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RHEOLOGY, PROCESSING, AND CHARACTERIZATION OF ISOTROPIC,

ANISOTROPIC, AND MIXED PARTICLE FILLED POLYMER SYSTEM

A Dissertation

Presented to

The Graduate Faculty of The University of Akron

In Partial Fulfillment

of the Requirement for the Degree

Doctor of Philosophy

Kwang-Jea Kim

May, 1998


UMI Number: 9826258

UMI Microform 9826258 Copyright 1998, by UMI Company. All rights reserved.

This microform edition is protected against unauthorized copying under Title 17, United States Code.

UMI300 North Zeeb Road Ann Arbor, MI 48103


RHEOLOGY, PROCESSING, AND CHARACTERIZATION OF ISOTROPIC,

ANISOTROPIC, AND MIXED PARTICLE FILLED POLYMER SYSTEM

Kwang-Jea Kim

Dissertation •'

Approved: Accented:

.viser

Cnair

o liege

Dean of the Graduate School

yT /YML- [ W bDate

11


ABSTRACT

We describe a study of the rheology, processing and

characterization of talc, calcite, and mixtures of their

particles in thermoplastics. Processing operations such as

capillary, slit, rectangular, annular die extrusion, and

compression molding are carried out to investigate the

influence of talc, calcite, and talc/calcite particles on

polymer processing.

The talc and mixed particle orientation in various

processing flows are characterized using wide angle x-ray

diffraction. The talc particles orient with their surface

parallel to the plate surface of the capillary, slit,

rectangular, annular die, and compression molding die wall.

However capillary die extrudate showed complex behavior

i.e. degree of orientation increase with talc volume

loading up to 10 v% and decrease from 20 v% to 40 v%.

Capillary die extrudate sample's cross-sections were

investigated using scanning electron microscope and

iii


compared with various other processing samples. Talc

particle showed radial direction orientation in the core

region. The orders of radial direction orientation were

represented as dimensionless analysis as a function of

volume loading, wall shear stress applied etc. Data

between 10-15 v% showed critical points occur in the radial

direction orientation.

A broad range of experimental measurements of the

shear, elongational and oscillatory flow behavior on

thermoplastic melts with high loadings of talc particles is

presented. The talc and calcite, mixed particle filled

thermoplastic melts at higher loadings exhibit yield

values. Elongational yield viscosity existed where shear

yield value existed. In the IUPAC 4.2.1 Working Party

Project "Comparative Rheology & Material Characteristics of

Mineral Filled PP", surface treated calcite showed lower

level of viscosity than untreated calcite particle and talc

particle filled system did not show considerable changes.

The implication of yield values in anisotropic

compounds is considered. A 3-dimensional rheological model

has been developed to interpret the anisotropic and plastic

characteristics of talc-thermoplastic compounds. The

anisotropic plastic viscoelastic fluid model is specializediv


to a transversely isotropic form to represent the behavior

of suspensions of oriented disc particles. This model was

derived from the continuum equation. We first expressed

this model on our experimental result from elongational

yield values and shear yield values.


ACKNOWLEDGEMENTS

Prof. James L. White my dissertation advisor and post doctoral director.

Prof. Donald N. Robinson my committee.

Prof. Joo-Whan Shon my thesis advisor.

Wife Hyekycng Kim.Daughter Carol Tongyon Kim.

Mother Jung-Ja Choi.Father Jun-Girle Kim.

vi


T A B L E O F C O N T E N T S

PageLIST OF TABLES............................................. xxii

LIST OF FIGURES............................................ xxiv

CHAPTER

I. INTRODUCTION ........................................ 1

II. BACKGROUND AND LITERATURE SURVEY ................... 3

2.1 Crystal Structure and Characteristics ofTalc, Mica, and C a l c i t e ........................... 3

2.1.1 T a l c .....................................3

2.1.2 M i c a .....................................6

2.1.3 Calcium Carbonates..................... 9

2.2 Particle Behavior in Suspended Systems and Influence on Rheological Properties............12

2.2.1 Particle Interactions inSuspensions........................... 12

2.2.1.1 Large Isotropic Particles . . . 12

2. 2.1.2 Anisotropic Particle Motionsand Interactions................ 13

2.2.1.2.1 Dilute Systems ........... 13

2.2.1.2.2 Concentrated Anisotropic Particles.................. 13

vii


2.2.1.3 Characteristics Of LiquidCrystals......................... 17

2.2.2 Influence of Particles onRheological Properties ............. 18

2. 2.2.1 Shear F l o w ......................18

2.2.2.1.1 Rheological Models of Dilute Suspensions System .18

2.2.2.1.2 Rheological Properties Of Concentrated Particle Suspensions................ 20

2.2.2.1.2.1 Large Particles .20

2.2.2.1.2.2 Small Particles .22

2.2.3 Rheological Properties in MixedParticle S y s t e m .......................27

2.3 Orientation Development of AnisotropicParticles During F l o w ..................... 28

2.3.1 Introduction...........................28

2.3.2 Representation of UniaxialOrientation........................... 29

2.3.3 Representation of BiaxialOrientation........................... 35

2.3.4 Representation of Mixed ParticleOrientation........................... 41

2.4 Characterization by Using X-ray Diffraction . .42

2.4.1 Introduction...........................42

2.4.2 Quantitative Analysis of ParticleFilled Compounds .................... 43

2.4.3 Wide Angle X-ray Flat FilmTechnique............................. 48

viii


2.4.4 Wide Angle X-ray Pole FigureTechnique............................. 51

2.5 Scanning Electron Microscopy (SEM) ........... 56

2.6 Modeling of the Flow of Particle FilledCompounds..........................................60

2.6.1 Phenomenological Constitutive Equations for Dilute Suspensionsof Anisotropic Particles ........... 60

2.6.2 Isotropic Compounds with YieldV a l u e s .................................63

2.6.3 Anisotropic Formulation.............. 68

III. EXPERIMENTAL....................................... 81

3.1 G e n e r a l .......................................... 81

3.2 Experimental.....................................82

3.2.1 Materials.............................. 82

3.2.1.1 Particles........................82

3. 2.1.1.1 T a l c s .......................82

3. 2.1.1. 2 M i c a ........................87

3.2.1.1.3 Calcium Carbonates(Calcite).................. 88

3. 2.1.2 Polymers........................ 91

3.2.1.2.1 Polystyrene (PS) ......... 91

3.2.1.2.2 Polypropylene (PP) . . . . 92

3.3 Compounds Prepared ............................ 92

3.4 Compounding......................................96

ix


3.5 Rheological Measurements ...................... 97

3.5.1 Steady Shear Flow Measurements . . . 97

3.5.1.1 Sandwich Rheometer.............. 97

3.5.1.2 Cone-Plate Rheometer........... 100

3.5.1.3 Capillary Rheometer............ 104

3.5.2 Elongational Flow Measurements . . .106

3.5.3 Oscillatory Flow Measurements . . . 110

3.6 Processing Studies and Flow Geometries . . . .113

3.6.1 Extrusion Through D i e s .............. 114

3.6.1.1 Capillary D i e ...................114

3.6.1.2 Rectangular Dies .............. 114

3.6.1.3 Annular D i e ..................... 115

3.6.1.4 Converging F l o w .................115

3.6.2 Compression Molding ................ 115

3.7 X-ray Characterization of Fabricated Parts . .116

3.7.1 Orientation Studies from WideAngle X-ray Diffraction (WAXD) . . .116

3.7.1.1 WAXD Bragg Angle Scanning . . .116

3.7.1.1.1 Amorphous H a l o ............118

3.7.1.1.2 Particle Size ........... 119

3.7.1.2 WAXD Flat Film Measurements . .120

3.7.1.3 WAXD Pole Figure Measurements .120

3.7.1.3.1 Uniaxial Orientation . . .122

x


3.7.1.3.2 Biaxial Orientation . . . 122

3.7.2 X-ray Intensity Studies forComposition Analysis of Particle Filled S y s t e m ..................... 123

3.7.2.1 Introduction .................. 123

3. 7.2.2 Binary Mixture (SingleParticle) S y s t e m ............... 124

3.7.3 Scanning Electron Microscopy (SEM) .127

3.7.3.1 Introduction .................. 127

3. 7. 3.2 Experimental.................... 129

IV. RHEOLOGICAL MEASUREMENTS IN STEADY ANDOSCILLATORY SHEAR FLOW ........................... 131

4.1 Introduction..................................... 131

4.2 R e s u l t s .......................................... 132

4.2.1 Steady Shear Flow Measurements . . .132

4.2.2 Oscillatory Flow Measurements . . . 151

4. 2.2.1 Dynamic Viscosity...............151

4.2.2.2 Storage and Loss Modulus . . . 153

4.3 Discussion....................................... 160

4.3.1 Particle Loading Dependence ofShear Viscosity.................. 160

4.3.1.1 PS Matrix S y s t e m ................160

4.3.1.2 PP Matrix S y s t e m ................165

4.3.2 Yield V a l u e s ..........................166

4.3.2.1 PS Matrix S y s t e m ................166

xi


4.3. 2. 2 PP Matrix S y s t e m ................168

4. 3.2.3 Comparison To EarlierLiterature......................169

4.3.3 Viscosity-Shear Stress Plateau . . .173

4.3.4 Comparison Between Single ParticleFilled System And Mixed Particle Filled S y s t e m .........................175

4.3.4.1 PS Matrix S y s t e m ................175

4.3. 4. 2 PP Matrix S y s t e m ................176

4.3.5 Comparison Between Stearic AcidTreated Particle Filled System And Untreated Particle Filled System . .179

4.3.5.1 PP Matrix S y s t e m ................179

4.3.6 Comparison Between Complex ViscosityAnd Shear Viscosity................. 183

4.3.7 Comparison Between Talc ParticleFilled System and Calcite Particle Filled S y s t e m .........................185

V. ELONGATIONAL FLOW RHEOLOGICAL MEASUREMENTS . . . .188

5.1 Introduction....................................188

5.2 R e s u l t s ......................................... 189

5.2.1 Silicone Oil Bath Elongational Flow(S B M ) .................................189

5.2.1.1 Polystyrene (PS) .............. 189

5. 2.1.2 Calcite Compounds.............. 191

5.2.1.3 Talc Compounds ................ 199

5.2.1.4 Talc/Calcite Compounds . . . . 204

xii


5.2.2 Nitrogen Bath Elongational Flow( N C M ) .................................215

5.2.2.1 Polystyrene (PS) .............. 215

5.2.2.2 Calcite Compounds.............. 215

5.2.2.3 Talc Compounds ................ 216

5.2.2.4 Talc/Calcite Compounds . . . . 216

5.3 Discussion...................................... 217

5.3.1 Polystyrene ( P S ) ..................... 217

5.3.1.1 Comparison To Shear ViscosityAnd Earlier Investigation . . .217

5.3.2 Talc Compounds....................... 218

5.3.2.1 Estimation Of Yield Values From Nitrogen Bath Method( N C M ) ........................... 218

5.3.2.2 Comparison Of Silicone BathData To Shear Viscosity . . . .221

5.3.2.3 Investigation Of Silicone OilAbsorption......................222

5.3.2.4 Shear Flow CharacterizationOf SBM Elongational Flow Specimens.......................226

5.3.3 Calcite Compounds .................. 229

5. 3. 3.1 Estimation Of Yield Values FromNitrogen Bath Method (NCM) . . 229

5.3.3.2 Comparison Of Silicone BathData To Shear Viscosity . . . .230

5.3.3.3 Comparison To EarlierInvestigations ............... 233

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5. 3. 3. 4 Investigation Of Silicone OilAbsorption......................233

5.3.3. 5 Shear Flow CharacterizationOf SBM Elongational Flow Specimens.......................234

5.3.4 Talc/Calcite Compounds.............. 237

5.3.4.1 Estimation Of Yield Values FromNitrogen Bath Method (NCM) . . 237

5.3.4.2 Comparison Of Silicone Bath ToShear Viscosity................ 237

5.3.4.3 Investigation Of Silicone OilAbsorption......................238

5. 3. 4. 4 Shear Flow CharacterizationOf SBM Elongational Flow Specimens.......................241

