman et al. [lo]. The latter follows essentially from the work of Nagai with minor corrections, and has been adopted in the analysis of segmental orientation in short chains [ll]. Here, we give the series expansion up to the second order terms [16]

S(x)=

f [..

(A2

- x-1)

+ D1

A4

+ -A

-

+D2 A6

+ -A3

- -x-3

( (

31 5

34 5

)

)]

(12)

where

The various coefficients in Eqs. (13)-(15) are defined in terms of the mo-

474

I. Bahar, B. Erman

ments (rZk)o and (r2kcos20 ) o of unperturbed chains as

The expressions given by Eqs. (12)-(19) are derived for a network whose junction points transform affinely with macroscopic deformation. Following the argument that led to Eq. (lo), the higher order expression corresponding to phantom network is obtained by multiplying Eq. (12) by (1 - 2/4). The coefficient Do in Eq. (12) is of the order n-l while D1 and 0 2 are of the order n - 2 . Retaining only t72 in Eq. (13) leads to the first order approximation given by Eq. (7). The expressions in Eqs. (16)-(19) show that the determination of segmental orientation up to any desired accuracy rests on the evaluation of the statistical moments of free chains. These moments may be evaluated, in principle, by the rotational isomeric state formalism [9,17,18] or more easily by the Monte Carlo technique [10,11]. It should be noted that, for chains with N freely jointed segments, the same expression as Eq.(12) has been obtained by Roe and Krigbaum [13] for s ( ~ ) , the coefficients for this simplified model being given by DO = 1/(5N), L)I = 1/(75N2) and DZ= 1/(105N3). 5. Experimental determination of segmental orientation in rubbery networks Strain birefringence experiments have been the most commonly adopted technique in determining segmental orientation in networks [19-221. However, due to uncertainties in bond polarizabilities and the presence of large contributions from intermolecular interactions, this technique cannot be reliably used for quantitative determination of orientation of specific vectorial quantities in network chains. Polarized Fourier transform infrared [27,35] (FTIR) and deuterium nuclear magnetic resonance [23-253 (2HNMR) spectroscopy are two very specific and precise spectroscopic techniques [6]. Recent comparison of FTIR measurements on well-defined model poly(dimethylsi1oxane) (PDMS) networks with rotational isomeric state

Segmental orientation in deformed rubbery networks

475

calculations applied to segmental orientation [35],for example, led to satisfactory agreement between experiment and theory. Both the FTIR and the (2H-NMR) techniques directly measure the orientation of specific label on a chain relative to a laboratory-fixed axis. The orientation is suitably induced by stretching the specimen uniaxially. Inasmuch as the applied deformation may be sustained indefinitely in a network, segmental orientation at equilibrium may be obtained by performing the measurements after allowing sufficient time for equilibration. Furthermore, the system may be swollen with a suitable diluent to eliminate local intermolecular orientational correlations [27]. In this section, the use of infrared spectroscopy for determining segmental orientation and its theoretical analysis will be considered; the reader is referred to the work of Deloche et al. [26] for a comprehensive presentation of the application of the NMR technique to segmental orientation. Absorption bands associated with transition moments having a definite orientation with respect to the chain backbone are studied in FTIR dichroism measurements. The vector u of Figure 1 may, for instance, be assumed to be the transition moment observed in infrared measurements. As a common practice, the orientation of a local chain axis is considered in data interpretation rather than the orientation of the specific transition moments. The chain axis is essentially a fictitious and somewhat ambiguous entity, defined as an axis of cylindrical symmetry with respect to u . If one denotes the angle between u and the axis of symmetry by a,and the angle between the axis of symmetry and the direction of stretch by 0,segmental orientation S(x) may be related to the orientation function S ( 0 ) of the symmetry axis by

where S ( a ) = (1/2)(3cos2 (Y - l ) , and S ( 0 ) is given by an expression similar to Eq. (5). Equation (20) was introduced by Fraser [28] and applied t o orientation in deformed polymers by Read and Stein [29]. In the latter work, the angle 0 has been referred to as the angle between the stretch direction and the “segments” of the chains. For incident radiation polarized along the direction of stretch, which has been identified above with the X-axis, the absorbance of u may be resolved into two components, one parallel, all, and another perpendicular, a l l to the X-axis. In terms of the angle x, all and a 1 are expressed as

The factor of 1/2 in Eq. (21) results from averaging of all rotations of u about the stretch direction, which constitutes an axis of cylindrical sym-

476

I. Bahar. B. Erman

metry. The dichroic ratio R measured in infrared studies is defined as I

I

where h(X) is the distribution function for the Eq. (21) in Eq. (22), and using Eq. (5) leads to

x

angles. Substituting

R-1 S(X) = R+2 The components all and a 1 may alternatively be expressed in terms of the angles Q and 0.In this case, the dichroic ratio takes the form [30,31]

R=

1 + (2 cot2 Q - 1)(cos20)

1

+ (cot2 a - 1/2)( 1 - (cos2 0))

(24)

which, using Eq. ( 5 ) , leads to

S(0)=

2 R- 1 3c0s2a- 1 R + 2

Equation (25) is implicitly based on the presence of a chain-embedded local axis with respect to which u is assumed to undergo cylindrically symmetric rotations. However, the anisotropy of chain structure and of rotational isomeric states, might invalidate the adoption of an axis of cylindrical symmetry on a local scale, as recently discussed [32]. Thus, direct comparison of experimental measurements of S(x)with theoretical predictions seems more reliable, in general. 6. Theoretical interpretation of infrared dichroism measurements of segmental orientation in rubbery networks

Strain-orientation data may suitably be interpreted in terms of the reduced defined as orientation,

[q

S

S

'4 = (P - ~ - 1 ) - (vZe/v2)2/3(a2- a-1)

Defined in this manner, and by analogy with the definition of the reduced stress, [qmay be seen as the orientational modulus of the network. In the first order approximation, given by Eq. (lo), the reduced orientation is

Segmental orientation in deformed rubbery networks

7 0 0

I 0

I

0

1

0

...........9......................._.......-

I 0.Wo'. 0.0

' 0.2

.

'

0.4

.

1/a

' 0.6

'

'

0.8

.

II

i.0

477

Figure 2. Segmental orientation in dry PDMS networks with indicated molecular weights. Circles represent FTIR dichroism measurements of Besbes et al. [27]. The horizontal lines are calculated from Eqs.(7) and (lo), adopting the phantom network model. The curves are theoreticallv obtained using- the constrained junction model [34]

independent of deformation both for the affine and the phantom network models. Results of polarized FTIR experiments on well characterized PDMS networks from the work of Besbes et al. [35] are presented in Figure 2, where the reduced orientation is plotted as a function of inverse extension ratio. The circles represent experimental data for two networks with the indicated molecular weight M , of network chains. The horizontal dashed lines represent prediction for the phantom network model from the second of Eq. (10) with 4 = 4 and DOobtained theoretically from Eq. (7) as DO= 1.045 x for M , = 23,000 and 2.405 x for M , = 10,000. Although agreement between experiment and theory is reasonable according to Figure 2, data points are always above the phantom network prediction. Experiments on other systems have also indicated to the same feature [43]. The departure from phantom network behaviour is generally attributed to the effects of entanglements that constrain fluctuations at the molecular level [20,33]. This explanation has been recently verified for segmental orientation in well defined PDMS networks, measured by polarized FTIR technique [34]. The curves in Figure 2 illustrate the predictions of the constrained junction model of rubber elasticity, applied to the segmental orientation of the PDMS networks with given molecular weight and functionality [34]. It should be noted that the constrained junction model prediction converge to that of the phantom network in the limit of infinite extension. The dependence of segmental orientation of chain length is shown in Figure 3. The circles are from polarized FTIR experiments of Besbes et al. [35] for four different networks. The affine and phantom predictions shown by the straight lines are obtained theoretically from Eq. (10). The Kuhn model prediction is obtained by simply taking DO as 1/5N, where the number of bonds in Kuhn segments is taken to be equal 17, i.e. n / N = 17, following the work of Flory and Chang [36]. This comparison shows

I. Bahar, B. Erman

478

that experimental data yield results closer to the phantom network model, and that the Kuhn model predicts much higher orientations. A critique of segmental orientation based on the Kuhn model has been recently presented [15].