VI. WIDE ANGLE X-RAY DIFFRACTION (WAXD)CHARACTERIZATION ................................. 247

6.1 Introduction.....................................247

6.2 R e s u l t s .......................................... 248

6.2.1 Composition Analysis of Particle Filled System Using Bragg AngleX-ray Intensity......................248

6.2.1.1 PS/Calcite S y s t e m ...............248

6.2.1.2 PS/Talc System ................ 256

6.2.2 Flat Film Measurements Of ParticleOrientation.......................... 272

6.2.2.1 Uniaxial Extrudates............ 272

6.2.2.2 Compression Molded Sheets . . .276xiv


6.2.3 Pole Figure Measurements............280

6.2.3.1 Capillary Die Extrudates . . . 280

6.2.3.2 Rectangular Die Extrudates . . 282

6. 2.3.3 Slit Die Extrudates............ 282

6.2.3.4 Annular Die Extrudates . . . . 285

6.2.3.5 Compression M o l d i n g ............ 287

6.3 Interpretation...................................289

6.3.1 Composition Analysis of ParticleFilled System Using Bragg Angle X-ray Intensity......................289

6.3.1.1 Theoretical Background . . . . 289

6.3.1.2 Ternary Mixture System . . . . 294

6.3.1.3 PS/Calcite S y s t e m ...............295

6. 3.1.4 PS/Talc S y s t e m .................. 299

6.3.1.5 PS / Talc / Calcite System . . 301

6. 3.1.5.1 Pseudo binary mixture system ofPS/(Talc/Calcite) . . . . 301

6.3.1.5.2 Pseudo binary mixture system of(PS/Talc)/Calcite . . . . 302

6.3.1.6 Summary of PS/Talc,PS Calcite, and PS/Talc/Calcite System ................ 309

6.3.1.6.1 PS/Talc, and PS/Calcite S y s t e m .....................309

6.3.1.6.2 PS/Talc/Calcite System . .310 xv


6.3.2 Flat Film Measurements OfOrientation.......................... 311

6.3.3 Orientation Factors And Pole FigureMeasurements......................... 313

6.3.3.1 Capillary Die Extrudates . . . 313

6.3.3.2 Rectangular Die Extrudates . . 316

6.3.3.3 Slit Die Extrudates............ 316

6. 3.3.4 Annular Die Extrudates . . . . 319

6. 3.3.5 Compression M o l d i n g ............ 319

6.3.3.6 Mixed Particle Filled System . 322

6.3.3.6.1 Capillary Die Extrudates .322

6.3.3.6.2 Slit Die Extrudates . . . 324

6.3.3.6.3 Compression Molding . . . 326

6.3.3.7 S u m m a r y ..........................326

VII. CHARACTERIZATION OF LOCAL PARTICLE ORIENTATIONIN PROCESSED COMPOUNDS........................... 332

7.1 Introduction.................................... 332

7.2 R e s u l t s ..........................................333

7.2.1 Compression Molded S a m p l e s .......... 333

7.2.2 Extrudates............................ 336

7. 2. 2.1 Capillary D i e ................... 336

7.2.2.2 Slit D i e .........................346

7.2.2.3 Rectangular D i e .................351

7.2.2.4 Annular D i e ..................... 356xvi


7.2.2.5 Capillary Dies For Various Diameter........................359

7.2.2.6 Capillary Die EntranceAngle 135° F l o w ................. 362

1.2.2.1 Capillary Die Attached To Twin Screw Extrusion Machine . . . .364

7.2.3 Flow Into Die Entrance ...............364

7.3 Discussion......................................368

7.3.1 Summary Of Flow Observation InLong D i e s ............................ 368

7.3.2 Correlation Of Observations FromDifferent Experiment................ 369

7.3.2.1 Feed History E f f e c t ............ 369

7.3.2.2 Dimensionless Correlations . .376

7.3.3 Characteristics Of CircumferentialA r r a y s ................................377

7.3.4 Flow Mechanism Hypotheses........... 379

7.3.5 Mechanism Of Particle Orientation . 384

VIII. ALTERNATE MODELS FOR THE YIELD SURFACE OF A TRANSVERSELY ISOTROPIC PLASTIC VISCOELASTIC F L U I D ............................................. 388

8.1 Introduction....................................388

8.2 Constitutive Relationships 391

8.2.1 Three-Dimensional Modeling ofPlastic-Viscous F l u i d s ..............391

8.2.2 Thixotropic Plastic-ViscoelasticF l u i d s ................................393

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8.2.3 Three-Dimensional Modeling OfPlastic-Viscoelastic Fluids . . . . 396

8.2.4 Theory Of Transversely IsotropicPlastic Viscoelastic Fluids . . . . 398

8.2.2 New Yield S u r f a c e ....................401

8.3 Application To Shear Flow And UniaxialExtension........................................403

8.3.1 Shear F l o w ............................403

8. 3.1.1 Simple shear flow parallelto disc surfaces (a i 2 = a si, or CT3 2 = CTs 3 ) ........................................... 403

8.3.1.2 Flow direction shear flow perpendicular to disc stacking (CT1 3 = ° s 2 ) ......................... 406

8.3.2 Uniaxial Extension F l o w ............. 409

8. 3.2.1 Perpendicular to the DiscAxes (1-direction, aeii) • • • .409

8.3.2.2 Parallel to the Disc Axes (2-direction, aei2 ) .............415

8.3.3 Two-Dimensional S h e a r ............... 417

8.3. 3.1 Shear Flow Parallel To DiscLayers (CJi 2 + <73 2 ) ............... 417

8. 3.3.2 Two-dimensional shear flownormal to disc layers (a ’i 2 + a i3) .420

8.4 Yield Surface Of Anisotropy Parameter a As AFunction Of Various Yield Stress Ratios . . . 423

8.4.1 Simple shear flow parallel to discsurfaces and 1-direction UniaxialFlow (Yeii/Ysi)........................ 423

xviii

R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission.

8.4.2 Simple shear flow parallel to discsurfaces and shear flow perpendicular to disc stacking (YS2/Ysi) ............425

8.5 Development of Stress Explicit ConstitutiveEquation for New Yield S u r f a c e ................ 427

8.5.1 M values for Simple Shear Flow . . .431

8.5.2 M Values For 2-Dimensional FlowParallel To Disc Layers (CTi2+CT32) . . 432

8.5.2 M Values For Uniaxial F l o w ......... 433

8.5.3 M Values For Biaxial F l o w ...........434

8.6. Interpretation of M v a l u e s .....................435

8.6.1 Simple Shear F l o w ....................435

8.7 Discussion and Interpretation ................ 437

IX. A THEORY OF TRANSVERSELY ISOTROPIC PLASTICVISCOELASTIC FLUIDS TO REPRESENT THE FLOW OF ANISOTROPIC/ISOTROPIC PARTICLE SUSPENSIONS IN THERMOPLASTICS......................................... 440

9.1 Introduction..................................... 440

9.2 Linear Transversely Isotropic PlasticViscoelastic Fluids ........................... 441

9.2.1 Isotropic Linear PlasticViscoelastic F l u i d .................. 441

9.2.2 Transition of Transversely IsotropicLinear Plastic Viscoelastic Fluid. .443

9.3 Application Of Non-linear TransverselyIsotropic Plastic Viscoelastic Fluid Model . .446

9.4 Considerations from experimental rheologicalmeasurements.................................... 449

xix


9.4.1 Shear Flow Behavior For SimpleShear F l o w ........................... 449

9.4.2 Comparison of Experimental Resultswith Constitutive Equation with New Yield S u r f a c e ........................ 452

9.4.2.1 Yield Surface from Constitutive Relationships . . 457

9.4.2.2 Yield Surface of Anisotropy Parameter a as a Function of Various Yield Stress Ratios . .458

9. 4.2.2.1 Simple shear flowparallel to disc surfacesand 1-direction Uniaxial Flow (Yeii/Ysi) ............. 458

9.4.3 Experimental Results for PS/Talc,PS/Calcite, PS/Talc/Calcite System .458

9.4.4 Discussion............................ 462

9.5 Conclusions....................................463

X. CONCLUSIONS AND RECOMMENDATION .................... 4 67

10.1 Introduction.................................... 467

10.2 Conclusions..................................... 468

10.2.1 Orientation Stusies from WideAngle X-ray Diffraction ........... 468

10.2.2 Quantitative Analysis of FillerComposite using X-ray Intensity M e t h o d ................................469

10.2.3 Rheological Considerations-Experimental......................... 469

10.2.4 Rheological M o d e l i n g .................470

xx


10.3 Recommendations.................................471

REFERENCES................................................. 473

xx i


L I S T O F T A B L E S

Table Page3.1 Characteristics of materials and supplier for

Polystyrene system..................................... 85

3.2 Characteristics of materials and supplier forIUPAC 4.2.1 Working Party Polypropylene Project. . .86

3.3 PS compounds investigated.............................. 94

3.4 PP compounds investigated for IUPAC................... 95

3.5 Various processing geometries and condition in PSmatrix s y s t e m ......................................... 117

4.1 Shear and threshold yield values of particlefilled PS at 200 °C.................................... 167

4.2 Yield values of particle filled PP at 210 °C. . . . 170

4.3 Yield values of particle filled thermoplastics. . .171

4.4 Viscosity reduction by stearic acid coating of talc, calcite, and talc/calcite particles in PPat 25 v % .............................................. 182

5.1 Elongational yield values of particlefilled PSat 200 °C................................................198

5.2 Silicone oil absorption from compounded material. .225

6.1 Mass absorption coefficient of elements for CuKaat *-=1.5418 A ........................................... 293

6.2 Orientation factor for talc, and talc/calcite filled system from capillary die (L/D=28.5,D=1.6 mm) extrudate at Q=29.9 (mm3/s) 200°C......... 315

xxii


6.3 Orientation factor of talc, and talc/calcitefilled system from slit die extrudate_ (W/T=20,T=0.3 mm) extrudate at Q = 9049.5 (mmVs) 200°C . . 318

6.4 Orientation factor of talc, and talc/calcitefilled system from compression molding at 5 MPa compression (Thickness = 1 mm) at 200 ° C ............. 321

9.1 Parameters of empirical equations for particle filled thermoplastics................................ 453

9.2 Yield values of shear and elongational flow experiments for PS/talc, PS/calcite, and PS/talc/calcite filled s y s t e m ....................... 461

9.3 The anisotropy parameter a for various particle filled systems as a function of Y e i i / Y s i.............. 465

xxiii


LIST OF FIGURES

Figure Page2.1 Unit cell structure of T a l c ........................... 5

2.2 Unit cell structure of Mica............................ 8

2.3 Unit cell structure of Calcite........................11

2.4 Stein coordinate system and definitions forspecifying orientation modes of crystallographicaxes................................................... 33

2.5 White and Spruiell orientation triangle ...... 39

2.6 Schematic representation of x-ray diffractometer. . 44

2.7 WAXD flat film pattern.................................45

2.8 Schematic perspective of diffraction by specimensusing wide angle x-ray beam...........................49

2.9 3-Dimensional expression of the sphericalprojection of a crystal............................... 52

2.10 Angular coordinates used for obtaining a polefigure............................................ 54

2.11 Schematic diagram of scanning electron microscope (SEM)................................................... 58

2.12 Contrast mechanisms of scanning electron microscope (SEM)................................................... 59

2.13 Flow direction coordinates in Cartesian geometry. . 73

3.1 SEM photograph of Talc particles................... 8 4

3.2 SEM photograph of Mica particles................... 8 9xxiv


3.3 SEM photograph of Calcite particles.................. 90

3.4 Scheme of modified sandwich rheometer................. 99

3.5 Schematic diagram of cone-plate rheometer...........102

3.6 Schematic diagram of compression mold forRheometrics............................................ 103

3.7 Schematic diagram of capillary rheometer............ 105

3.8 Schematic diagram of silicone oil bath elongationalrheometer.............................................. 108

3.9 Scheme of elongation rheometer for measurementyield value............................................ Ill

3.10 Schematic diagram of parallel plate rheometer. . . 112

4.1 Shear viscosity as a function of shear rate fortalc filled system at 200°C........................... 133

4.2 Shear viscosity as a function of shear stress fortalc filled system at 200°C........................... 134

4.3 Shear strain creep as a function of time at 200°Cfor various creep levels for PS/talc 0.4 volume loading compound...................................... 136

4.4 Shear viscosity as a function of shear rate forcalcite filled PS system at 200°C.....................137

4.5 Shear viscosity as a function of shear stress forcalcite filled PS system at 200°C.....................138

4.6 Shear strain creep as a function of time at 200°Cfor various creep levels for PS/calcite 0.4 volume loading compound...................................... 140

4.7 Shear viscosity as a function of shear rate fortalc/calcite filled PS system at 200°C............... 141

4.8 Shear viscosity as a function of shear stress fortalc/calcite filled PS system at 200°C............... 142

XXV


4.9 Shear strain creep as a function of time at 200°C for various creep levels for PS/talc/calcite(a) 0.78/0.10/0.12 (b) 0.60/0.20/0.20 volume loading compounds......................................143

4.10 Shear viscosity of PP/fillers as a function ofshear rate at 210°C.....................................146

4.11 Shear viscosity of PP/fillers as a function ofshear stress at 210°C.................................. 148

4.12 Shear strain creep as a function of time at 210°C for various creep levels for PP/talc/calcite 0.75/0.13/0.13 volume loading compounds.............. 150

4.13 Dynamic viscosity of PP/fillers as a function of frequency at 210°C......................................152

4.14 Storage modulus (G') of PP/fillers as a functionof frequency at 210°C.................................. 155

4.15 Loss modulus (G") of PP/fillers as a function of frequency at 210°C......................................156

4.16 Strain(%) sweep of PP/fillers as a function ofstorage modulus G' at frequency lrad/sec and 210°C .158

4.17 Strain(%) sweep of PP/fillers as a function ofloss modulus G" at frequency 1 rad/sec at 210°C. . .159

4.18 Relative viscosity as a function of shear rate for talc-PS compounds......................................161

4.19 Relative viscosity as a function of shear rate for calcite-PS compounds.................................. 162

4.20 Relative viscosity as a function of shear rate for talc/calcite-PS compounds.............................163

4.21 Relative viscosity as a function of shear rate for talc/PP, calcite/PP, and talc/calcite/PP compounds.164

xxvi


4.22 Viscosity as a function of shear stress for 10 v% talc, calcite, and talc/calcite filled PS systemat 200°C.................................................177

4.23 Viscosity as a function of shear stress for 40 v% talc, calcite, and talc/calcite filled PS systemat 200°C.................................................178

4.24 Comparison between complex viscosity and shear viscosity of PP/fillers as a function of frequency/shear rate at 210°C...........................184

4.25 Viscosity as a function of shear stress for talcand calcite filled system at 200°C...................... 186

5.1 Elongational viscosity measurements of PS systemat 200°C.................................................190

5.2 Elongational viscosity measurements of PS/calcite (95/05 v%) system at 200°C.............................192



5.5 Elongational viscosity measurements of PS/calcite (60/40 v%) system at 200'C.............................195

5.6 Elongational viscosity as a function of elongational rate for calcite filled systemat 200°C.................................................196

5.7 Elongational viscosity as a function of elongational stress for calcite filled systemat 200°C.................................................197