Figure 3. Reduced orientation as a function of chain length for phantom, affine and Kuhn model chains for PDMS networks [35]. Experimental points, indicated by the filled circles a p proximate the phantom network

behaviour The results of Fourier transform infrared measurements on poly (dimethylsiloxane) networks presented in the preceding paragraph are also in reasonable agreement with the 2H-NMR data of Deloche et al. [23,24,26]. Although predictions of the theory [33] based the constrained junction model of rubber elasticity [37], agree reasonably well with experimental data [27,43], a complete understanding of orientation in non-phantom-like networks is still missing. In Figure 4, for example, the reduced orientation obtained from Eq. (11) with higher order terms is shown by the curve. The horizontal line is obtained by retaining the first term only and corresponds to the first order theory. The strong upturn of the reduced orientation with higher order terms is representative of non-Gaussian contributions at large extensions. Such an upturn is not observed, however, in experimental data obtained from non-crystallizing networks. A further contribution to orientation associated with trapped entanglements has been suggested by Kerz et al. [38], and Deloche and collaborators [39,40]. These contributions are asserted to persist even in the swollen network, but their effects should vanish if the networks are originally formed in the highly diluted state. One might therefore separate the contributions from intermolecular sources into two parts, a local and an entanglement component, and express the effective configurational factor as

Segmental orientation in deformed rubbery networks

479

0.040

0.W

0.030

0.025

0.020

2

1

first order approximation

/

chains using the first and second order approximations, given by Eqs. (10) and (12), respectively

0.015 C

where Df" reflects the contributions from local intermolecular correlations and D p is due to trapped entanglements. A lattice model recently developed for structurally anisotropic semi-rigid model chains allows one to express the intermolecular contributions to segmental orientation in terms of the strength of nematic interactions between neighboring chains and the length-to-width ratio of the anisotropic segments composing the network chains [41,42]. Strong contributions from Df" have been reported for the orientation of polyisoprene (PIP) networks by polarized fluorescence measurements [43]. Results of FTIR experiments on swollen PDMS networks show, on the other hand, that Df" is not significant for this system [27]. The effects of swelling on segmental orientation are compared in Figure 5 for PIP and PDMS networks. The upper set of filled points represents the experimental measurements on a dry PIP network. The curve through the points is obtained using the constrained junction model [41]. Results for the PIP networks in the swollen state with v 2 = 0.88 and 0.81, are shown by the empty circles and triangles, respectively. A very strong decrease in [Sl is obtained by small amounts of swelling as seen in the figure, which could not be theoretically reproduced unless a modification in the configurational front factor, conforming with Eq. (27) was introduced. This decrease is then attributed to the disappearance of intermolecular effects upon swelling. The lowest theoretical curve and the indicated experimental data points are obtained for the PDMS networks with v 2 = 1 and 0.56 [34]. The differences between the two data sets are not discernible in the figure in parallel with the predictions of the constrained junction model. This indicates that intermolecular contributions to the configurational factor D are negligible in PDMS networks, in contrast to PIP. Calculations performed for PDMS networks having various solvent content during cross-

I. Bahar, B. Erman

480 0.03

0.02

0.01

PDMS

-

0.00 0.

0

0.58.1.0

Figure 5. Reduced orientation as a function of reciprocal extension ratio a, for PIP and PDMS network chains, swollen to various extents, as indicated by the labels, prior to deformation. The curves for the dry states 212 = 1 of both chains are theoretically calculated [34]. The curves for swollen swollen states of of PIP are obtained by considering intermolecular contributions to configurational factors

lla

linking, i.e. with different v2e values, also yielded good agreement between theory and experiments [34], confirming further the negligibly weak effect of intermolecular interactions on segmental orientation in PDMS. Acknowledgement

Partial support from Bogazici University Research Funds project 93P0084 is gratefully acknowledged. References 1. F. T. Wall, P. J. Flory, J. Chem. Phys. 19, 1435 (1951) 2. P. J. Flory, “Principles of Polymer Chemistry”, Cornell University Press, Ithaca, New York 1953 3. H. M. James, E. Guth, J. Chem. Phys. 15, 669 (1947) 4. H.M. James, E. Guth, J. Chem. Phys. 11, 455 (1943) 5. H. M. James, E. Guth, J. Chem. Phys. 21, 1039 (1953) 6. J. E. Mark, B. Erman, “Rubberlike Elasticity: A Molecular Primer”, W i e y Interscience 1988 7. P. J. Flory, Proc. R. SOC.London A , 351, 351 (1976) 8. K. Nagai, J. Chem. Phys. 40, 2818 (1964) 9. P. J. Flory, “Statistical Mechanics of Chain Molecules”, Interscience, New York 1969 10. B. Erman, T. Haliloglu, I. Bahar, J. E. Mark, MacromoJecules 24,901 (1991) 11. T.Haliloglu, I. Bahar, B. Erman Comp. Polym. Sci. 1, 151 (1991)

Segmental orientation in deformed rubbery networks 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41.

48 1

W. Kuhn, F. Griin, Koloid-2. 101,248 (1942) R. Roe, W. R. Krigbaum, J. Appl. Phys. 35,2215 (1964) J. P. Jarry, L. Monnerie, Macromolecules 12,316 (1979) B. Erman, I. Bahar Macromolecules 21,452 (1988) The coefficients DO,D1,and Dz of the present manuscript were given respectively as D I , Dz,and D3 in the previous treatment P. J. Flory, Y. D. Yoon, J. Chem. Phys. 61,5360 (1974) Y. D. Yoon, P. J. Flory, J. Chem. Phys. 61,5366 (1974) L. R. G. Treloar, “The Physics of Rubber Elasticity”, Clarendon Press 1975 B. Erman, P. J. Flory, Macromolecules 16, 1601 (1983) B. Erman, P. J. Flory, Macromolecules 16, 1607 (1983) B. Erman, J. P. Queslel, in: Encyc. Matls Sci. a n d Engn’g. John Wiley & Sons Inc. 1989, Supplement Vol., 2nd Ed., p.18 A. Dubault, B. Deloche, J. Herz, Polymer 25, 1405 (1984) A. Dubault, B. Deloche, J. Herz, Macromolecules 20, 2096 (1987) P. Sotta, B. Deloche, Macromolecules 23, 1999 (1990) B. Deloche, A. Dubault, J. Herz, A. Lapp, Europhys. Lett. 1,629 (1986) S. Besbes, L. Bocobza, L. Monnerie, I. Bahar, B. Erman, Polymer (1993) in press R. D. B. Fraser, J. Chem. Phys. 21, 1511 (1953) B. E. Read, R. S. Stein, Macromolecules 1,116 (1968) B. Jasse, J. L. Koenig, J. Macromol. Sci., Chem. C 17,61 (1979) B. Jasse, J. F. Tassin, L. Monnerie, Progr. Colloid Polym. Sci. (1993), in press I. Bahar, B. Erman, Macromolecules (1993) submited B. Erman, L. Monnerie, Macromolecules 18,1985 (1985) B. Erman, I. Bahar, S. Besbes, L. Bokobza, L. Monnerie, Polymer (1993) in press S. Besbes, I. Germelli, L. Monnerie, I. Bahar, B. Erman, J. Herz, Macromolecules 25, 1949 (1992) P. J. Flory, W. C. Chang, Macromolecules9, 33 (1976) B. Erman, P. J. Flory Macromolecules 15,800 (1982) J. Herz, J. P. Munch, S. Candau, J. Macromol. Sci., Phys. B 18,267 (1980) B. Deloche, E. T. Samulski, Macromolecules 14,575 (1981) A. Dubalt, B. Deloche, J. Herz, Macromolecules 20,2096 (1987) B. Erman, I. Bahar, A. Kloczkowski, J. E. Mark, Macromolecules 23, 5335

(1990) 42. I. Bahar, B. Erman, A. Kloczkowski, J. E. Mark, Macromolecules 23,5341 (1990) 43. J. P. Queslel, B. Erman, L. Monnerie, Macromolecules 18, 1991 (1985)

Oriented Polymer Material> Stoyko Fakirov Copyright 0 2002 Wiley-VCH Verlag GmbH & Co. KGaP

Chapter 17

Orientation effects on the thermal, mechanical and tribological performance of neat, reinforced and blended liquid crystalline polymers

R. Schledjewski, K . Friedrich

List of symbols

AP AP' B

c

da/dN E Ebond

E' GI, Ah AIi' ICI, N N'

P P" P

anti-parallel sliding orientation, see Figure 19 sliding orientation transverse to A P , see Figure 19 bulk thickness in mm core layer thickness in mm crack velocity in mm.cycles-' elastic modulus interatomic bonding energy in eV complex dynamic modulus in GPa energy release rate in kJ.m-2 penetration depth in mm dynamic stress intensity factor in M P a f i fracture toughness in M P a f i normal sliding orientation, see Figure 19 sliding orientation transverse to N , see Figure 19 parallel sliding orientation, see Figure 19 sliding orientation transverse to P , see Figure 19 pressure in MPa

Orientation effects on liquid crystalline polymers

483

skin layer thickness glass transition temperature in "C time in hours sliding velocity in m.s-' specific wear rate in mrn3.N-'.m-' time dependent wear rate in pm.h-' coefficient of linear thermal expansion in OC-' tensile strength in MPa 1. Introduction

The covalent linkage within macromolecules offers important potentialities for the development of high-strength and high-stiffness polymers. The bonding energy (,!?!bond) of covalent linkages is similar to that of ionic ones (,!?bond % 5 . . . l o e v ) and higher than that of metallic ones (,!?!bond M 1 e v ) . But, whilst the latter two bonding types are able to build up dense crystal structures, the covalent one is restricted due to the strong orientation of the linkage. Furthermore, in the case of polymers the covalent linkages are usually built up more or less one-dimensionally ; especially for commodity polymers, the macromolecules are statistically oriented. An additional restriction results from the fact that the intermolecular bonding energy (e.g. hydrogen bonding ,!?bond x 0 , 1 eV) is lower by more than one order of magnitude compared to the intramolecular covalent bonding energy. It is well known, that molecular orientation within a polymeric material results in higher strength and stiffness parallel to this orientation. Unfortunately, such an orientation is only attainable by e.g. very special flow conditions during molding or additional drawing after molding, e.g. drawing of polypropylene filaments increases the modulus parallel to the draw axis by a factor higher than five [l]. For many applications such an additional treatment is impossible or just too expensive (see also Chapters 1 and 2). An important aim within the research activities in the field of synthetic polymers is to develop polymers which are easily orientable. Liquid crystalline polymers (LCPs) offer this possibility, since they exhibit an ordering already in the molten state. Due to shear and elongational flow during molding these materials reveal a highly oriented structure. The mechanical properties of e.g. poly(ethy1ene terephthalate) (PET) can be improved significantly by modifying the molecular build-up in a way that P E T exhibits a liquid crystalline behaviour [a]. Orientation effects on thermal, mechanical and tribological properties of neat, reinforced and blended LCPs will be described below (see also Chapters 11, 12, 14).

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2. Liquid crystalline polymers

Generally, liquid crystals can be divided into monomeric and polymeric ones [2-51. The latter will be described in this chapter, starting with a comprehensive overview of the history and the structure of LCPs.

2.1. Liquid crystals and their history Liquid crystals have been known for little more than a century. In 1888 the Austrian botanist Friedrich Reinitzer described the liquid crystal phenomena in his article: “Contributions to the Knowledge of Cholesterol” [6]. This and many posterior works were done on monomeric materials. In the twenties Vorlander predicted that liquid crystal phenomena should also exist for polymeric materials. In 1956 Flory described theoretically the lyotropic behaviour [7]. One decade later, in 1968, the first main chain LCPs (aramids) were synthesized by Kwolek [8]. A well-known result of this work was the lyotropic aramid fibre. Based on the knowledge gained from the lyotropic LCPs, very intensive research work was done to develop thermotropic LCPs. In the mid 70s Eastman Kodak brought to the market the first well characterized thermotropic LCP which was based on a development by Jackson and Kuhfuss [9]. Due to its low heat deflection temperature ( x 7OOC) this product, named X7G, did not attain high commercial significance. Since the end of the 70s many different thermotropic LCPs have been developed and one of them which got a commercial significance is the polyester based Vectra produced by Celanese. Although the number of commercial LCP types tend to decrease, e.g. the RhBne Poulenc product Rhodester CL, also described in this chapter, is not produced any more, the research and development activities in the field of thermotropic LCPs are quite coniderable. Table 1 lists companies which brought out patents concerning LCPs in the last decade [2]. Table 1. List of material codes

A950 C950 E950 Rhod. N

base LCP of the Vectra series; A-grade LCP (Hoechst Celanese Corp.) high temperature, low viscosity LCP of the Vectra series; C-grade LCP (Hoechst Celanese Corp.) high temperature LCP of the Vectra series; E-grade LCP (Hoechst Celanese Corp.) high viscosity LCP of the Rhodester CL series (RhBne Poulenc Chimie)

485

Orientation effects on liquid crystalline polymers

Figure 1. Three different kinds of ordering within the mesophase can be distinguished

2.2. Structure of LCPs

Thermoplastic polymers are normally built up of flexible entangled macromolecules which are randomly oriented in the melt. In the case of amorphous thermoplastics this arrangement is preserved in the manufactured parts. Therefore a nearly isotropic behaviour can be realized. Since the beginning of polymer research it has been known that linear and parallel oriented macromolecules exhibit higher strength and stiffness since loading is acting mainly on the intramolecular bondings [lo]. To take advantage of this higher performance parallel to the molecular axis, researchers have

Flexible Spacer

Flexible Spacer

Mesogenic Group

Main-Chain Main-Chain Mesogenlc Group

Side-Chain LCP

Main-Chain LCP

Figure 2. Build-up of side- and main-chain LCPs

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R. Schledjewski, K . Friedrich

tried to develop polymers which are easily orientable. The use of rigid rodlike segments, the so-called mesogenic groups, which prevent the entanglement of the molecules, led to an ordering of the molecules in the liquid state. However, this liquid crystalline behaviour, also called mesophase, occurs only if a distinct aspect ratio (higher than six) of the mesogenic groups is present. Polymers exhibiting such a mesophase are called liquid crystalline polymers. Depending on the molecular arrangement, different types of mesophase can be distinguished (Figure 1).If the molecules exhibit orientation along a director, the mesophase is called a nematic one. In case of an additional long-range order, e.g. a positional order, the mesophase is a smectic one. A cholesteric phase is observed when plies of nematic phases change their director from ply to ply. Liquid crystalline polymers can be divided into two groups (Figure 2). In the case of flexible main chains with mesogenic side groups, the so-called side-chain LCPs, mainly optical and electronic properties are of interest. In the second group, main-chain LCPs, the mesogenic groups build up the molecular chain. These materials are characterized by extraordinary mechanical properties. Main-chain LCPs can be divided into two additional groups. Lyotropic LCPs exhibit their liquid crystalline behaviour in solution. These polymers are mainly built up of mesogenic groups and the melting temperature of these materials is higher than their decomposition temperature. To get meltable main-chain LCPs, flexible spacers are introduced between the mesogenic groups, leading to a reduction of the melting temperature below the decomposition temperature. These thermotropic LCPs can be processed by conventional methods such as injection molding or extrusion. Main-chain LCPs, both lyotropic and thermotropic, exhibiting a nematic mesophase, are highly orientable. In the material the mesophase is built up of microscopic domains which can be oriented macroscopically by the flow and shear conditions occurring during processing. 3. Thermotropic liquid crystalline polymers and their properties

Since the beginning of the 80s, extensive research activities have been undertaken in the field of thermotropic LCPs. Their extraordinary spectrum of properties [11] together with their ability to be produced into complex parts by common production methods, e.g. injection molding and extrusion, have generated great interest in these materials. Thermotropic LCPs are known to have a very interesting viscosity behaviour during processing. The very low viscosity of sheared LCP melts allows them to fill very fine cavities over longer distances. Furthermore, the linear thermal expansion parallel to the molecular axis is very low, in the range characteristic of metals or ceramics. This behaviour is favourable for applications in which metal and LCP parts have to work together over a wide temperature range

Orientation effects on liquid crystalline polymers

487

without posing temperature dependent fitting problems. Mechanical properties like strength and stiffness parallel to the molecular orientation as well as friction and wear properties are extraordinary. Additionally, the flame and chemical resistances of LCPs are very good. The combination of all these characteristics is not found for any other thermoplastic material. In injection molded or extruded neat thermotropic LCPs, a high degree of anisotropy is found for many material properties. Using reinforcements or fillers, this anisotropy can be reduced. A special field for LCPs application is their use as reinforcement to other thermoplastics, high-temperature as well as commodity ones. 3.1. Neat, filled or reinforced LCPs 3.1.1. Microstructure