5.8 Elongational viscosity measurements of PS/talc(95/05 v%) system at.200°C............................ 200

5.9 Elongational viscosity measurements of PS/talc(90/10 v%) system at.200°C............................ 201

xxvii


5.10 Elongational viscosity measurements of PS/talc(80/20 v%) system at 200°C............................ 202

5.11 Elongational viscosity measurements of PS/talc(60/40 v%) system at 200°C............................ 203

5.12 Elongational viscosity as a function ofelongational rate for talc filled system at 200°C. .206

5.13 Elongational viscosity as a function of elongational stress for talc filled systemat 200cC ................................................ 207

5.14 Elongational viscosity measurements of PS/talc/calcite (90/05/05 v%) system at 200°C. . . .208




5.18 Elongational viscosity measurements of PS/talc/calcite (60/20/20 v%) system at200°C....................................................212

5.19 Elongational viscosity as a function of elongational rate for talc/calcite filledsystem at 200°C........................................ 213

5.20 Elongational viscosity as a function of elongational stress for talc/calcite filledsystem at 200°C........................................ 214

5.21 Shear/elongational(SBM) viscosity as a function ofshear/elongational stress rate for PS at 200°C. . . 219

5.23 Shear/elongational(SBM) viscosity as a function of shear/elongational rate for talc filled system at 200°C................................................ 223

xxviii


5.24 Shear/elongational(SBM) viscosity as a function of shear/elongational stress for talc filledsystem at 200°C.........................................224

5.25 Shear(SBM)/elongational(SBM) viscosity as a function of shear/elongational rate for talc filled system at 200°C.........................................227

5.26 Shear(SBM)/elongational(SBM) viscosity as a function of shear/elongational stress for talc filled system at 200°C................................. 228

5.27 Shear/elongational(SBM) viscosity as a function of shear/elongational rate for calcite filled systemat 200°C................................................ 231

5.28 Shear/elongational(SBM) viscosity as a function of shear/elongational stress for calcite filled systemat 200°C................................................ 232

5.29 Shear(SBM)/elongational(SBM) viscosity as a function of shear/elongational rate for calcite filled system at 200°C................................. 235

5.30 Shear(SBM)/elongational(SBM) viscosity as a function of shear/elongational stress for calcite filled system at 200°C................................. 236

5.31 Shear/elongational(SBM) viscosity as a function of shear/elongational rate for talc/calcite filled system at 200°C.........................................239

5.32 Shear/elongational(SBM) viscosity as a function of shear/elongational stress for talc/calcite filled system at 200°C.........................................240

5.33 Shear(SBM)/elongational(SBM) viscosity as a function of shear/elongational rate for talc/calcite filled system at 200°C.................. 242

5.34 Shear(SBM)/elongational(SBM) viscosity as a function of shear/elongational stress for talc/calcite filled system at 200°C.................. 243

xxix


6.1 Intensity distribution of polystyrene............249

6.2 Intensity distribution of PS and PS/calcite (5 v%).250

6.3 Intensity distribution of PS and PS/calcite(10 vl)................................................. 251

6.4 Intensity distribution of PS and PS/calcite(20 v%)................................................. 252

6.5 Intensity distribution of PS and PS/calcite(40 v%)................................................. 253

6.6 Intensity distribution of calcite powder............254

6.7 Intensity distribution of various calciteloadings................................................ 255

6.8 Intensity distribution of PS and PS/talc (5 v%). . 257

6.9 Intensity distribution of PS and PS/talc (10 v%). .258



6.12 Intensity distribution of talc powder............261

6.13 Intensity distribution of various rale loadings. . 262

6.14 Intensity distribution of PS and PS/talc/calcite(90/05/05 v%) ........................................ 264

6.15 Intensity distribution of PS and PS/talc/calcite (84/04/12 v % ) ........................................ 265

6.16 Intensity distribution of PS and PS/talc/calcite (54/03/43 v%) ........................................ 266



XXX


6.19 Intensity distribution of PS and PS/talc/calcite (53/05/42 v % ) .........................................269

6.20 Intensity distribution of PS and various PS/talc/calcite (88:12: wt) loadings .............. 270

6.21 Intensity distribution of PS and various PS/talc/calcite (77:23: wt) loadings .............. 271

6.22 Typical x-ray pattern of 20v% talc particles from capillary extrudate (D=1.6mm, L/D=28.5)............273

6.23 Typical x-ray pattern of 20v% calcite particlesfrom capillary extrudate (D=1.6mm, L/D=28.5) . . . 274

6.24 X-ray pattern of PS/talc/calcite (90:05:05 v%) system from capillary die extrusion (D=1.6mm,L/D=28 .5)............................................. 275

6.25 Flow direction x-ray pattern of talc particle filled system from compression molding (a) 5 v%,(b) 10 v%, (c) 20 v%f (d) 40 v%...................... 277

6.26 X-ray pattern of PS/talc/calcite system from compression molding (a) 90:05:05 v%,(b) 84:04:12 v%, (c) 84:10:06 v%,(d) 78:10:12 v%,(e) 75:19:06 v%, (f) 60:20:20 v%.....................278

6.27 The pole figures for the (001) plane of the 5 v% talc compound from capillary die extrusion experiment............................................. 281

6.28 The pole figures for the (001) plane of the 5 v% talc compound from rectangular die extrusion experiment............................................. 283

6.29 The pole figures for the (001) plane of the 5 v% talc compound from the slit die extrusion experiment............................................. 284

6.30 The pole figures for the (001) plane of the 5 v% talc compound from annular die extrusion experiment............................................. 286

xxx i


6.31 The pole figures for the (001) plane of the 5 v%talc compound from compression molding

experiment............................................. 288

6.32 Comparison of theoretical intensity-concentration curves (solid line) and experimental measurements (open circle) for PS/calcite mixtures............... 297

6.33 Comparison of theoretical intensity-concentration curves (solid line) and experimental measurements (closed hexagon) for PS/calcite mixtures............298

6.34 Comparison of theoretical intensity-concentration curves (solid line) and experimental measurements (closed circle) for PS/talc mixtures................ 30U

6.35 Relative intensity distribution of various talc/calcite mixed particle as a function of PS concentration........................................ 305

6.36 Relative intensity distribution of various talc/calcite mixed particle as a function of PS concentration........................................ 306

6.37 Relative intensity distribution of various (PS/talc,88:12 wt%)/calcite mixed particle systemas a function of PS+talc concentration ........... 307

6.38 Relative intensity distribution of various (PS/talc,77:23 wt%)/calcite mixed particle systemas a function of PS+talc concentration ........... 308

6.39 White and Spruiell orientation triangle for capillary die extrusion...............................314

6.40 White and Spruiell orientation triangle for slit extrusion.............................................. 317

6.41 White and Spruiell orientation triangle for compression molding................................... 320

6.42 Orientation function of talc as a function of volume loading of calcite from capillary die extrudates............................................. 323

xxx ii


6.43 Orientation function of talc as a function of volume loading of calcite from slit die extrudates............................................. 325

6.44 Orientation function of talc as a function of volume loading of calcite from compressionmolding.................................................327

6.45 Orientation function as a function of volume loading of capillary extrudates, sheet extrudates, and compression moldings............................. 330

7.1 Cross-section of 5 v% and 40 v% talc particlefilled compression molded polystyrene sheets. . . .334

7.2 Cross-section of 5 v% and 40 v% mica particlefilled compression molded polystyrene sheets. . . .335

7.3 Cross-section of (a) 5 v%, (b) 10 v%, (c) 20 v%and (d) 40 v% talc particle filled capillary die extrudated filaments.................................. 337

7.4 Dimensionless analysis of radial ratio d/D vs.extrusion rate of capillary extrudates..............340

7.5 Dimensionless analysis of radial ratio d/D vs.volume loadings of capillary extrudates.............341

7.6 Dimensionless analysis of radial ratio vs. diewall shear stress based upon different volume loadings from capillary extrudate................... 342

7.7 Dimensionless analysis of n value vs. Talc v%(L/D 28.5, D=1.6 mm, 200°C, Capillary)............... 344

7.8 Cross-section of 5 v% and 40 v% mica particlefilled capillary die extrudated filaments.......... 345

7.9 Cross-section of 05/05 v% and 04/12 v%talc/calcite particle filled capillary die extrudated filaments ............................... 347

7.10 Cross-section of 10/06 v% and 10/12 v%talc/calcite particle filled capillary die extrudated filaments ............................... 348

xxxiii


7.11 Cross-section of 20/10 v% and 20/20 v%talc/calcite particle filled capillary die extrudated filaments ...................... 3 4 9

7.12 Cross-section of 5 v% and 40 v% talc particlefilled slit die extrudated polystyrene sheets. . . 350

7.13 Cross-section of 5 v% and 40 v% mica particlefilled slit die extrudated polystyrene sheets. . . 352

7.14 Cross-section of 5 v% and 40 v% talc particle filled rectangular die extrudated filaments. . . . 354

7.15 Cross-section of 5 v% and 40 v% mica particlefilled rectangular die extrudated filaments. . . . 355

7.16 Cross-section of 5 v% and 40 v% talc particlefilled annular die extrudated sheets................ 357

7.17 Cross-section of 5 v% and 40 v% mica particlefilled annular die extrudates..................... 358

7.18 Cross-section view of 5 v% and 40 v% talc particles from 0.03 inch capillary diameter extrudates..........................................360

7.19 Cross-section view of 5 v% and 40 v% talc particles from 4.6 mm capillary diameter extrudates..........................................361

7.20 Cross-section view of 5 v% and 40 v% talcparticles from capillary die entrance 135°.......... 363

7.21 Cross-section view of 5 v% and 40 v% talc particles from twin screw extruder extrudates. . . 365

7.22 Normal direction cross-section view of 20 v% talc particles from reservoir to capillary die entrance at 45°......................................... 366

7.23 Summary of schematic observation from capillary extrudates with volume and extrusion rate changes .370

xxxiv


7.24 Geometric Orientation Instability Effect of talcfrom different capillary dies at 5 v % .............. 371

7.25 Geometric Orientation Instability Effect of talcfrom different capillary dies at 40 v % ............. 372

7.26 Summary of reservoir to capillary entrance flow of talc particles........................................ 374

7.27 Schematic representation of twin screw extruder extrudates of talc filled thermoplastics ......... 375

7.28 Schematic representation of particle-particleangle and their diameter............................. 378

7.29 Geometric Orientation Instability Effect of talcfrom different aspect ratio dies at 5 v % ........ 380

7.30 Geometric Orientation Instability Effect of talc from different aspect ratio dies at 40 v % ..........381

7.31 Geometric Orientation Instability Effect of talc from annular die at 5 v% and 40 v % ............... 382

7.32 Cross-section texture of pitch fibers fromH. H o n d a ............................................ 387

8.1 Schematic representation of simple shear flow parallel to disc surfaces (a) a i2=a si (b) G 32=<Js3 . . .404

8.2 Schematic representation of flow direction shearflow perpendicular to disc stacking (G i 3 = G s2) . . . .407

8.3 Schematic representation of perpendicular to theDisc Axes (1-direction, Geii)......................... 410

8.4 Schematic representation of parallel to the Disc Axes (2-direction, aei2 ).............................414

8.5 Schematic representation of shear flow parallelto disc layers (Gi2+G32) ................................418

8.6 Schematic representation of two-dimensional shear flow normal to disc layers (Gi2+Gi3)................. 421

XXXV


8.7 Yield surface for yield stress ratio Yeii/Ysi

as a function of anisotropy parameter a . . . 424

8.8 Yield surface for yield stress ratio YS2/Ysi as a function of anisotropy parameter a ............... 426

9.1 Comparison of empirical equations with experimental data for talc filled PS systemat 200 ° C .............................................. 454

9.2 Comparison of empirical equations with experimental data for calcite filled PS systemat 200 ° C .............................................. 455

9.3 Comparison of empirical equations with experimental data for talc/calcite filled PSsystem at 200 ° C ......................................456

9.4 Yield surface of anisotropy parameter a as a function of minimum yield stress ratio Yeii/Ysi for talc(40v%), calcite(40v%), and talc/calcite(40v%) filled polystyrene ................................. 460

xxxvi


CHAPTER I

INTRODUCTION

Minerals are compounded into plastics for several

purposes: (i) as mechanical reinforcements, (ii) as

pigments, (iii) for enhancement of electrical conductivity

or thermal behavior and (iv) to lower material cost.

Mineral fillers such as talc, mica, clay, wollastonite, and

calcite have obtained an important position in the polymer

industries because of their ability to fulfill some of

those roles.

Many of the mineral particles used are anisotropic in

shape. Such particles may take states of orientation due

to flow or packing processes. The orientations developed

should influence phenomena ranging from rheological

properties to compound processability in industrial

processing equipment to electrical characteristics and

mechanical performance.

1

Reproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission.

2In this dissertation we investigate the behavior of

small disc shaped particle compounds in thermoplastics.

Specific variables considered are as follows (i)

rheological behavior from low loadings to high loadings

using various rheological instruments, (ii) orientation of

disc particles developed during different states of flow,

(iii) behavior of mixed particle systems, (iv) development

of a three dimensional rheological model to represent the

behavior of disc-like and mixed particle systems.


C H A P T E R I I

BACKGROUND AND LITERATURE SURVEY

2.1 Crystal Structure and Characteristics of Talc, Mica,

and Calcite

2.1.1 Talc

Talc is considered a hydrated magnesium silicate. It

is one of a series of lamella silicate minerals involving 2-

dimensional silicate sandwich with other minerals (1-5).

The structure of this class of minerals was first worked out

by Pauling (5-7) (compare Moeller (8) ) . The basic chemical

composition of talc is (MgO) n (Si02) n (H20) p where n=3, m=4, and

p=l, this has been expressed variously in forms such as

3Mg0'4Si02'H20, Mg3'Si4'O10‘ (OH) 2, Mg3-Si4'H20i2, Mg3‘ (Si05) z (H20) n.