Unfilled, injection molded liquid crystalline polymers exhibit an inherent layered structure [12,13]. Weng, Hiltner and Baer [12] proposed a hierarchical model of the LCP’s layer structure (Figure 3). Macroscopically, three layers can be found: two skins ( S )with a core (C) inbetween. The relative contribution of each layer to the bulk thickness ( B )is in the range of about one third, depending on the specific LCP type, and is rather unaffected by the bulk thickness (Figure 4). The skin layer consists of a fine sublayer structure with a molecular orientation parallel to the mold flow direction. Within the skin the molecular orientation decreases from outside to inside [12] and for some LCPs a subdivision of the skin into an outer and an inner portion (Soand Si) is possible by the naked eye. SEM micrographs

0 to

m

Less Ordered

-

Major Flow Direction ( MFD )

Figure 3. Hierarchical model of the layer structure of LCPs as proposed by Weng, Hiltner and Baer [7]

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R. Schledjewski, K . Friedrich

of fracture surfaces depict the layer structure (Figure 5). In the outer skin the sublayers are built up of fibrillar microlayers [12,131. This third level of organization is lost in the inner skin. And finally, the core exhibits no hierarchical organization and is mainly characterized by parabolic flow lines. Within the core the molecules are also oriented, but the orientation direction depends strongly on the flow conditions during molding and can vary between parallel and transverse to the mold flow direction. Fillers or reinforcements, which are normally used (i) to increase the materials performance or (ii) to reduce the materials price, affect the selfreinforcing behaviour of the LCPs by increasing or decreasing the degree of molecular orientation. The former effect is rarely observed whereas the latter one can be detected for most of the filled or reinforced LCPs. Con-

0,2/

090

I 3 0

1

2

4 5 Total Thickness in rnrn

Figure 4. Effect of bulk thickness on the layer dimensions of neat and differently filled LCPs (basic polymer: Rhodester CL)

Figure 5. Fracture surface of neat LCP. T h e layer structure with distinct outer (SO)and inner (S,) skin layers and a core (C) layer (the fracture surface is tilted out of the page plane) is visible

489

Orientation effects on liquid crystalline polymers

c

100

E 90 u)

8 ao

5V E

?

f

70 60 50 40 30 20 10 0

Neat LCP core

Talc 1 LCP

GF I LCP Inner Skln

Graphite I PTFE I LCP M o S I~ LCP Outerskin

Figure 6. Contribution of the individual layers to the bulk thickness of LCP as a function of the materials composition (Rhodester CL-series)

cerning the microstructure, the typical three-layer structure is preserved when fillers or reinforcements are used. However, the hierarchical substructure of the skins is found if only low contents of relatively small sized compound materials are used, e.g. PTFE, graphite or molybdenum disulphide. For larger sized particles, e.g. glass fibres or talc, the substructure in the skins disappears. In addition to this effect, the kind and content of fillers or reinforcements also influence the relative contribution of the layers t o the bulk thickness (Figure 6). In contrast to the neat material, the core-to-bulk ratio of filled or reinforced LCPs strongly depends on the bulk thickness itself (Figure 4). 3.1.2. Linear thermal expansion

One of the first mentioned advantages of liquid crystalline polymers is their low coefficient of linear thermal expansion. In fact, the linear thermal expansion parallel to the molecular orientation is very low, i.e. in a range typical of metals and ceramics (Figure 7). In some cases, especially for LCPs with a molecular orientation parallel to the mold flow direction within the core, the thermal expansion is even negative. In both directions transverse to the molecular orientation, i.e. transverse to the mold plane or transverse to the mold flow direction but in the mold plane, the linear thermal expansion is clearly higher. In plane but transverse to the mold flow direction the linear thermal expansion coefficient is higher by nearly two orders of magnitude, which refers to the level found for other thermoplastics. Above room temperature, a n additional slight increase can be observed for the direction transverse to the mold plane, where the molecular orientation in both skin and core is not parallel to the measurement axis. Using nonpolymeric fillers or reinforcements, the degree of anisotropy

490

R . Schledjewski, K . Friedrich

of the coefficient of linear thermal expansion can be reduced (Figure 8). This effect is not only due to the rather low coefficient of linear thermal expansion of the materials used, e.g. glass: CY = 5 x 10-60C-1, because different amounts of e.g. glass fibres would then result in different thermal expansion performance. Actually the coefficients of linear thermal expansion of 30wt.-% and 50wt.-% glass fibres filled Vectra A-grade LCP are nearly the same. Consequently, a second effect, e.g. the various degrees of both molecular and fibre orientation, acts here as well. Compared t o metals or ceramics the obtainable "quasiisotropic" coefficient of linear thermal expansion is higher, on a level of about a = 30 x 10-60C-'.

3.1.3. Viscoelastic behaviovr Isotropic materials are characterised by material properties which are independent of the orientation of individual test samples relative to characteristic plate parameters such as mold filling direction. The opposite is true for anisotropic materials for which LCPs are a typical example. This is especially valid for their complex dynamic modulus (Figure 9). Separate skin and core layers have been investigated and the highest anisotropy between measurements parallel and transverse to the mold flow direction was observed with the skin layer. Nearly one order of magnitude is the difference in the complex dynamic modulus measured for both directions. The results for the core point again to a preferred molecular orientation parallel to the mold flow direction, but here the anisotropy is less pronounced compared to the skin. Concerning the effect of temperature two characteristic differences can be observed on comparison with a high temperature thermoplastic material, e.g. polyetheretherketone (Figure 10). First, the modulus of LCP decreases continuously with increasing temperature, and second,

Figure 7. The linear thermal expansion behaviour of neat LCP exhibits a high degree of anisotropy (Vectra A-series)

49 1

Orientation effects on liquid crystalline polymers

1

.!i

.-tat LCP

GFIPTFEI LCP

f

Graphite I GFILCP

GF I LCP

Figure 8. Effect of the materials composition on the degree of anisotropy of the coefficient of linear thermal expansion observed with differently filled LCP compounds (basic polymer: Vectra A950) the effect of glass transition (LCP: TgM 12OOC; PEEK: T, M 160OC) is less pronounced. Comparison of LCP and PEEK elucidates also another important detail of LCPs. Although PEEK is more expensive, the LCP performs. better than PEEK, but only in the direction of molecular orientation. Reinforcements such as glass fibres can increase the complex dynamic modulus, but they do not reduce significantly the anisotropy in stiffness.

3.1.4. Mechanical properties Tensile properties of neat LCPs are strongly dependent on the monomen used and their individual amounts (Figure 11). High-strength or highstiffness LCPs can be obtained which exhibit properties comparable to or even higher than those of much more expensive high-performance thermoplastics. But the tensile properties of LCPs are highly anisotropic due to orientation of the molecules. The degree of anisotropy depends mainly on the molecular build-up (Figure 12) and the part thickness (Figure 13). The latter affects the flow conditions in the various layers across the thickness, i.e. the flow character (shear or elongational) and the gradients within it; they are responsible for the local degree of orientation of the nematic domains. Subordinated are effects that result from injection molding parameters, e.g. injection velocity. Tensile tests on separated skin layers reflect the real capacity of oriented thermotropic LCPs. Compared to the bulk material the strength and also the stiffness obtained if tested parallel to the mold filling direction are higher by up to fifty percent, depending on the materials composition. However, although fillers or reinforcements sometimes result in a significant property increase for the skin, they usually affect only slightly the tensile properties of the bulk material. In fact. the tensile strength of LCP-composites is often lower compared to the neat

492

R. Schledjewski, K . Friedrich

LCP. This can be explained mainly by the additional change in the relative layer thickness when reinforcements are used, as shown for a GF/LCP compound in Figure 14. Whilst neat Rhodester CL LCP is made up of two skins having a relative contribution of 2 x SIB x 0.8 of the total thickness B , this value is reduced to 2 x S IB s 0.6 in the case of a 25 wt.-% glass fibre reinforcement (Figure 6). Furthermore, due to their molecular structure, LCPs normally exhibit a very poor bonding to the reinforcements used. For loading parallel to the fibre orientation there will still be a significant load transfer from the matrix to the fibre (as long as the fibres are longer than their critical length) and an increase in strength and especially in stiffness will be observed. But in case of transversely oriented fibres, the normally loaded interface fails even under very low load. Due to the laminate-like build-up of bulk, injection molded LCPs, a rule

.-up" 12

z:

0"'; x 2

%f 5= 0

lo 8 6 4 2 0

20

40

60

80 100 Temperature in "C

Figure 9. From the ranking of the complex dynamic modulus of the individual layers of neat LCP it can be established that the molecules in the core layer are also oriented parallel to the mold filling direction (the values obtained by testing parallel to the mold filling direction are generally higher than those found for the transverse direction)

,,,*,,,

*I ,111

,.,,,# ,,

..............-

2:::::;

% ' ,

*%, -===I

*,.'.

LCP 11 MFD LCP 1 MFD

lo2, 0

50

100

150 200 Temperature in "C

Figure 10. Complex dynamic modulus of neat LCP (Rhodester CL), tested in tensile configuration with specimen orientation parallel and transverse to the mold flow direction, compared to results obtained for PEEK

493

Orientation effects on liquid crystalline polymers

of mixtures-approach can be used for their stiffness and strength properties (Figure 15). The individual values of core and skin layers are combined with their relative contribution to the total thickness of the bulk:

c

2 x s

u=u* x B+u,x

-

B

where u is the tensile strength, B is the bulk thickness, S is the skin thickness, and C - the core thickness. The agreement between the calculated and measured material data is quite satisfactory for many different material compositions [14]. The fracture toughness of neat LCP is strongly related to the relative orientation of the crack plane to the direction of molecular orientation. Cracks which are oriented parallel to the mold filling direction can propagate very easily. Here only intermolecular bondings resist against crack growth. The resulting fracture toughness values are in a range of K I , = 2 - 4.5 MPaJm depending on the specific type of LCP, which is low compared t o values of about K I , = 5 MP aJm and K I , = 7 M P a f i obtained for nylon 6 and PEEK compounds, respectively. On the contrary, the crack resistance transverse t o the molecular orientation is so high, that tests on compact tension specimens result in a deviation of crack propagation in the direction parallel to the load axis. Voss and Friedrich investigated the fracture behaviour of neat and glass fibre reinforced LCPs [15]. They also observed crack deviation parallel to the load axis in the case of loading parallel to the molecular orientation. Their estimation of the real fracture toughness value of neat LCP for this orientation suggests the same ten-

.-

Vectra A-Grade+lOwt%GF +1Owt%GnphiteA 301

!p J

V V e c t r a A-Grade+SOwP/GF

-0

V V e c t r a A-Grade+30wt%GF

20

aJ A r

Neat Vectra A-Grade Vactra C-Grade+30wlXGF AGWPEEK UGFIPOM Vectra A-Grade+3Owt%Mineraia WVectra A-Grade+lSwt%Mlnerals

0

I-

10-

0

A-Grade+15wW.GF? Neat Rhodesler CL@Neat vectra E-Grede

100

Neat Vectn C-Grade 0GFIPA6

200

300

Tensile Strength in MPa

Figure 1 1 . Comparison between tensile properties of different LCP compounds and those of other thermoplastic materials. Different fillers or reinforcements cause variations of the tensile properties in a wide range. A significant stiffness improvement is possible

R. Schledjewski, K . Friedrich

3 93

"b 5

0

8332

2882

Figure 12. Effect of the molecular build-up of neat LCPs on the tensile properties

Figure 13. Tensile properties of neat LCP (Rhodester CL) as a function of bulk thickness and injection velocity during molding. Whilst the injection velocity hardly affect the tensile properties, a strong effect was found for the bulk thickness

dency as found here, i.e. a K I , value nearly twice as high as that found for crack propagation parallel to the molecular orientation. This anisotropy is reduced if high amounts of fibres are used as reinforcement. Valid fracture toughness values for crack growth transverse to the mold filling direction can be achieved e.g. for Vectra A-grade LCP containing 30 wt.-% or greater amounts of glass fibres (Figure 16). Compared to neat LCP, reinforcements improve the fracture toughness only slightly and only for crack propagation parallel to the molecular orientation. This can be explained by the low fibre/matrix interfacial bond quality. Although the fibres oriented transverse to the crack in the core should increase the energy release rate (GI=)mainly due to a fibre pull out failure, this effect is compensated by the stiffness ( E )

495

Orientation effects on liquid crystalline polymers 150

60

30

Neat LCP

GFACP

Figure 14. Differences in the effect of glass fibres on the tensile properties of the individual macrolayers of LCP (basic polymer: Rhodester CL)

g 1ZlYnLaver *.

Calculated

*, \

Bulk Material : Calculated Measured

2 core Layeh

Figure 15. Recalcula ion of the t e r d e properties :P filled with 40 wt.-% talc c ~. using a rule of mixture-approach in which the individual tensile properties of core and skin layers are combined with their relative contribution to the total bulk thickness

reduction due to the poor interface properties. Fracture toughness (KI,) and energy release rate are related by:

A calculation of GI, using the tensile modulus leads to the expected tendency, an increasing value with increasing glass fibre content (Figure 17). For the fatigue crack growth performance of LCP, only crack growth

R. Schledjewski, K . Friedrich

496

parallel to the mold filling direction causes a significant advance of the crack tip. In this case, the fatigue crack growth range can be, depending on the specific LCP type, in the range found for PEEK and its glass fibrereinforced composites tested under the same crack orientation (Figure 18). In contrast to the static fracture toughness, the fatigue crack propagation behaviour of the neat Vectra A-grade LCP is not improved by using reinforcements.

3.1.5. Tribological properties

Sliding wear. The tribological properties of LCPs have not been studied so far very intensively [16-201. However, from some of the relevant reports it is known that they can exhibit quite an anisotropy in wear resistance depending on the molecular orientation relative to the sliding direction. Due t o the oriented microstructure of the LCPs different sliding directions have t o be distinguished (Figure 19). To characterize the wear behaviour of a material, the specific wear rate is quite often used, which describes the volume loss per sliding distance and normal load. Investigations of Voss and Friedrich [16] on LCP produced by Celanese Corporation in the mid80s showed that, for distinct orientations, the wear behaviour is strongly affected by the test conditions, i.e. the contact pressure ( p ) and the sliding velocity (v). Even at a low pv product the specific wear rate found if worn in A P orientation, i.e. on the injection molded surface, starts to increase with increasing the pv product (Figure 20). From recent studies on Vectra LCP (also a Celanese Corporation product) it can be seen that the wear resistance (inverse of the wear rate) for the parallel and normal orientations is still clearly better, and much more constant over a wide

0

0

10

20

30 40 50 Short Glees Fibre Content in W h

Figure 16. Fracture toughness of glass fibre reinforced LCP. For crack propagation transverse to the mold filling direction (T) relevant values are determinable for higher glass fibre contents only

497

Orientatioii effects on liquid crystalline polymers

range of the yv product. Although the neat LCP is highly oriented parallel to the mold filling direction, the wear rates obtained in normal and parallel orientation differ only slightly (Figure 21). Additional changes in the sliding orientation, i.e. in the same plane b u t rotated by 90" ( N * , P* and A P * ,respectively) d o not change the test results. T h e same was found by Friedrich et al. [16,20]. Using fillers or reinforcements, t h e differences in wear behaviour occurring under parallel or normal sliding are additionally reduced (Figure 22). A slight improvement in t h e wear behaviour of t h e LCP investigated was found only for carbon fibres used as reinforcement. Fretting wear performance. In addition to unidirectional sliding,

Figure 17. A calculation of the energy release rate results in the expected tendency. Due to fibre pull-out effects G I , increases with increasing glass fiber content. The decrease in fracture toughness is mainly a result of the stiffness reduction by higher glass fibre amounts

.-

1

2

3

4

5

d K / (MPa mln)

Figure 18. Fatigue crack propagation behaviour of different neat LCPs compared to different filled LCPs and PEEK (neat and glass fibres reinforced)

498

R. Schledjewski, I(. Friedrich

bidirectional sliding with small slip amplitudes, i.e. fretting, and the resulting wear behaviour are of interest for the LCPs application, e.g. in stepper motors. The fretting wear behaviour of neat and reinforced LCPs has been studied with motion parallel to the injection molded plane (AP- and AP*orientation). The tests were performed with a sphere on flat configuration and the wear was characterized by the penetration depth of the sphere. Penetration depth (Ah) vs. time ( t ) curves obtained from prolonged tests illustrate the effect of microstructure on the wear behaviour (Figure 23). Whilst an isotropic material results in a decreasing slope of the curve due to the increasing contact area with increasing penetration depth of the sphere, the results found for neat LCP exhibit an increasing slope for a penetration depth of about 0.45 mm and more; this corresponds to the thickness of the outer skin layer of this material. It can be concluded that the wear resistance of the outer skin is significantly higher compared to the inner skin and the core. The core causes no change in the slope of the measured Ah vs. t curve, consequently the wear resistances of the inner skin and core layers are similar. General tendencies in the effect of the specific motion orientation on the wear resistance of neat LCPs were not found (Figure 24). The orientation exhibiting the highest wear resistance can vary depending on the specific LCP modification. For the basic polymer of the Vectra series (A-grade) the injection molded surface reveals significantly lower specific wear rates compared to the normal orientation. On the contrary, the low-viscosity, high-temperature Vectra LCP (C-grade) exhibits only a slight effect on the sliding orientation with the highest anisotropy between A P and AP*-orientation. Similar to the A-grade Vectra, only a low degree of anisotropy between A P and AP*-orientation was observed for the high-temperature Vectra LCP (E-grade). Compared to neat LCP, glass fibre reinforced A-grade compounds have higher wear rates (Figure 25).