The basic structure of talc is a sheet of brucite (Mg(OH)2)

3


4

in between two silicate (Si02) layers (9, 3JD) . Talc layers

are bonded with weak van der Waal type forces. The mean

particle size of most industrial talc is in the 2 to 20

micron range. Talc is usually in plate form with an aspect

ratio between 10 and 30. Depending on the source from which

it is mined, talc is said to show different surface

characteristics. The Montana talcs are hydrophobic in

nature while the California talcs are predominantly

hydrophilic (^). Talc is a soft mineral (having Moh's

hardness of 1.0) and its layers easily slide past each other

by shearing action.

In 1934 Gruner (3J.) reported a monoclinic unit cell

structure of talc based upon x-ray diffraction measurements.

Gruner indexed the diffraction patterns on the basis of a

monoclinic unit cell with a=5.26 A, b=9.10 A, c=18.81 A,

P=100.0°. Subsequently using new x-ray diffraction

measurements, Hendricks (12) , Zvyagin and Pinsker (3 3) , and

Stemple and Brindley (1_4) have also reported monoclinic unit

cells for talc with similar dimensions.


5

o Oxygen (O) © Hydroxyl (OH) • Magnesium (Mg)

O and • Silicon (Si)

Figure 2.1 Unit cell structure of Talc


6

In 1966 Rayner and Brown (L5,16), using new x-ray

diffraction measurements, carefully reexamined the crystal

structure of talc and reported a triclinic unit cell with

a=5.293 A, b=9.179 A, c=9.496 A, a=90.57°, P=100.0°,

Y=90.03°. Ross et al. (3/7), Akizuki and Zussman (3J3) , and

more recently Perdakatsis and Burzlaff (3 9) have also more

recently reported triclinic unit cells for talc (Figure

2 .1).

2.1.2 Mica

Mica is classified into the phyllosilicate group and

shows platy and flaky habits (5-7). The principal sheet

structured micas with their chemical formulae are very

complex, owing to substitution. The mica group includes

Muscovite [KA12 (AlSi3Oi0) (0H)2], Paragonite [NaAl2 (AlSi3Oi0)

(0H)2], Phlogopite [KMg3 (AlSi3Oi0) (0H)2], Biotite [K(Mg,Fe)3

(AlSijOio) (OH) 2] , Lepidolite [ K L i 2A l ( S i 40ia) (F,OH);],

Zinnwaldite [KLiFeAl (AlSi3Oi0) (F,OH)2] (20). There is also

brittle mica group includes Margarite [CaAl2 (Al2Si2Oi0)

(0H)2], Seybertite [Ca(Mg,Al)3 ( S i , A l ) 4 Oio (OH)2], Chloritoid

[ (Mg, Fe2") 2 Al2 (Al2Si2Oi0) (OH)2] (20). The difference between


Muscovite, Phlogopite, and the Biotite mica structure is

that variously Al, Mg, and Fe atoms are located between two

layers of the hexagonal network of silicon-oxygen

tetrahedral groups (Figure 2.2) respectively. Micas, both

Phlogopite and Muscovite types consist of high-aspect-ratio

particles which are generally coarser than talcs and range

from 40 to 600 microns in average particle size. Mica

flakes are large platelets and reinforce in two directions.

Recently, pearlscent pigments have been developed which are

based on synthetic mica (21). These have been used for

coating application in the automotive industry because they

generate brilliant interference colors when combined with

other pigments.

In 1927 Mauguin (22), using wide angle x-ray

diffraction first reported monoclinic (pseudohexagonal) unit

cells and suggested symmetries of different types of mica

structures. Pauling (5) in 1930 established a general

scheme of their structure by determining the sequence of

sheets of atoms parallel to their cleavage planes.

According to Pauling (5), the cell parameters of Muscovite

mica are : a=5.19A, b=8.99A, c=20.14A, a=Y=90°, P=96°. Mica

exhibits perfect cleavage along the (001) plane and thin


8

•&*f-OZA

iK c'ZO-OJ-A

Figure 2.2 Unit cell structure of Mica.


9

cleavage allow the mineral to be split into very thin sheets

which are flexible and elastic. The first complete

structural analysis of Muscovite mica was made by Jackson

and West (2_3) in 1930.

2.1.3 Calcium Carbonates

Of the rock-forming carbonates, calcite (CaC03, see

Figure 2.3) and dolomite (Ca (Mg,Fe) (C03);) are the most

abundant, accounting for more than 90% of natural

carbonates. Calcium carbonates are popular additives for

thermoplastics because of their combination of low cost,

high brightness, and the ability to be used at high

loadings. They generally are categorized as fillers or

extenders since they are used for cost reduction. However,

they also provide increases in modulus and tensile strength

and must be considered as reinforcements as well.

There is a long history of crystal structure

investigations for the common rhombohedral carbonates. The

general structure of calcite was established in 1914 by

Bragg (2jj) . He determined the unit cell structure of

calcite as rhombohedral by using x-ray diffraction. Modern


1 0

descriptions of rhombohedral carbonates are represented

almost exclusively in terms of a hexagonal cell. In 1927

Harrington {21) proposed that the unit cell of calcite is

hexagonal with a:=a2=a3=4.993 A, c=17.061 A, a=46J06' (angle

between any two of the three equal length edges), r=6.37 6 A (the edge length), (Figure 2.3). The structure involves

ions of Ca*+ and C03"~. The general form of the C03 group is

an equilateral triangle with oxygen atoms at the corners and

a carbon atom in the center. Layers of Ca** atoms alternate

with carbonate layers along the c axis.

Carbonates are supplied in five forms: water-ground,

dry-ground, ultra fine-ground, precipitated, and surface-

treated. Precipitated carbonates are chemically produced.

Carbonates usually have a broad mean particle size range.

Some precipitated carbonates have a mean particle size of

less than 0.1 micron while some dry-ground types have a mean

particle size of over 20 micron.


(a) (b) (c)

(a) Closed large circles represent Ca*" ions, small closedcircles surrounded by open circles represent C 4 ionsand open circles represent 0 ions.

(b) Side view of calcite unit cell.(c) Plan view of calcite unit cell.

Figure 2.3 Unit cell structure of Calcite.


1 2

2.2 Particle Behavior in Suspended Systems and Influence on

Rheological Properties

2.2.1 Particle Interactions in Suspensions

2.2.1.1 Large Isotropic Particles

When particles are suspended in a matrix the

interaction between particles increases as the particle

concentration increases. Concentrated suspensions of large

isotropic particles give rise to the phenomenon of

'dilatancy'. Dilatant suspension behavior was originally

hypothesized by Reynolds (2Q_) . He argued that concentrated

systems would dilate (expand) in shear flow because this

should disrupt the packing. Subsequently, Freundlich

described dilatant systems as those whose shear viscosity

increases with shear rate. The relationship of these two

'dilatant' phenomenon has given rise to much discussion.

The best observations were by Hoffman (29-32).


1 3

2.2.1.2 Anisotropic Particle Motions and Interactions

2.2.1.2.1 Dilute Systems

Jeffery (33) in 1922 theoretically investigated the

rotary motion of rigid ellipsoids in dilute suspensions of a

Newtonian fluid. During shear flow, the particles undergo

motions involving regular orbits which have become known as

Jeffery orbits. The long axes of prolate and oblate

particles are immersed in a fluid in laminar motion. They

will tend to set themselves parallel to the flow direction.

Taylor (34-26) subsequently verified Jeffery's (33)

analysis for the motion of ellipsoids. Subsequently, Mason

and his coworkers (37-46) made extensive efforts to

visualize anisotropic particle motions in dilute suspensions

during flow. These have also verified the observations of

Jeffery.

2.2.1.2.2 Concentrated Anisotropic Particles

There have been many researches on concentrated

suspensions of small anisotropic particle from the second


1 4

decade of the century (47-61) . In 1921 Zocher (_50) observed

the behavior of aniline-blue sol, a rod-like particle

suspension of micron level particle size. These suspensions

showed birefringence in a state of rest.

In 1923 Szegvari (51-54) published a photomicrograph of

a birefringent suspension of V205 obtained using a

polarizing microscope. In 1925, Zocher (5_5, 5_6) described

the characteristics of fine Fe203 suspensions. He argued

that the particles have a disc-like form and exhibit an

anisotropic birefringent phase at high concentrations under

the microscope. Later observations by Zocher et al (57)

using the optical microscope show a parallel orientation of

the Fe203 disks with a uniform spacing of order a micron.

In 1937 Freundlich (6_1) reported that vanadium pentoxide

suspensions become increasingly birefringent over a critical

concentration until their suspensions are completely

birefringent.

In 1936 Bernal, Bawden, Pirie, and Fankuchen (58-60)

observed the development of localized orientation in a

slightly concentrated suspension of tobacco mosaic virus

(diameter 150 A, length 1500 A ) . They found a nematic rod

like order of asymmetric particles using small angle x-ray


1 5

scattering. Upon sedimentation, tobacco mosaic virus

suspensions separate into two layers; the top layer is a

dilute isotropic suspension; in the bottom layer the viruses

are arranged in a two dimensional hexagonal close packing

order of parallel rods. The distance between the particles

was found by small angle x-ray scattering to vary from zero

up to 300 A and more, depending upon the concentration of

protein in the bottom layer. Freundlich (61) contrasted

this behavior to the result of his investigations on V;05

suspensions.

In the late 1960s Lees (62), Schierding (63), and Kitao

and his coworkers (64) proposed the quantitative

characterization of chopped fiber orientation in composites

and polymer compounds using wide angle x-ray diffraction.

Schierding (63) used ceramic fibers. Kitao, et al. (64) ,

investigated melt spun polystyrene filaments containing

carbon fibers. In this period other investigations made

quantitative fiber orientation using soft x-rays (65-68 ) . In

1984 Menendez and White (69) investigated chopped aramid

fibers suspended in polymethyl methacrylate matrix through a

circular die. In 1988-90 Lim and White (70, 71)

investigated the orientation of chopped aramid fibers in


1 6

thermoplastic compounds which had been processed in various

fashions.

In 1987 Monge, Vincent and Haudin (7_4) investigated the

orientations of mica and talc particles in injection molded

thermoplastic compounds using wide angle x-ray diffraction.

Their results show that the particles are parallel near the

mold surface and nearly perpendicular in the core. In

papers published in 1990-1991, Lim and White (7_1, 81)

investigated the orientation of suspensions of talc and mica

in extrudates from various shaped dies, calendered sheets

and injection and compression molding using wide angle x-ray

diffraction. They found that the talc and mica particles

are parallel near the mold surface and nearly perpendicular

in the core. In 1991 Fujiyama et.al. (73-79) investigated

the orientation of disc particle filled thermoplastics (PP)

in injection molded bars. The results of their work are

similar to those of the above researches.

More recently, Suh and White (8_2-8_5) investigated the

state of orientation of talc particles in blow molded and

thermoformed thermoplastic parts. They found that the talc

particles are parallel near the mold surface for blow molded

and thermoformed parts independent of thermoplastic matrix.


1 7

2.2.1.3 Characteristics Of Liquid Crystals

Common liquids are optically isotropic in the state of

rest. Liquids are sometimes cloudy in the state of rest.

These substances been have known for a century and are

called liquid crystals. The term 'mesomorphic' has been

applied. They possess a state of aggregation midway between

the true crystalline state and irregularity of the amorphous

state. The molecules may lie symmetrically about an axis,

for instance threads in soap, the position of each molecule

being quite accidental; or they may be piled in layers, the

position of the molecules of a single layer being random.

Such states of aggregation Friedel (8_6) are called

mesomorphic. Mesomorphic particles are most likely found in

soap solutions (ammonium oleate). Under some special

conditions these solutions are found to contain very long

threads whose lengths reach up to lOOM-m while their

thickness is often less than micron size (ultramicroscopic)

(92) .

At high loadings some authors have reported, rod and

disc particles orient and arrange in a quasi lattice array


to form a mesophase. This occurs in carbonaceous pitches

(82~91.) which have been found to be birefringent. In 1956

Flory (87.) gave a statistical mechanical argument based on

fitting macromolecules into a lattice that suspensions of

rigid rods would not be isotropic at a high concentration

but would form locally anisotropic structures.

2.2.2 Influence of Particles on Rheological Properties

2.2.2.1 Shear Flow

2.2.2.1.1 Rheological Models of Dilute Suspensions System

Hydrodynamic analyses of flow in suspensions date to

Einstein's (^3) study of dilute suspensions of spheres in

1911. He developed a theory for predicting the viscosity

a dilute suspension of rigid spheres in a Newtonian fluid

matrix. He showed that viscosity H of a dilute suspension

is equal to

n = Ho (1 + 2.5$) (2.1)


1 9

where Ho is the viscosity of the suspending medium and ^ is

the volume fraction of the spheres. Equation (2.1) is valid

only for extremely dilute suspensions, in which interactions

between neighboring particles are negligible (i.e., in the

absence of hydrodynamic interactions).

Following Einstein (93), Jeffery (33) investigated the

motion of non-spherical particles (rigid ellipsoidal

particles) in a shear field of Newtonian liquid in 1922.

Using the creeping flow Navier-Stokes equations, he derived

an expression for the effective viscosity

n = n0 (i + H>) (2.2)

where v is a parameter which depends on the aspect ratio

and orientation of the ellipsoidal particles. Jeffery

reported that v is less than 2.5, which is the value for

spherical particles derived earlier by Einstein (93). The

significance of Jeffery's studies lies in the derivation of

equations of anisotropic particle motion in a Newtonian

liquid. He predicted the shear flow rotates the disc/rod in

shear planes.


2 0

2.2.2.1.2 Rheological Properties Of Concentrated Particle

Suspensions

2.2.2.1.2.1 Large Particles

Particles of varying sizes and shapes have been added

to polymer melrs and solutions. It is convenient to begin

our discussion with large isotropic particles and then

proceed to anisotropic particles and finally to very small

particles. The influence of glass spheres of diameter 10-60

on the viscosity of polypropylene (PP), styrene-

acrylonitrile (SAN), and polystyrene (PS) matrix has been

investigated by Chapman and Lee (105) , Nazem and Hill (96),

and White, Czarnecki and Tanaka (97_) . They all found that

the viscosity is constant at lower shear rates and then

decreases with increasing shear rates. The viscosity vs.

shear rate behavior of the compound resembled that of the

initial pure thermoplastic melt.

Studies of the influence of glass fibers of diameter

10-15 ^m on the viscosity of polymer melts and solutions

have been reported by various investigators (98-102). Most


2 1

have been carried out at high shear rates using capillary

rheometers. The studies of Chan et al.(9^) and Czarnecki

and White (9_9) indicate that the melt exhibits a low-shear-

rate Newtonian viscosity and then decreases with increasing

shear rates. Similar observations were made for aramid

fiber and cellulose-filled melts (97, ^9) .

Elongational flow studies have been reported by Chan,

White and Oyanagi in glass fiber-filled high density

polyethylene and polystyrene melts in 197 8. They found the

elongational viscosity to be very high relative to the shear

viscosity and to decrease with increasing elongation rate.

The basis of the behavior comes from the work of Batchelor

(94^, and Batchelor et al. (9_5) later expanded by Goddard

(103, 104). Goddard suggests that the elongational

viscosity function of fiber filled compounds seems to

reproduce the shear viscosity function. This is due to the

shearing motions induced by fibers moving past each other

during the elongational flow.


2.2.2.1.2.2 Small Particles22

Measurements of the shear viscosity of particle

suspensions date to early in the century.

In the 1930s Freundlich and his co-workers first

observed time dependent viscosities i.e. thixotropy for

suspensions in low viscosity liquids (108-110) . Freundlich

and Jones (110) contrasted the rheological behavior of a

wide range of concentrated particle suspensions in 1936.

They note that suspensions of small particles differ from

large particles in exhibiting significant agglomeration

which gives rise to yield values of low shear rates and are

time dependent, that is, thixotropic viscosities.

In 1931 Scott (111) investigated small particle filled

natural rubber using a compression rheometer at very low

applied stresses. He found that these compounds exhibit a

yield value, Y. He proposed a relationship between the

shear stress, a , and shear rate, Y. This had form

= Y + K Yn (2.3)


2 3

In 1950 Mullins and Whorlow (112) reported that shear

viscosity of concentrated compounds of rubber exhibits a

strong time dependence. Further, if the deformation is

temporarily ended, it takes a very long time for the

material to recover its initial transient stress build up

behavior.

In 1962 Zakharenko et al. (113) studied the flow

behavior of carbon black filled polyisobutylene (PIB) by

using parallel plate viscometer to achieve very low shear

rates. They showed that the flow behavior of carbon black

filled PIB conformed to the power law model i.e. the shear

viscosity varied with the n-th power of the shear rate. The

power law index decreased with increasing loading of carbon

black.

In 1969^1978 Matsumoto and Onogi (114-117) found

various particle-filled polymer solutions appeared to

exhibit yield values. The system included polystyrene

particles in diethyl phthalate solution, and carbon black in

diethyl phthalate solution, carbon black in liquid

paraffins, and polyacrylamide and aluminum hydroxide in

aqueous solutions.


2 4

In 197 0 Chapman and Lee (105) investigated the

influence of talc particles on the shear viscosity behavior

of polypropylene (PP). They found apparent yield values at

volume fractions 15-20%. They also studied the effect of

surface treatment and particle size on rheological behavior.

They found that decreasing the particle size increases the

yield value. Adding surface treatments such as stearic acid

to the filler reduces the yield value of the molten polymer

compounds. They suggested that such shear viscosity

behavior could result from the interaction of talc particles

and the resultant agglomeration of the particles within

polymer melts to form a network structure.

Subsequently in 1972, Vinogradov et al. (118) examined

the shear flow of carbon black filled polyisobutylene (PIB)

by using a series of different rheometers. Yield values

were found for carbon black (2.5 -13 % by volume) filled PIB

compounds. They argued that carbon black particles could

form a 3-dimensional structural skeleton which caused the

appearance of yield values in the filled polymers.

In 1978 and 1979 Kataoka et al. (119, 120) observed

apparent yield values in glass bead and calcium carbonate


2 5

filled low density polyethylene (LDPE) and polystyrene (PS)

melts.

More systematic studies of the influence of different

particles were carried out by White et al. (81-85, 97-99,

102, 106, 107, 121-139) beginning in the mid 1970s. They

determined the shear viscosity behavior of compounds

containing carbon black, titanium dioxide, calcium

carbonate, wollastonite, glass beads, glass fibers, aramid

fibers, cellulose fibers, etc. They also investigated the

influence of particle size, volume fraction of particles,

and surface treatment on the rheological properties of

filled polymer melts. Yield values in Ti02 (97, 107, 121,

122, 123), carbon black (97, 106, 107, 124-127, 128-132),

and CaCOi (97_, 107, 123, 133) filled polymer melts were

surmised. They were found to increase with increasing

volume loading of small particles and with decreasing

particle size. Early studies of the flow of suspended

particles in polymer melts used Scott's Equation (2.3) to

represent the flow behavior of these compounds. White

et.al. (125, 126, 131, 132) later developed a second

empirical relationship for the shear viscosity behavior of

carbon black-rubber compounds with the expression,


2 6

cx= Y + ------------------ (2.4)i + b r~n

At high shear rate, it could be seen that A/B of Equation

(2.4) was the same as K of Equation (2.3). White and his

coworkers (82, 85) have compared this empirical Equation

(2.4) with their experimental data for various particle

filled systems.

Lobe and White (106), Suetsugu and White (133) and

Montes et al. (139) studied stress transients at the start

up of flow and at the end of flow. Startup transients of

shear stresses were larger than for pure polymer melts and

depended upon volume loading. Yield values were observed in

elongational flow as well as shear flow.

Generally, the magnitude of the yield value increases

with particle loading and with decreases in particle size.

Suetsugu and White (133) found that the apparent yield value

Y varied inversely with the particle diameter in calcium-

carbonate-filled polystyrene.

Most of the above researchers surmised yield values

from low shear stress data. More recent researchers


2 7

beginning with Osanaiye et al. (127, 136), and later Li and

White (271) and Araki and White (257) have actually

determined yield values using creep experiments.

The elongational flow of small particle filled polymer

melts has been investigated by several researchers. Lobe

and White (106) and Tanaka and White (107) have studied

carbon black filled polystyrene polymer melts. Tanaka and

White (107) have also investigated calcium carbonate,

titanium dioxide filled polystyrene. They found the

elongational viscosity function appears to exhibit yield

value whenever the shear viscosity exhibits a yield value.

2.2.3 Rheological Properties in Mixed Particle System

Interactions of different types of particles of varying

size, shape, and particle-particle interaction can exist and

may affect the rheological properties of mixed particle

filled compounding systems.

There have been many researches of single particle

filled compounds systems and their rheological behavior has

been reported. However, there seems to be essentially no

researche in multiple particle filled system in


28thermoplastics. In 1980 Sugama et al. (141) investigated

mixtures of calcium oxide and silicon dioxide fillers to

make polymer concretes for hydrothermally stable products.

Lim and White (7]J studied the particle orientation

characteristics of compounds containing aramid fiber and

talc/mica flakes. The above studies do not include

rheological researches on multiple particle filled systems.

There seems to be no rheological investigations of particle-

particle interactions in different particle filled systems.

2.3 Orientation Development of Anisotropic Particles During

Flow

2.3.1 Introduction

The reinforcement of thermoplastics with mineral and

organic particles is an important aspect of polymer

technology. In general, such particulates include

reinforcing aramid, carbon and glass fibers, as well as

minerals such as mica, talc, and wollastonite which are

highly anisotropic. The mechanical (142-146), thermal (146-

148), and electrical (149) behavior of these composites


2 9

depend upon the orientation of the particulates. In most

polymer processing operations, products are shaped in the

manner of extrusion and injection molding, which influence

but do not fully control the orientation of anisotropic

particulates.

It is clear that the experimental determination of

anisotropic particle orientation in filled thermoplastics is

an area of great importance. It is important that such an

approach be quantitative as it should be applicable to the

relative variations in orientation with processing

conditions.

2.3.2 Representation of Uniaxial Orientation

The representation of uniaxial orientation of

anisotropic particles has an important effect on physical

and mechanical properties.

The first representation of uniaxial orientation seems

to be by Hermans and Platzek (152) in 1939. They argued

that the birefringence of a uniaxially orient filament was

given by


3 0

AnA"~

3cos' <p - 1 2 (2.5)

where ‘t* is the angle between the polymer chain axis and the

fiber axes.

In 1941 Muller (150, 151) built on the earlier work of

Hermans and Platzek (152) and represented the uniaxial

orientation distribution function for oriented polymer

chains as an expansion of Legendre polynomials:

between the fiber axis and the polymer chain axis. Odd

F(4>) = F0[l + AiPi(<t>) + AzPz^) (2 .6)

The Pj (<(>) s are Legendre polynomials in the mean angle

Legendre polynomials involve averaging terms such as cos'(j>

and cos5<t> are zero. The first term in the expansion for

P-j (4*) from Equation (2.6) is of form:

(2.7)

The second term is


3 1

P4 (♦) = ^ [35 cos4 <f> - 30 cos: (j) + 3] (2.8)O

The mean orientation may be represented in terms of

these Legendre polynomials. The first term in P:(§) often

represented as of a fa given by Equation (2.7) is known as

the Herman orientation factor (152-158) . The values of fH

or P;^) range from (+1) to -1/2 according to whether the

chains are parallel to the symmetry axis,

$ = 0 fH = 1 (2.9)

or perpendicular to the symmetry axis,

4> = | f„ = -1/2 (2 .10)

or characterized by isotropy,

— n 1cos-0 = - fH = o (2 .11)


3 2

For a crystalline polymer, the angles ^ between the

crystallographic j axis and the fiber axis suggest the

distribution functions f:^) between the crystallographic

axes and the symmetry axis may be defined as in Figure 2.4.

In 1958, the Hermans orientation factor was generalized by

Stein (159) to represent the orientation of crystallographic

axes :

3 cos2! - 1fj = -----J----- (2.12)

where j represents the a, b, c crystallographic axes.

The cos'^ are not independent, but are tied together

through trigonometric relationships. For an orthorhombic

unit cell such as polyethylene, we may use the Pythagorean

theorem:

cos + cos1 <f>b + cos1 = i (2.13a)

f a + f b + f c = 0 (2.13b)


3 3

Figure 2.4

1

Stein coordinate system and definitions for specifying orientation modes of crystallographic axes.


3 4

In multiphase polymer blend systems, orientation

distribution functions and orientation factors f: need to be

defined for each individual phase.

Initial attempts at quantitative characterization of

chopped fiber orientation in composites dates to the late

1960s (62) . Schierding ((53) , and Kitao and his coworkers

(64) proposed that if highly oriented crystalline fibers are

used, wide angle x-ray diffraction may be applied to

determine fiber orientation. Schierding (63) used ceramic

fibers. Kitao, et al. (64), investigated melt spun

polystyrene filaments containing chopped carbon fibers.

Subsequently, there have been numerous qualitative studies

of chopped fiber orientation using soft x-rays (65-613) .

Menendes and White (69) used WAXD to determine uniaxial

orientation of aramid fibers in polymethyl methacrylate

(PMMA) .

In 1971, Broady and Ward (142) proposed a theoretical

model for a short fiber reinforced composite. They gave

more explicit discussion of uniaxial orientation of glass

and carbon fibers in terms of Herman's orientation factors.

They introduced second order elastic constants to the

composite. They concluded that a fourth-order description


can predict the effect of orientation on mechanical

properties.

i.e.

(2 .2 1 )

where ^ is stress, sKi is strain, ci:ki is a fourth-order

stiffness constant.

2.3.3 Representation of Biaxial Orientation

In 1958 Stein (159) introduced an analytical

representation for biaxial orientation using Euler's angle

This was later greatly extended by Nomura, Kawai et al.

(160-162). White and Spruiell (163) subsequently proposed

orientation factors based on the angles and ^ system in

1981:

fa. = 2 cos20, + cos-0; _ 1 (2.14a)

fB2 = 2 cos” 0, + cos” 0| _ 1 (2.14b)


3 6

where is the angle between the 1 laboratory axes (1 =

flow direction) and the polymer chain axis; 2 is the angle

between the 2 laboratory axis (2 = transverse direction) and

the polymer chain axis. The angles ‘ft and ^ are not

independent of each other but are restricted by the

Pythagorean theorem. Equations (2.14a), and (2.14b) are

symmetric with regard to angles ‘K and ■ The and 2

angles have the advantage over the Euler's angles of Stein,

Nomura and Kawai in being symmetric. They yield a symmetric

set of orientation factors. The orientation factors based

on angles and ^ are much more readily interpretable than

those based on Euler's angles and (159, 160-162). It

may be seen from Equations (2.14a) and (2.14b) that for

uniaxial orientation in the 1 direction,

i = 0, ^ = f : fiB = 1 f2S = 0 (2.15)

and in the 2 direction,


♦l = f , *2 = 03 7

fLa = o f23 = 1 (2.16)

For uniaxial orientation in the 3 direction,

For random orientation,

cos2<0, = cos2 , = I : f,a = f,3 = o (2.18)

The characteristics of fiB and f2B suggest representations in

an isosceles triangle of the type shown in Figure 2.5.