Plate Figure 19. For oriented materials three different sliding planes each with two different motion orientations have to be distinguished, i.e. normal ( N and N * ) , parallel ( P and P') and anti-parallel ( A P and AP')

499

0rient.ation effects on liquid crystalline polymers

'The orientation effect occurs in a fashion similar to that for neat LCP, but the degree of anisotropy changes depending on the reinforcement content. As found for the mechanical properties, the main problem with fillers and reinforcements is the poor interface performance between matrix and compound which results in broken glass particles in the wear region. The high difference in hardness between the polymeric matrix and the broken glass particles results in an increase of the abrasive part of the wear. Furthermore, in the case of reciprocating motion, the transport of the abrasive particles out of the wear region is additionally hindered. The free distance which an Material

Orientetion v I m-1

0 Celanese LCP

A VectraA950 1,o

A VeCtraA950

.g 1r5 104

Figure 20. LCPs produced in the mid-80s (Celanese LCP [15]) show a strong effect of the characteristic pv product on sliding in anti-parallel orientation, whereas the wear resistance for normal and parallel sliding are unaffected over a wide range of the pv product

N'

N

P*

P

Figure 21. The differences in sliding wear behaviour between normal (N) and parallel (P)orientation are only slight. Rotation of the sliding orientation by 90°, by retaining the sliding plain ( N * ,P') does not change the wear rate significantly

500

R. Schledjewski, K . Friedrich

'

-

i

r

105i

Glass Fibres

2

Direction AP' N

9 Carbon Fibres

'kb..

pv= 1,O [MPa d s ]

pv= 1,7 [MPa d s ]

10-7

0

10

0 1 0 2 0 3 0 4 0 Glass Fibre Content in VOI.-YO

20 30 40 50 Filler Content in wt.-%

a)

b)

Figure 22. Effect of fillers and reinforcements on the sliding wear behaviour of (a) different reinforced LCPs of the Vectra series and (b) glass fiber reinforced LCPs produced by DuPont and Celanese [20]. Significant orientation effects are almost always found only for neat LCP

abrasive particle can plough through the polymeric material without being stopped by a glass fibre in the material is the longest for low glass fibre amounts. In this case the increase in wear should be quite significant. For the A-grade LCP all fillers or reinforcements studied resulted in an increase in specific wear rate with increasing content (Figure 26). On the contrary, low or medium amounts of glass fibre reinforcement improved the wear resistance of the C-grade LCP. It was found (SEM), that the fibre matrix adhesion is slightly better compared to the A-grade LCP-compounds. 3.2. LCP Blends

There are various reasons to blend a thermoplastic material with LCP. Among them is the fact that low volume fractions of LCP can form a fine fibrillar phase in the polymer matrix. This is due to the large stretch ratio which is locally achieved especially in the skin regions during mold flow. A kind of short polymer fibre reinforcement is formed [21-241. A further reason can be the viscosity reduction found for several polymers blended with small amounts of LCP [25,26]. 3.2.1. Blends of LCP and polyethersulfone ( P E S )

PES, an amorphous thermoplastic, is moldable in the same temperature range as LCP (T w 35OOC). During molding both materials are molten and depending on the individual content one of the materials is a phase dispersed in the second one, the latter representing the matrix. Injection molded neat PES is transparent due to its amorphous structure. Even small

50 1

Orientation effects on liquid crystalline polymers

0

Figure 23. Due to the change in wear resistance from the outer to the inner skin layer, the penetration depth vs. time curve changes the slope from decreasing t o increasing values (Ah z 0.4 mm)

A950

C950

€950

Rh4.N

Figure 24. Fretting wear behaviour of different neat LCPs. Although orientation affects the wear resistance, general tendencies were not found. An outstanding high wear resistance was found for the injection molded surface ( A P and AP' orientation) of the A-grade Vectra L C P

amounts of LCP induce a layer structure consisting of two skins and a core inbetween, visible by the naked eye. Similar to the results reported by Joseph et al. [21] for PET/LCP blends, a preferred concentration of the LCP phase in the skin region can be expected. The layer structure, found for all specimens containing LCP, and the increase of the tensile modulus with increasing LCP content (Figure 27) are hints for the molecular orientation of the LCP phase within the different blends, as found for other blends containing LCP [25]. In addition to the mechanical properties, the thermal

R. Schledjewski, K . Friedrich

502

55

'O-=

E

IW

0

10

20

30 40 50 Glass Fibres Content in wt-%

Figure 25. Compared to neat LCP, glass fibre reinforcement increases the wear of the A-grade Vectra LCP

1

Glass Fibres I C950

I

0

10

20

30

40 50 60 Filler Content in wt-%

Figure 26. Effect of different fillers and reinforcements on the fretting wear behaviour of LCP

expansion behaviour is also affected by the LCP content. The coefficient of linear thermal expansion of PES is clearly higher than that of LCP. Blends of both materials exhibit a behaviour which is better than it could be expected from a linear rule of mixtures-approach (Figure 28). The reason therefore is probably the concentration of the LCP phase in the skins where the LCP fibrils are highly oriented. With increasing LCP content, the LCP distribution is more homogenous over the entire cross section and especially in the core the degree of alignment of the LCP molecules decreases. Concerning the sliding wear behaviour against steel counterparts, the neat PES performance is relatively poor (Figure 29). It can be improved, however, if small amounts of LCP (M 5 wt.-%) are added. This is particularly true for the normal orientation, for which the wear rate is lower by

503

Orientation effects on liquid crystalline polymers

almost one order of magnitude compared to that of the neat PES matrix. A further increase in LCP content stabilizes the wear rates for the different directions on various plateaus, that of the AP-direction being the highest whereas the N-direction maintains almost on the same low level as already measured for the 5 wt.-% LCP-content. Finally, above an LCPcontent of about 50 wt.-%, which corresponds to a transitional region from PES-matrix to LCP-matrix morphology, the wear rates for all directions start to decrease further. The degree of wear anisotropy remains the same as already discussed in connection with Figures 20 and 22(a). 4. Conclusions

Injection molded liquid crystalline polymers are highly oriented due to their molecular structure and the flow conditions during molding. Although the layer structure of LCPs is strongly affected by fillers and reinforcements, the anisotropy especially in mechanical properties is at most reduced but not eliminated. Unfortunately, the majority of the outstanding properties of LCPs, e.g. low thermal expansion, high stiffness or high wear resistance, manifest themselves almost always for a preferred orientation only; and just these outstanding properties are adversely affected when fillers or reinforcements are used. The main reason for this negative effect of the compounds is the normally low interfacial adhesion between fillers and the LCP matrix. Consequently the possible stiffness increase is much more pronounced than the strength improvement if reinforcements are added. Concerning the fracture mechanical properties, the fracture toughness is improved mainly due to an increase in energy release rate due to fibre pull-out effects, while for crack propagation the cracks tend to propagate along the ends of the

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'

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50

1

100

'

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.

......

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Figure 27. Increase of the complex dynamic modulus of PES-LCP blends with increasing LCP content (the curves are marked by the percentages of PES and

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K. Schledjewski, K . Friedrich

504 100-

b

i

80'

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60'

. -. F

40' 20'

Figure 28. Coefficient of linear thermal expansion of PES-LCP blends measured parallel t o the mold filling direction as a function of the LCP content

IU

0

20

40

60

80 100 LCP Content in wt.-YO

Figure 29. Sliding wear behaviour of LCP-PES blends. Whilst the neat PES exhibit a nearly isotropic wear behaviour, the blends and especially the neat LCP reveal wear rates which depend on the relative sliding orientation

reinforcements and therefore there is no improvement found for crack propagation behaviour by using reinforcements. The wear performance of LCP is most often adversly affected by the poor quality of the interfacial bonding between matrix and reinforcement, e.g. for the basic polymer of the Vectra series (A950) the specific wear rate is always increased when fillers are used. Through the use of LCP as reinforcement in a thermoplastic material the wear behaviour can be significantly improved if small amounts of LCP are used.