These were subsequently applied to characterize biaxiaiiy

stretched films (164-172) and blow molded bottles (166,

173) .

The previous representation of orientation may be

generalized for crystalline polymers to represent all three

crystallographic axes (157). They may be readily obtained

from Equations (2.14a) and (2.14b) by introducing angles

between appropriate crystallographic axes and the laboratory

axes. We may write


3 8

fsL , = 2 cos2^ + cos:0Lj - i (2.19a)

fB2>] = 2 cos2^ + cos2 j - i (2.19b)

For an orthorhombic unit cell, the cos'0tJ and cos‘ ,j are

related by the Pythagorean theorem.

cos20Ia + cos20lb + cos2^lc = i (2 .20a)

cos2 <f>2i + cos20:b + cos2 <p2C = 1 (2 .20b)

White and Knutsson (148) have discussed fiber

orientation in terms of two orthogonal axes and biaxial

orientation factors.

In 1987, Monge, Vincent and Haudin(797 investigated

orientation of mica and talc platelets in injection molded

polyamide composites by WAXD. Qualitatively, they showed

that the normals to the platelets are nearly perpendicular

to the plane of the molded plaque in the core, and parallel

to it in the skin.


3 9

U niaxial (Flow Direction)

Planar(Film Surface)Planar(Flow Direction and

Perpendicular to the Surface) E q u a l B iaxial

-0.5

U niax ial (Transverse Direction)-0.5Iso tro p ic

(-1 .-1)

Figure 2.5 White and Spruiell orientation triangle


4 0

They suggested that these orientations are related to the

shear and elongation rate distribution in the thickness of

the molding.

Subsequently, particle orientation was characterized in

terms of biaxial orientation factors by Lim and White (7 0,

71, 80, 81) , and Suh and White (82-8_5) . Lim and White (71,

81) described the variation of aramid fibers, talc and mica

particles in fabricated thermoplastic parts. They showed

that the particle orientation at the core of injection

molded parts was lower than in the wall region.

In 1987 Advani and Tucker (174) developed a formulation

similar to orientation factors to represent orientation in

fiber filled thermoplastics. They showed planar orientation

states which is biaxial orientation using fourth planar

orientation tensors. They concluded a fourth-order

description can predict the effect of orientation on

mechanical properties more accurately than second-order

description. They subsequently extended this to derive

equations of change for the fourth order tensors to predict

the orientation of fibers by flow,

i.e.


<V = l*v'M)p.p,PtPid,i>

4 1

(2 .22 )

where anu is a fourth-order orientation tensor depending on

angle ^ and $. V is the probability distribution function

for orientation. The component p is fiber unit vector

related to & and 0. However, their work was only true for

dilute systems, where the fibers are far enough apart that

they do not interact.

2.3.4 Representation of Mixed Particle Orientation

When two different type of particles are compounded

together the interactions of each particle's varying size,

shape, and particle-particle interaction can exist and may

affect the character of the orientation.

There have been many studies of orientation in

compounds of single particles (62-69, 158, 159, 175).

Particle orientation in mixed particle systems has only been

studied by Lim and White (72., 80) . The particles they used

(71, 80) for mixed particle systems were fibrous aramid

(Dupont KevlarR) and disc-like particles such as talc, and


4 2

mica. They found that when fiber and disc-shaped

anisotropic particles are mixed in a polymer matrix the

degree of orientation of each particle was reduced compared

to the state of orientation in the pure particle filled

systems.

2.4 Characterization by Using X-ray Diffraction

2.4.1 Introduction

Rontgen, the German physicist, discovered x-rays in

18 95. In German they are called Rontgen rays (Rontgen

Strahlung or Rontgen). In English they are called x-rays.

When x-rays are incident upon an object, the diffracted

rays are distributed in all directions in space, centered

upon the object. If the orientation of the object with

respect to the incident x-rays is changed, a different

diffraction pattern results, depending upon the object's

internal structure. The object of all x-ray diffraction

investigations is to find one or more of the following three

essential quantities. First, the Bragg angle direction (in

terms of 2®) in which the scattered x-rays are diffracted


4 3

(see Figure 2.6). Second, the features of the diffraction

pattern (whether sharp or broad spots, lines, or arcs, or

broad halos (see Figure 2.7)). Third, the intensity of the

diffraction in the various directions (in the case of a

continuous pattern, the intensity distribution within the

pattern). The importance of these quantities, and the

precision with which they must be determined, will depend on

the objective of the analysis (17 6).

2.4.2 Quantitative Analysis of Particle Filled

Compounds

For a mixed particle system, Hull (177) and others have

pointed cut that each component in a mixture exhibits the

characteristic scattering and absorption intensities of its

corporates proportional to the amount material present in

1919. In 1936 the first quantitative analysis was carried

out by Clark and Reynolds (178) , for mine-dust. Gross and

Martin (179) developed an internal-standard method for

analysis of quartz in mixtures containing sodium chloride.


4 4

sample

solar slitsolar slit ^ receiving slitdivergence j

s lit 'scatterslit

x-ray tube counter tube

Figure 2.6 Schematic representation of x-raydiffractometer.


4 5

X-Ray

Figure 2.7 WAXD flat film pattern.


4 6

Around the same time Taylor (180) and Brindley (181) showed

when the crystal size is large, it absorbs the incident x-

rays and emits lesser quantities. This is called

microabsorption and is associated with crystal size. The

mathematical relationship between the scattered beam

intensity and absorptive properties of a sample has been

discussed by Alexander and Klug (182) in 1948. Alexander

and Klug (182) represented diffraction from a flat specimen

in 1948. Their representation can be used for the analysis

of a binary mixture (single particle) system.

In 1955 Clark and Terford (183) sought to characterize

the amorphous phase in wood pulps quantitatively, using x-

ray intensities. They produced amorphous cellulose by

mechanical degradation of fibers in a vibratory ball mill

and obtained an amorphous halo intensity from x-ray

measurements. They also obtained crystalline peak from the

(002) plane of cellulose. They then determined the

crystalline portion of wood pulps from the ratio of

crystalline to the total (including crystalline) intensity.

Lennox (184) presented an 'Internal Standard Method'

analysis of a two-particle mixture system, in 1957. In 1958

Copeland and Bragg (185) presented a quantitative x-ray


4 7

analysis to determine the amount of calcium hydroxide in the

presence of hydrated calcium silicates. They used magnesium

hydroxide as the internal standard. In 1959 Copeland et al.

(186) presented a quantitative x-ray analysis of four phases

of Portland cement by using x-ray peak areas. Jahanbagloo

(187) described a film technique which had restrictions for

mixtures containing amorphous phases in 1968. Following

these investigations there have been few researches on the

quantitative analysis of mixed particle systems. There

seems to be no subsequent quantitative analyses for the x-

ray intensities of crystalline particles suspended in

amorphous media.

Menendez and White (69) sought to characterize

composites using x-ray intensity on chopped aramid fibers to

measure uniaxial orientation of the fibers. They had great

concern for fiber peaks' interferences with the amorphous

halo of the polymer matrix. Uniaxial orientation factors

were reported. More recent studies of this type have been

reported by Lim and White (7£, 11) using aramid, talc and

mica and Suh and White (£2-85) using talc. The latter

authors (70, 71, £2-£5) determined biaxial orientation

systems of the suspended particles.


4 8

2.4.3 Wide Angle X-ray Flat Film Technique

The flat film x-ray photographic technique has been

widely used in the study of the state of orientation for

crystalline fibers. This method has been reviewed by

Alexander (189), Kakudo and Kasai (176) , Klug and Alexander

(189), and Samuels (190), among others.

Figures 2.7 and 2.8 show the geometry of diffraction by

specimens using a transmission camera. A is the collimator,

a device used to produce a narrow incident beam made up of

rays as nearly parallel as possible. It usually consists of

two pinholes in line, one in each of two lead disks set into

the light-tight film holder, or cassette, made of frame, a

removable metal back and the paper. B is the beam stop,

designed to prevent the transmitted beam from striking the

film and causing excessive blackening. X-rays are

diffracted from a specific crystallographic(hkl) plane

according to Bragg's law:

^ = 2 dhki s in ®hki (2.23)


4 9

I Meridian

Film

-- \ :quator

Figure 2.8 Schematic perspective of diffraction byspecimens using wide angle x-ray beam.


5 0

where ^ is the wavelength of the x-ray, dh)ci the interplanar

spacing, and 0hki Bragg's angle.

The Bragg angle 0 corresponding to any transmission

spot is found very simply from the relation

tan 20 = ^ (2.24)

where r = distance of spot from center of film (point of

incident of transmitted beam) and D = specimen-to-film

distance.

The optimum thickness 'tm' of the specimen which will

produce the maximum intensity of diffracted beam is found to

be (181) [compare(188, 18 9) ]

1t» = - (2.25)M

where M- is the linear absorption coefficient of the specimen

for the x-ray wavelength used.


5 1

2.4.4 Wide Angle X-ray Pole Figure Technique

Pole figures are stereographic projections of the

diffracted intensities of normals of crystallographic planes

(see Figure 2.9) . Weber (191) introduced the single-crystal

stereographic projection referred to as a pole figure, in

1924. Earlier pole figure analyses were used for metal work

such as Decker, Asp, and Harker (193). Later, Sisson (192)

first applied this to polymers. He exhibited qualitative

classification of the orientation modes observed in

crystalline cellulose forms, in 1936. Later Sisson's pole

figure efforts were modified and extended by Heffelfinger

and Burton (194) in 1960, and subsequently by Wilchinsky

(199-201) in the early 1960s. They were determined in the

reflection mode. The pole figure method (163, 188, 195,

196) is a convenient technique to describe and represent the

degree of preferred orientation of the crystallites in

fabricated specimens as the stereographic projection

procedure. A pole is the point of intersection of the

normal to a crystal plane with the surface of a sphere

having the crystal at its center.


5 2

Figure 2.9 3-Dimensional expression of the sphericalprojection of a crystal


5 3

If the radius of the sphere is r* = l/d(hkl), the pole

coincides with the reciprocal lattice point density

distribution.

Pole figures can be obtained from the diffraction

intensities measured during a rotating specimen at a fixed

angle, 2®, by using x-ray diffractometer. Figure 2.6 is a

schematic representation of an x-ray diffractometer. Figure

2.10 shows the angles (a , longitude, P, latitude and ^ co

latitude) where the specimen is rotated when measuring the

diffraction intensities. Using this intensity distribution,

I ( , P), the value of the mean square cosines can be

calculated averaging over the entire surface of the

orientation sphere as follows:

The pole figure technique has been applied to oriented

synthetic polymers by Heffelfinger and Burton (194),

Wilchinsky (199-201), Desper (195), Choi, Spruiell, and

cos <f>m , (2.26)


5 4

3

Figure 2.10 Angular coordinates used for obtaining a polefigure


5 5

White (165), Shimamura, Spruiell and White (167), Cakmak,

White and Spruiell (169), Maemura and Cakmak (170) , Kang and

White (171, 172) and to the orientation of anisotropic

fillers in polymer matrices by Lim and White (70, 71, 80,

81) , Suh and White (82-8J3) Morales and J. R. White (197) ,

Chen, Finet, Liddell, Thomson, and J. R. White (198) .

Wilchinsky (199-201) developed the analyses for

specifying orientation modes in crystalline materials

especially to calculate values of the mean square cosines

relative to specified axes from pole figures. This method

can be applicable to all crystal systems, including non-

orthogonal crystal systems. His generalized model is where

“1" is the reference direction and a, b, and c are the

crystallographic axes and U, V, c are Cartesian coordinate

axes. From this model, he proposed the generalized equation

cos2 hki.i = e2 cos2 0!U + f2 COS2 IV + g ~ COS2 (f>|c

+ 2 e f COS 01LI -COS0|V

+ 2 f g COS <PXW -COS<f)w

+ 2 e g COS <f)w -COS UJ

(2.27)


5 6

where e, f and g are the direction cosines of (hkl) plane

normal direction with regard to the axes U, V and c

respectively. In general, cos'^, cos' iv, and cos'f; are

determined from five reflections of cos^i.i- On the right-

handed side of Equation (2.27), one or more terms may

cancel, depending on the type of macro- and microsymmetry of

the material (188, 200).

2.5 Scanning Electron Microscopy (SEM)

The SEM is a versatile and powerful machine and

consequently a major tool in research technology (202) . The

basic components of the SEM are the lens system, electron

gun, electron collector, visual and recording cathode ray

tube (CRT's), and the electrons associated with them.

Figure 2.11 shows a basic schematic diagram of the SEM and

Figure 2.12 shows the basic contrast mechanism of SEM.

Development of the scanning microscope was described by

Busch (203) who studied the trajectories of charged

particles in axially-symmetric electric and magnetic fields

in 1926. Busch (203) showed that such fields could act as


5 7

electron lenses and thus laid the foundations of geometrical

electron optics. Following this discovery the idea of an

electron microscope began to take shape. The earliest

recognized work describing the concept of a scanning

electron microscope is that of Knoll (204) who was working

at the Technische Hochschule in Berlin, Germany. In 1942

the first SEM used to examine thick specimens was described

by Zworykin et al.(205). They recognized that second-

electron emission would be responsible for topographic

contrast and the secondary-electron collected on it. A

resolution of 11% was attained. In 195 6 Smith (206)

inserted a stigmator (a part of an objective lens that

focuses the image) into the SEM. The first successful

commercial packaging of these components was offered in 1965

from the Cambridge Scientific Instruments Mark I as

"Stereoscan". Subsequently, there were many improvements

such as cathode parts, x-ray detectors (attached to an

electron probe microanalyzer) (207), coupled to a computer

to provide a digital signal, etc. resulting in improved

bright contrast, focus, and resolution.