505

Orientation effects on liquid crystalline polymers ‘L 10-4,

E

V

E .-c

Neat A-Grade LCP

I

2 105-

PTFE I A-Grade LCP

L

A OF I PTFE I AOrede LCP 0 OF I Grephlle I A-Grade LC 0 CF I PTFElA-Grede LCP

V OF I C-Grade LCP

In 1044 090

091

092

03

0,4

Friction Coefficlent

Figure 30. Tribological properties under dry and lubricated (“Lub.” ) fretting conditions of different LCP compounds compared to those of POM

Acknowledgements T h e authors appreciate the help of several students a t the University of Kaiserslautern for carrying out some of the experimental work. The materials supply by Hoechst AG, Frankfurt, Germany; Rh6ne Poulenc Chimie, Paris, France; and Imperial Chemical Industries, Wilton, Great Britain, is gratefully acknowledged. Finally the authors also want t o thank the Commission of the European Community for the financial support of a part of the work presented here (BE-3231-89/BREU-O127-C [MBJ).

References 1. I. M. Ward, D. W. Hadley, “ A n introduction to the mechanicalproperties of solid polymers”, 1st edition, J. Wiley & Sons, Chichester 1993 2. H.-R. Dicke, B. Willenberg, V. Eckhardt, “Flussigkristalline Polyestep, in: Kunststof-Handbuch, 313. Hochleistungs- Kunststoffe, 1st edition, edited by L. Bottenbruch, Hanser, Munchen/Wien 1994, p. 41219ff. 3. A. A. Collyer, “Liquid Crystal Polymers: From Structures to Applications”, Elsevier Science Publisher Ltd, London 1992 4. J. H. Wendorff, Zcunststofe 73,524 (1983) 5. W. Brostow, Polymer 31,976 (1990) 6. F. Reinitzer, Monatsh. Chem. 9, 421, (1888) 7. P. J. Flory, Proc. Roy. SOC.London A234, 73 (1956) 8. British Patent 1283064 (1968), E.I. DuPont de Nemours and Co, inv.: S. L. Kwolek 9. W. J. Jackson, H. F. Kuhfuss, J. Polym. Sci., Part A : Polym. Chem. 14, 2043 (1976)

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R. Schledjewski, K . Friedrich

10. G. Kirsch, H. Terwyen, “lfennzeichen und Eigenschaften uon thermotropen, jbissigkristallinen Polymeren (LCP)”, in: Fliissigkristalline Polymere (LCP) in der Praxis, VDI Verlag, Diisseldorf 1990, Iff. 11. T. Okada, “Recent Development Status of L C P Applications”, in: Progress in Pacific Polymer Science 2, edited by Y. Imanishi, Springer Veralg, Berlin Heidelberg 1992 12. T. Weng, A. Hiltner, E. Baer, J. Mater. Sci. 21,744 (1986) 13. L. C. Sawyer, R. T. Chen, M. G. Jamieson, I. H. Musselman, P. E. Russell, J . Mater. Sci. 28, 225 (1993) 14. R. Schledjewski, K. Friedrich, J. Mater. Sci., Lett. 11,840 (1992) 15. H. Voss, K. Friedrich, J. Mater. Sci. 21, 2889 (1986) 16. H. Voss, K. Friedrich, Tribology International 19, 145 (1986) 17. Y. Uchiyama, Y. Uezi, A. Kudo, T. Kimura, Wear 162-164, 656 (1993) 18. R. Schledjewski, K. Friedrich, “Fretting Wear Behavior of Filled LCPSystems Under Dry and Lubricated Conditions”, in: Advanced Materials a n d Structures from Research to Application, edited by J. Brandt, H. L. Hornfeld, M. Neitzel, SAMPE European Chapter, Niederglatt Switzerland 1992, 93ff 19. J. Song, “Reibung und Verschleijleigenverstiirkter Polymerwerkstofle”, Fortschr.-Ber. VDI Reihe 5 Nr. 220, VDI Verlag, Diisseldorf 1991 20. K. Friedrich, “Tribology of Polymer Composites”, in: Advanced Composites ’93, edited by T. Chandra, A. K. Dhingra, TMS Publ. Warrendale Pennsylvania 1993, llff 21. E. G. Joseph, G. L. Wilkes, D. G. Baird, Polym. Eng. Sci. 25, 377 (1985) 22. B. Y. Shin, S. H. Jang, I. J. Chung, B. S. Kim, Polym. Eng. Sci. 32, 73 (1992) 23. T. C. Hsu, A. M. Lichkus, I. R. Harrison, Polym. Eng. Sci. 33,860 (1993) 24. G. Crevecoeur, G. Groeninckx, Polym. Eng. Sci. 33, 937 (1993) 25. T. Sun, D. G. Baird, H. H. Huang, D. S. Done, G. L. Wilkes, J . Comp. Mater. 25, 788 (1991) 26. A. Golovoy, M. Kozlowski, M. Narkis, Polym. Eng. Sci. 32,854 (1992)

Oriented Polymer Material> Stoyko Fakirov Copyright 0 2002 Wiley-VCH Verlag GmbH & Co. KGaP

Author index Alan. 41 Argon. 265. 198 Arruda. 275 Baer. 487 Bahar. 467. 472 Bartczak. 265. 266, 271. 280 Besbes. 477 Biangardi, 363. 366 Black. 355 Bonart. 99, 193 Bowden. 266. 298 Bovce. 273 Braam, 220 Bragato. 367 Brandrup, 99 Bresler. 3 Brestkin. 1.6 Bronnikov. 30 Bueche. 341 Bunn. 328 Calvet. 188 Chang, 477 Chevvchelov. 204 Chop. J06 Cohen. 265 Dahoun. 279 d e Daubenv. 328 Deloche. 475. 478 DiMarzio. 20. 23, 24, 25, 33 Dole. 3.10 Eichhoff, 366 Elias, 31 Erman, 467. 472. 473 Fakirov. 346. 354, 422

Farris, 184, 185 Farrow, 366 Fischer, 344. 346 Flory, 23, 24, 471. 4 i 7 . 484 Frank, 335 Fraser, 475 Frenkel, J., 28 Frenkel, S., 1 Friedrich. 99, 482, 493, 496, 497 Galeski, 265, ?91-298 George, 367 Gianotti, 367 Godovsky, 184, 187 Groeninckx, 354 G r i n , 472 Grubb, 356, 462, 464 G'Sell. 279 Gupta, 331 Haggege, 363 Harburn, 364 Harrah. 234 Haudin, 266 Herz, 478 Hess, 117 Heuvel, 346 Hiltner, 487 Holoubek, 255 Hosemann, 111, 117 Hosford, 282, 285 Huisman, 346 Immergut, 99 Ishizuka, 366 Ivantsov, 384 Jackson, 484

508 .Jarecki. 367 .Jarrv. 472 Kalb. 446 Kargin. 9 Katavama. 366 Katz. 106 Kausch. 29, 204 Kavesh. 445 Kawai. 322 Keller. 17. 298 Kiessig. 117 Killian. 315 Kip. 464 Knipping. 99 Kramer. 462. 464 Krause. 282. 285 Krigbaum. 309. 472, 474 Kuhfuss. 184 Kuhn. 471 Kunugi. 394. 435 Kwolek. 484 Lee. 265. 281. 288-292 Lemstra. 446 Leung. 306 Lin. 298 Lindner. X'2 Lovinger.. 324 Lyon. 186 Mackley. 355. 356 Mandelkern. 340 Marikhin. 38, 43 Mark. 4-14 Matsuo. 302. 303 MijUer. 210 Moneva. 241 Monnerie. 452 Miller. 185. 186 Murray. 363 Myasnikova. 30. 38