5 8

Electron gunCathod ray tube (CRT)

1st condenser lens

Stigmator

Scanning coils

Beam deflection system2nd condenser lens

Signal amplifier

Electron detector and scintillation counter

Secondary electronsSample

Figure 2.11 Schematic diagram of scanning electronmicroscope (SEM)


5 9

Induced currents

Primary electrons

Elastically scattered primariesCharacteristicx-rays

Low energy secondariesCathodoluminescence

Specimen

VTransmitted primaries

Induced voltages

Figure 2.12 Contrast mechanisms of scanning electronmicroscope (SEM)


6 0

Today, the very best modern SEMs have magnification in

the nanometer range and are thus directly comparable in

their performance with Transmission Electron Microscopes

(TEM) in many situations. The SEM has the added advantage

that the specimen need not be made thin enough to transmit

electrons.

2.6 Modeling of the Flow of Particle Filled Compounds

2.6.1. Phenomenological Constitutive Equations

for Dilute Suspensions of Anisotropic

Particles

A 3-dimensional phenomenological anisotropic

rheological model to represent the flow of anisotropic

particles was first developed by Ericksen (208-213),and

subsequently by Hand (215) and Green (216-218) in 1960-5.

This formulation obviously also derives out of Jeffery's

theory for ellipsoids. Ericksen expressed the stress field

for a suspension of anisotropic particles as

= -pi + F[d,n] (2.35)


6 1

where d is the deformation rate tensor and n. is a unit

vector indicating the preferred direction of anisotropic

particles. He suggested the simplest properly invariant

theory of anisotropic fluids using the form

cr = -pI + alN + a2d + a3d2 + a4 (Nd + cjjj) +a5 (Nd2 +d2N)

(2.36)

where N = nn and the a 's are polynomials in the invariants,

tr N, tr Nd, tr Nd2, tr d2 and tr d3. As a simplification,

he linearized the stress field with respect to the rate of

deformation so that Equation (2.36) reduced to

= -pi + 2Hd + [ai + a;tr (Nd) ]N + a3 (Nd + dN)

(2.37)

where ai, a2, a3 are constants. This was supplemented by a

second equation which governed the time and deformation rate

variation of n. He showed that the term aiN gave rise to a

yield value.


6 2

Subsequently, Hand devised a theory of anisotropic

fluids using Rivlin's (219) general expression for 3 x 3

symmetric matrix expressed as a polynomial in two other

symmetric 3 x 3 matrices with coefficients which were

polynomials in the elements of the invariants of two

matrices.

= -pi + PiN + P2d + P3N2 + P4d2 + P5(Nd + dN)

+ P€(N2d + dN2) + P7(Nd2 + d3N) + P8 (N2d2 + dV)(2.38)

where P's are polynomials in the invariants, tr N, tr N~, tr

N3, tr d, tr d~, tr d\ tr Nd, tr N‘d, tr Nd“, and tr N'd'.

He simplified Equation (2.38) by stipulating that the stress

field was linear in the rate of deformation.

= -pi + 2Tld + [Pi + P2 (tr Nd) + P3(tr N2d) ]N

+ P4 (Nd + dN) + P5(N2d + dN2)(2.39)


6 3

His formulation in the form of Equation (2.38) includes

Ericksen's theory as a special case.

2.6.2 Isotropic Compounds with Yield Values

The simplest of plastic viscous fluid models is Bingham

plastic where the shear stress is given by

y = 0 or <r = Gj (<* < Y)

cf = Y + tib y (CT > y ) (2.40)

This equation is first given by Schwedoff (220) and

later in approximate form by Bingham (221). It was restated

correctly by Buckingham as Equation (2.40).

In 1890 Schwedoff (220) developed a theory of plastic

linear viscoelastic fluids of which Equation (2.40) was a

special case.

Scott (111) in 1931 proposed to represent the shear

flow properties of particle filled rubber compounds.

n

a = Y + K y (2.41)


6 4

He applied it to analyze flow in compressional rheometer.

The characteristics of the flows are similar to those of the

Bingham plastic and involve solid plugs at the center of the

cross section.

A 3-dimensional theory of the rheological properties of

particles filled fluid including the existence of yield

values was developed by Hohenemser and Prager (223) in 1932

to represent strain hardening of metals. They introduced

the use of invariants into the theory of non-Newtonian

fluids. Their paper builds on the von Mises theory of

plastic yielding. The von Mises yield criterion is based

upon the theory of invariants. The von Mises yield

criterion for isotropic materials is

tr T‘ = 2 Y‘ (2.42)

where T is the deviatoric stress tensor and Y is the shear

yield stress of isotropic materials. The von Mises yield

criterion is equivalent to a critical distortional strain

energy which is equivalent to Equation (2.42)


6 5

(Tn-Tzz)2 + (T2;-T33)2 + (T33-Tu )2 + 6 (T^+'T^+'r^) = 6Y2

( 2 . 4 3 )

Below a stress field magnitude defined by Equation

(2.42), there is no flow. At high stresses they wrote

G = \ (tr a ) I + T (2.44!

T = , -J£ — T+2 nB d (2.45!

T is the deviatoric stress tensor and trT' its second

invariant.

Oldroyd (227) redeveloped Equation (2.45) to apply to

fluid media in 1947. He further showed that

(VtrT2 - V2y| =4^2trd: (2.4 6)

He noted that Equation (2.45) was equivalent to


Oldroyd (228) later generalized Equation (2.45) to non-

Newtonian fluids by expressing nB as a function of trd“.

Slibar and Pasley (229) modified Equation (2.47) to

include thixotropy in a paper published in 1964. They did

this by representing the yield value Y as a function of trd2

and time.

Plastic viscous fluid models are unable to represent

the behavior of particle filled systems with their inherent

complex memories. The first effort to develop a three-

dimensional form of a plastic viscoelastic fluid beyond

yield surface was by Hohenemser and Prager (223) who

suggested models with Voigt and Maxwellian behavior. The

problem was reconsidered by White (230) in 197 9 who wrote

T = —f==^L= T + H (2.48)V2 tr T2

where H is a general memory function. The matrix is

viscoelastic in character. Equation (2.46) was shown to be

equivalent to


6 7

T = —j = = = H + H V2 tr H- ( 2 . 4 9 )

The viscoelastic contribution is specified by H.A specific simple form for H was proposed by White(231)

for the purpose of illustrating the characteristics of

Equation (2.49). Particular detailed forms of H were

subsequently used by White and Tanaka (232) and White and

Lobe (233) to compare with the experimental data on filled

thermoplastics and elastomers. White and Tanaka (232)

represented H as a single integral constitutive equation

with a Maxwellian relaxation modulus function.

These authors suggested that M-(t) to a first approximate

could be expressed as

(2.50)

(2.51)


6 8

where £($) is a factor that depends upon volume loading and

c~l is a Finger deformation tensor (see Equation (2.72).

This theory was compared to experiments on particle filled

polymer melts.

More recently Suetsugu and White (133), and Montes and

White (234, 235) presented models similar to this in which H

depends on time.

2.6.3 Anisotropic Formulation

The plastic yielding of isotropic materials depends

only upon the magnitudes of the applied stresses and not

upon their directions. Von Mises (236) suggested that

yielding occurs when the second invariant of the deviatoric

stress tensor reaches a critical value. We may express his

yield criterion in the form Equation (2.42)

In 1928, von Mises (237) developed a generalized

anisotropic yield criterion for crystals as:

f(<*ij) = -j[ ki (<*22 - CT33)2 + k2 (<*33 - CTu ) 2 + k3 (<*u " <*22 T ]

- <*23 [ k.j (<*n - <*22) + k5 (<*11 - <*33) ]


6 9

- CT13 [ k€ (°zz - CT33) + k- (<*22 - G li) ]

— <*12 [ ka (<*33 ~ <*Ll) + kg (<*33 ~ <*22) ]

+ kio <*23 CT13+ k n <*L3 <*:2 + ki2 <*12 <*23

+ \ (ki3 <*‘23 + k:4 <*‘13 + k:5 G ":z)

(2.52)

f (ai:) = Const. (2.53)

where ki is the anisotropic yield criterion constants. In

the case of isotropy, Equation (2.59) reduces to the

isotropic von Mises yield criterion of Equation (2.42).

Subsequently, the problem of anisotropic materials

exhibiting plastic yielding has been also considered by Hill

(238, 239, 224) who re-expressed the anisotropic yield

criterion as

f(CTij) = F (a 22 - CT33)2 + G(<*33 - CTu ) 2 + K(<*u - CT22)2

+ 2L<*223 + 2Mcy2i3 + 2N<*212 = 1

(2.54)


7 0

F, G, K, L, M, N are six constants characteristic of the

current state of anisotropy. If Yu, Y22, Y33 are the tensile

yield stresses in the principal anisotropic directions, it

is seen that

G = K = r2 1 K + F = F + G = Y£

(2.55)

If Yu, Y23, Yi3 are the shear yield stresses with respect to

the principal axes of anisotropy, then

2N = tr, 12 2L = 1Y-,2- '

12M = -r13

(2.56)

If there is rotational symmetry about the 2-axis, then

F = K * G

L = N * M

N = F + 2K (2.57)

For complete spherical symmetry or isotropy,


7 1

F = G = K

L = M = N = 3F ( 2 . 5 8 )

In this case Equation (2.54) is then identical with the

isotropic von Mises yield criterion of Equation (2.42) when

2F is equal to 1/Y2.

This anisotropic formulation was extended to the

interpretation of the flow of particle suspensions by White

and Suh (240). Using Hill's simplified anisotropic yield

criterion with rotational symmetry about one axes,

subsequently, they presented a phenomenological theory of

flow of oriented disc-like fluids to represent this

behavior, in Cartesian coordinates. This theory represents

the relationship between stress and deformation rate through

the fourth order relaxation modulus tensor of anisotropic

linear viscoelastic materials as later described in Equation

(2.59).

T = Y + ds (2.59)


7 2

The relaxation modulus function, Gijicm(t) has 3 or 81

independent components. If we note the symmetry of the

stress and the deformation rate di; tensors, it follows

that

G i ] i o i i ( t ) G j j . ] a a ( t ) — G i:jml c ( t ) G - j l mj c ( t ) (2.60)

This restriction reduces Gijian(t) from 81 to 36 independent

components. For elastic materials, Love (241) and Green and

Zerna (242) have argued that the existence of a strain

energy function requires that

G 1] ) o n ( t ) — G i a n i : ( t ) (2.61)

This reduces the 36 components to 21 constants. We may

write the expression for Gi^ in the form of a symmetric

6 x 6 matrix.

G..

G n u G U 2 2 G 1133 G m 3 G 111 3 G 1112

G 1122 G 2222 G 2233 G 2223 G 2213 G 2212

G 1133 G 2233 G 3333 G 3 323 G 3 313 G 3312

G 1123 G 2223 G 3323 G 2323 G 2313 G 2312

G 1113 G 2213 G 3313 G 2313 G 1313 G 1312

,G 1112 G 2212 G 3312 G 2312 G 1312 G 1212

(2.62)


7 3

Figure

(3 )

(1)

(2)

2.13 Flow direction coordinates in Cartesian geometry.


Further simplification of the G^^tt) requires

considerations of rotational (transversely isotropic)

symmetry.

There has been substantial discussion given in the

literature to the mechanics of materials with rotational

symmetry about one direction (241-243). We take this

direction to be the '2' direction where 1, 2, and 3

represents flow, transverse, and flow direction,

respectively, in Cartesian geometry (see Figure 2.13). The

yield surface of Hill's deviatoric yield criterion leads to

f(T13) = F (Til - T:2)2 + G (T22 - T33)2 + K (T1: - T3b)2

+ 2LT2u + 2MT'u + 2NT“23 = 1

(2.63)

Equation (2.63) represents the symmetric anisotropic yield

criterion involving six constants. Symmetry about the '2'

axis requires the 21 independent moduli of Equation (2.63)

to reduce to 5 relaxation moduli. Specifically,

G3333 (t ) = G u u (t )

G3322 (t ) = Gi 122 (t )


7 5

G3232 ( t ) — Gi212 ( t)

Gllka(t) (k * m) = 0

Gi kk (t) (i * j * k) = 0

GiJkn(t) (i *j ) * (k * m) = 0

1Gi313 (t ) — 2 [Gim(t) - Gl123 (t ) ]

(2.64)

There are then 5 independent relaxation modulus functions,

Gmi (t) , G1122 (t ) , G1133 (t) , G2222 (t) , G1212 (t) . In linear

viscoelasticity we may write each of these moduli in an

expansion such as

- I G eijicm %10

and all the moduli Gi3tal(t) and relaxation times T,:tal for the

5 relaxation modulus functions are independent.

The six independent stress components of the three

dimensional generalization of Boltzmann superposition stress

are according to White and Suh (240) from Equation (2.59)


Ti2 = Y12 + 2 £ GlJ12(t - s)d12(s) ds7 6

T32 = Y32 + 2 G1212(t - s) d12(s) ds

T13 = Yi3 + 2 Gl3l3(t - s)d13(s) ds

= Y13 + - s) “ GU3j(t - s)]d,3(s) ds

T u = Y l1

+ J ^ [ G i m (t - s ) d , , ( s ) + G II22(t - s ) d „ ( s ) + G u33(t - s ) d 33(s)] ds

T22 = Y22

+ ^ [ G n a C t - s J d n C s J + G a j j O - s J d n C s J + G n n C t- s J d j jC s jJ d s

T33 = Y33

+ <£<D[ G II33(t — s) d , , ( s ) + G , | „ ( t - s) d „ ( s ) + G , m (t - s) d 33(s)] ds

(2 . 66 . a, b, c, d, e, f)

White and Suh (240) also suggested a 3-dimensional non

linear transversely isotropic plastic viscoelastic model.