Author index Nadkarni, 363 Nagai, 471, 473 Nakamae, 303, 304 Nakayasu, 318. 322 Odajima, 303 Ohta, 338 Parks. 265 Pennings, 12, 27, 30, 446 P e t e r h , 14, 42, 43, 54, 215, 296, 423, 425 Petermann. 167 Pope, 298 Prevorsek, 344, 346. 423, 444, 447 Prigogine, 11, 17 Read, 475 Reinitzer. 484 Rhodes, 244, 247 Rinne, 111 Roe, 309, 472. 474 Roentgen, 99 Ruland, 315 Sakurada, 303, 304. 306 Sapsford, 355, 356 Savitskii, 59 Schaper, 462, 464 Schledjewski. 482 Schultz, 361, 363. 383 Sheiko, 210 Siesler. 138 Smith, 59, 446 Statton, 118 Staudinger, 331 Stein, 244, 247, 475 Suehiro, 320 Takayanagi, 347, 349 Talmud, 3 Tashiro, 303 Termonia, 452 Tiller, 383 van Aartsen, 247

509

Author index van Aerle. 220 Vettegren. 30 von Laue. 99 Voriander. 484 Voss. 493. 496 Ward. ?7, 88. 346, 355, 366 Weng. 487

w u . 355 Wunderlich, 340. 424 Young, 266, 298 Zachmann, 363, 366 Zeigler, 234 Ziabicki. 367

Oriented Polymer Material> Stoyko Fakirov Copyright 0 2002 Wiley-VCH Verlag GmbH & Co. KGaP

Subject index Assemblage, 8. 22 Ballistic conditions, 189. 452-455 Birefringence, 14. 17. 138. 167, 241, 311-318. 342. 375, 398-420, 436 Bragg's law. 100. 101. 105. 126. 135 Bravais lattice. 99 Brownian motion. 14. 15, 18. 56. 412 Calorimet rv. Deformation. 184-207 Differential scanning, DSC. 66, 8190. 150. 314, 379. 403. 430 Computer simulation of Plastic deformation. 265-299 Texture evolution. 265-299 Configurational information. 1'. 3. 8. 10. 11. 13 Cracks. .57. 58. 66. 495-504 Creep. 79. 448-451 Cyanoethvlcellulose. 34 Damage tolerance. 444-465 Debve-Schemer rings. 101. 102. 104, 116 Debye t.emperqture, 29. 30. 33, 112 Defects. defect distribution, 66, 341 Deformation. 39, 62. 69. 138-164, 175, 265-299. 349. 451. 469 Degree of crystallinity? 63, 81, 150. -100-415. 436 Drawing. draw ratio. 48. 57.59. 67-77, 91. 149-163. 194. 323. 328, 396-420, 425-4138. 450 Electron spin resonance, ESR. 56, 57, 91

Entanglements, 17. 61 Epitaxial growth. 27. 31, 172

Ewald sphere, 125, 126 Fisher diagram, 4, 5, 31 Heaiing, Chemical, 438-441 Physical, 437 Infrared dichroism. 143, 145, 167, 225. 470, 476 I\'inks, 52. 58. 79 Lamellar stacks. 136. 168. 177-181. 213 Liquid crystalline polymers. 22, 136. 145-148, 257-261, 482-505 Mesogenic polymers, 25, 485 Microfibrils, microfibrillar structure, 39, 42, 46, 47, 74, 75, 85, 117, 221231 Microscopy, Optical, light. 129, 168, 173 Scanning electron. SEM.324, 487 Scanning force. SFM,210-237 Transmissiton electron. TEM. 43, 48, 168-181, 211-232. 295-298. 363, 371 hlodel of Affine network, 467 Fischer, 344, 346 Fraunhofer, 243 Fringed micelles. 332 Harrison, 45 Hess-Hearle. 54 Hoevel-Huisman. 344. 346 Hosemann, 115 Iiuhn, 14 P e t e r h . 42. 47, 54. 86 Peterlin-Prevorsek. 196

Subject index Phantom network, 467 Prevorsek. 344 Sachs. 276 Smith. 59 Structure development. 367 Talmud and Bresler, 3 Taylor. 276 Thermal dendrite, 383 Weng, Hiltner and Baer, 487 Molecular cybernetics. 1. 2. 8, 10, 13 Morphology, Fibrillar. 423 Fringed micellar. 168-179 Needle crystal (shish), 168-179 Shish-kebab. 171-179. 253. 332 Spherulitic, 267 Stacked lamellar. 168-181 ( o f ) Ultrastrong PE fibres. 462 Necking, 40. 42. 43. 61. 68. 298. 399 Needle-like crystals, 56. 86, 168, 177 Nematic state, phase. 25, 45. 111, 486 Optical diffraction, 113, 129, 131 Orientational catastrophe, 11, 16, 20, 21

Phase transition. 15. 40. 41 Polyacrylonitrile. 12. 451 Polvalkvlsilylenes. 232-237 Polyamides. Nylon 6. Nylon 66. 5 1 . 103. 108. 116, 117. 192-207. '298, 362. 410-113. 422-440 Poly( butvlene terephthalate), 107,108. 415-432 Polycaproamide. 43 Polycarbonate. 107 Polpchloroprene. 122 Poly( et her-et her-ketone), 4 13-4 17. 491 Polyethersulfone, 500

511 Polyethylene. HDPE, LDPE, UHMWPE, 17, 39-46, 50-65, 7192, 103, 107, 173, 192-237, 266-299, 305-328,334-355,398-401,446-451 Poly(ethy1ene terephthalate), 43, 52. '78, 107. 116, 117. 139, 148-160, 169,193. 246-298, 334-355,361-391 406-410. 422-440. 448, 483 Poly(hexanedio1 adipate), 106 Polyimide, Kapton H, 417-419 Polyisoprene, 452 Polymer blends. 232-237, 310, 324. 429, 500 Poly(methy1 methacrylate), 11, 12, 19, 20, 201 Polyoxymethylene. 72, 78, 192 Poly( pphenylene benzobisoxazole), 338 Poly( pphenylene terephthalamide), Kevlar. 78. 334-355, 440, 446. 457 Polypropylene, 32. 72, 172, 192, 305328, 336, 401-404. 448 Polystyrene, 12, 16, 43, 168, 201, 452 Polysulfurnitride, 177 Polyurethane elastomers, 104. 128 Poly(viny1 alcohol), 43. 404-406 Polv(viny1 chloride). 122, 301 Poly( vinylidene fluoride) 139. 160-163 Position sphere. 109, 110 Reciprocal lattice. reciprocal unit cell, 100-106, 132, 305 Rheological catastrophe, 13, Rheo-optical measurements, 142-164. 320 Scattering, Polarized light, PLS. 241-261 Small-angle neutron. SANS, 46, 303 Small-angle X-ray, SAXS. 50. 51.52, 54, 55. 63. 66. 82. 86, 117, 285296, 341, 364. 426-433

5 12

Subject index

Wide-angle X-ray, WAXS. 66, 8188. 161-163. 283-296. 363, 400, 428-432 Segmental orientation, 467-480

Semicrystalline polymers, 38, 39. 62, 150. 266 Single crystal, single crystal mat, 27, 41. 64. 7'7. 86

Solid state reactions, 424, 430-440 Spacer. 485 Spectroscopy, Fourier transform, FT, 124. 127, 130. 134. 138-164, 470, 474

Infrared. 30. 52. 53. 56. 57. 66. 138. 144. 399. 427

Nuclear magnetic resonance, NMR, i 3 , 54. 58, 66, 138, 228, 366, 478 Ranan. 30. 88. 139, 140, 231, 303

Vibrational, 46, 138-164 Spherulites. 40. 42, 47, 74, 103, 244, 260. 267. 321. 332

Stress-strain behaviour, 18, 153, 161, 180

Superoriented polymers, 28, 30, 39, 16'7. 199. 302-328, 425-428

Tensile strength, 75, 91, 410-420, 423

Texture Banded, 259 crystallographic, 268 Extended-chainl 394 Fibrillar, 324 Macromolecular, 268 Morpholi3gical, 268 Nematic, 259 Schlieren, 257 Thermal properties. 80, 184-207, 339342, 349, 489

Tie molecules, 39, 43, 53, 53, 54, 61, 79, 196, 423, 434

Ultraquenching, 425-430 van der Wads bonds, forces, 5i-59, 60, 108

X-ray data. 57, 120, 196-200, 303-328 Youngk (elasticity) modulus, 12. 39, 71-79, 182, 201, 303-328, 335-338, 346, 410-418, 423

Zhurkov's concept, equation, law, 12, 27-29, 34, 35, 76

Zone annealing, 394-420, 435-437 Zone drawing, 72, 78, 82,83, 252,394420, 422