They expressed the deviatoric stress tensor in the form


7 7

T = Y + H (2 . 67)

To obtain H, they generalize the basic formulation of

Equation (2.59). They put this equation into a formulation

using a deformation tensor. To do this, they introduce the

tensor relaxation function ^(t) defined by

<*>(t) = - T “ G(t) (2.68)dt

°i:i®(t) = - ~ G,:ta,(t) (2.69)dt

Sc Equation (2.59) can be rewritten as

= Y + jjty t - s) • e( s) ds (2 . 7 0 ]

where e is the infinitesimal strain tensor (241, 242)

1 du ^-(— - + -— ) of linear elasticity and ^-^(t) may be seen to2 dx, dx.

be


7 8

<D13 tan (t) = £ Titan.a e X:<=..' i3taa,s

(2.71J

For large strains and deformation rates one must expect that

e13 will need to be replaced by a suitable large strain

deformation measure. They suggested the Finger deformation

tensor c,.-,"1 (231, 232) where

, dx1 dx1Cij = -=^ (2.72)dx dx

(t) will become some rru:te (t, deformation) . This leads to

in place of Equation (2.70)

= Y + jj11 “ ' c~l(s) ds

= Y + £ m13kn(t - s) c^ts) ds (2.73)


7 9

This is of course a non-unique generalization of the earlier

linear theory. It is one of the finite infinity of proper

non-linear formulations. It further has the restriction

that tr T is zero.

If we accept the symmetries of Equation (2.64) for

itiijioa, the formulation leading to Equation (2.50) gives the

stress components

ds

ds

ds

Tu = Yu

+ j^JmnnCt - s ) c u''(s) + m ll22(t - s ) c I2’l (s) + rni m (t - s ) c 33''(s)j ds

T22 — Y22

+ £ J m 1I22(t - s ) c n''(s) + 1TI2222 (t - s ) c „ ' ( s ) + m ll22(t - ds


T33 = y 33

+ L [ m H33(t-

8 0

11 (s) + m u22( . t - s ) c22 (s) + m,|11(t — s)c33 (s)| ds

(2 . 74 . a, b, c, d, e, f)


C H A P T E R I I I

EXPERIMENTAL

3.1 General

In the experimental studies of this dissertation we

broadly investigate rheological properties, processing, and

x-ray characterization of compounds containing anisotropic

particles and mixtures of anisotropic particles with

isotropic particles.

81


3.2 Experimental8 2

3.2.1 Materials

This Dissertation involves the investigation of two

families of systems. One of these is based upon

polystyrenes with talc particles and mica particles . The

other system, based upon a polypropylene system, is part of

a program by the IUPAC Working Party 4.2.1.

The materials for the polystyrene system are summarized

in Table 3.1. The materials for the IUPAC polystyrene

system are contained in Table 3.2.

3.2.1.1 Particles

3.2.1.1.1 Talcs

Two types of talc particles were used in this

dissertation. For the polystyrene system the talc particles

used were Ultra talc 609 supplied by Specialty Minerals Inc.

The particle size reported by Specialty Minerals were based

upon the BET nitrogen adsorption method and presumption the


8 3

particles are spheres. We measured the thickness and

diameters of the talc particles using scanning electron

microscopy (SEM) (Hitach S-2150). SEM photographs of talc

are shown in Figure 3.1.

Specialty Minerals supplied an average diameter of talc

particles based upon BET measurements. This diameter

presumes, as mentioned above, that the particles are spheres

Specifically it presumes:

where dp is the particle diameter. The value of dp was

0 . 8 m .

As talc particles are actually discs, the value of AS£r

should be:

(3.1)

rA Bet ~ N • 2 - (3.2)v


Figure 3.1 SEM photograph of Talc particles


8 5

Table 3.1 Characteristics of materials and supplier for Polystyrene system

Materials SupplierParticle Size &

BET surface area

Aspect RatioMajor Usage

Polystyrene (Polystyrene

1 0 1 )

Talc 1 (Ultra talc

609)

Mica (280

Cosmetic mica)

Calcite 1 (Albaglos SF

Dry)

NOVACOR

Specialty Minerals

Inc.

Whittaker, Clark & Daniels,

Inc.

Specialty Minerals

Inc.

MI = 2.2

D= 1.2 4 Pm 4=0.08 Pm

BET=16.5 m'/g

D=4 5 Pm H=2.2 Pm BET=3 m;/g

0.8 Pm BET=7 m;/g

Amorphous

= 15 : I

20 : 1

= 20 : 1

= 1 : 1

Medical Molding Truck wall housewares

Sheet glaring Co-extrusion Improve heat

resistance with tensile,

compressive propert res

e>:, autcir.c t ; ve appliances, food

packing Mechanical improvement .

Elect: r icai, heat insulation

e:<; ??, ?37 , PETappliances housings, phenolics,■?CO" ’.*9?thermosets

Improve impact s extrusion properties e x ) PVC


8 6

Table 3.2 Characteristics of materials and supplier forIUPAC 4.2.1 Working Party Polypropylene Project

Materials SupplierParticle Size

&BET surface

area

Aspect Ratio

Polypropyl Solvay Crystallineene

(Eltex P)MI = 8.5Talc 2 Barrets 2.5 Mm = 15 : 1

(ABT-2500, Minerals Inc. 11.0-12.5 m V g ~Montana talc, 20 : 1

uncoated)Talc 3 Barrets 2. 5 Pm = 15 : 1

(Polytalc Minerals Inc. 11.0-12.5 m"/g2 62, 20 : 1

Montana talc,coated)

Calcite 2 Specialty 3.5 Pm = 1 : 1(Vicron 15- Minerals Inc. ->3 irT/g

15, uncoated)Calcite 3 Specialty 3. 5 Pm = 1 : 1(Hi-Pflex Minerals Inc. 3 nf/g

100,coated)


8 7

where H is thickness of talc and D is the diameter of disk

like talc. The average sphere diameter of talc particle was

0.8 ^m. By scanning electron microscopy, D/H is 15. This

indicates that H is 0.08Mm and D is 1.24Mm.

In the IUPAC 4.2.1 Working Party Project "Comparative

Rheology & Material Characteristics of Mineral Filled PP",

talc particles were also used. These are talc (ABT-2500,

Barrets Minerals Inc., 2.5^m) and talc (Polytalc 2 62,

Barrets Minerals Inc., 2.5Mm) stearic acid coated. For

these materials, the following was specified. ABT-2500

uncoated talc and Polytalc 262 stearic acid coated talc were

used to compare ( i) the stearic acid effect (ii) particle

shape effect and (iii) the mixed particle effect on

rheological properties .

3 . 2.1.1.2 Mica

Mica particles used in the polystyrene (see Table 3.1).

They were supplied by Whittaker, Clark & Daniels, Inc. The

trade name is 280 Cosmetic Mica.


8 8

The average equivalent particle sphere diameter, the

aspect ratio and particles suppliers are summarized in Table

3.1. SEM photographs of mica are shown in Figure 3.2. The

average diameter of the mica particles was 45Mm and the

thickness/length ratio was 1:20. The thickness was 2.2Mm.

We could not locate smaller mica particles.

3.2.1.1.3 Calcium Carbonates (Calcite)

The calcite particles used in the polystyrene study

were Albaglos SF Dry supplied by Specialty Minerals Inc.

The average sphere particle diameter indicated by the

suppliers of calcite is 0.8M-m.

We characterized the calcite particles using a SEM

(Hitach S-2150). SEM photographs of calcite are shown in

Figure 3.3. The average diameter of the calcite particle

was found to be 0.9Hm.

In the IUPAC 4.2.1 Working Party Polypropylene project

two calcites were used. These were Vicron 15-15 (Specialty


Figure 3.2 SEM photograph of Mica particles


9 0

Figure 3.3 SEM photograph of Calcite particles


9 1

Minerals Inc., nominal size 3. 5Mm) and Hi-Pflex 100

(Specialty Minerals Inc., nominal size 3.5Mm) .

Calcite (Vicron 15-15) uncoated, and calcite (Hi-Pflex

100) stearic acid, coated, were used to compare the stearic

acid effect and particle shape effect and mixed particle

effect on the rheological properties.

Table 3.2 summarizes the characteristics of the

calcites used and the suppliers.

3. 2.1.2 Polymers

3.2.1.2.1 Polystyrene (PS)

The polymer used in this study was a general purpose

polystyrene (PS) supplied by Novacor Co. (see Table 3.1).

The melt flow index of polystyrene is 2.2 and its specific

gravity is 1.04. The reason we chose this PS was that it is

a chemically stable but non-crystallizing polymer.


9 2

3. 2.1.2.2 Polypropylene (PP)


Rheology & Material Characteristics of Mineral Filled PP",

polypropylene Eltex P RV001P supplied by Solvay was used

(see Table 3.2). The melt flow index (MI) of the

polypropylene was 8.5 at 230°C.

Irganox B-225 (Phosphite) and calcium stearate were blended

in small quantities into the polypropylene to stabilize the

PP against oxidative degradation.

3.3 Compounds Prepared

Various volume loading (e.g. PS/talc, PS/calcite

0.95:0.05, 0.90:0.10, 0.80:0.20, 0.60:0.40 each) compounds

were made from low loadings to high loadings to see the

effect of particle concentration and particle shape on the

rheological properties, particle orientation, and packing

during the various types of processing.

Various mixed particle systems based primarily on the

PS/talc/calcite system including 0.90/0.05/0.05,

0.84/0.04/0.12, 0.84/0.10/0.06, 0.78/0.10/0.12,


9 3

0.60/0.20/0.20 volume loadings were studied to investigate

calcite-talc particle interaction on the rheoiogical

properties. Table 3.3 summarizes the compounds

investigated.


Rheology & Material Characteristics of Mineral Filled PP".

PP/talc/ calcite (xl = 6743/1, 0.6/0.2/0.2 wt%) uncoated,

PP/talc (x2, 0.6/0.4) uncoated, PP/talc (x3, 0.6/0.4)

coated, PP/calcite (x4, 0.6/0.4) uncoated, PP/calcite (x5,

0.6/0.4) coated, PP/talc/calcite (x6, 0.6/0.2/0.2) coated

were used to compare the effects of particle interaction,

shape, and interfacial chemistry upon shear viscosity and

yield stress. Table 3.4 summarizes the IUPAC compounds

investigated.


9 4

Table 3.3 PS compounds investigated.

PS/Talc

(vol%)

PS/Calcite

(vo1%)

PS/Talc/Calcite

(vol%)

1 95/05 95/05 90/05/05

2 90/10 90/10 84/04/12

3 80/20 80/20 84/10/06

4 60/40 60/40 78/10/12

5 60/20/20


9 5

Table 3.4 PP compounds investigated for IUPAC.

PP/Talc PP/Calcite PP/Talc/Calcite

(vol%) (vol%) (vo1%)

stearic 75/25 75/25 75/12.5/12.5acid

uncoated (6743/2) (6743/4) (6743/1)

stearic 75/25 75/25 75/12.5/12.5acid

coated (6743/3) (6743/5) (6743/6)


3.4 Compounding9 6

A JSW(Japan Steel Works) TEX-30 modular intermeshing

co-rotating twin screw extruder with three kneading disc

blocks were used to disperse minerals in the polystyrene

matrix. The screw diameter of the extruder is 30 mm and the

length/diameter (L/D) ratio is 32.5. The extrusion

temperature was 200 °C, and a screw speed of 80-100 rpm was

used.

A Werner and Pfleiderer ZSK-40 M32.5 modular

intermeshing co-rotating twin screw extruder was used in the

process laboratories of Werner and Pfleiderer in Ramsey, New

Jersey to disperse minerals in the polypropylene matrix for

the IUPAC 4.2.1 Working Party Project "Comparative Rheologv

& Material Characteristics of Mineral Filled PP". The

temperature of compounding was 210°C. Calcium stearate was

added to all the systems during compounding.


3.5 Rheological Measurements9 7

3.5.1 Steady Shear Flow Measurements

Steady shear flow measurements were carried out using a

capillary rheometer, a cone-plate rheometer, and a sandwich

rheometer. The sandwich rheometer was used in any extreme—0low shear rate region down to 10 (sec.) in order to detect

yield values of particle filled compounds experimentally not

from extrapolation.

3.5.1.1 Sandwich Rheometer

A sandwich rheometer (Figure 3.4) which was originally

developed by Toki and White (127) and later modified by

Osanaiye et al. (115) was used to detect rheological behavior

at low shear stresses and to determine the yield value in

creep experiments.

The samples were prepared using a Wabash compression

molding machine at 200 °C for PS/talc, PS/calcite, and

PS/talc/calcite filled compounds. The polypropylene

compounds were molded at 210°C. The molded samples were cut


9 8

into sheets 1.9 cm wide, 17.8 cm long and 2.5 mm thickness

and then inserted between the stationary plate and moving

plate which possess the same dimensions as the sample.

The sandwich viscometer experiments for the polystyrene

compounds were carried out at 2003C. The IUPAC Working

Party Project polypropylene based samples were characterized

at 210°C.

The instrument was operated in the creep mode. The

moving plate of the sandwich viscometer was pulled

vertically downward by an attached weight. The displacement

of the moving plate was measured by a micrometer dial gauge

that has gratings as small as 0.01 mm.

The instrument was placed in a heating chamber of

dimensions 30x30x7 0 cm. Nitrogen gas was introduced into

the chamber around the sample to prevent the sample's

oxidation degradation.

The shear rate in the sandwich viscometer was

calculated as follows :

• Vr = ~fi (3.3)


9 9

Therm om eter T em peratu re S en so r

Isothermal C ham ber

Stationary S teel P late

Sam ple

i l

O

LN,

Moving Part

D isplacem ent G auge (0.001 mm)

W eight

Figure 3.4 Scheme of modified sandwich rheometer


1 0 0

where V is the constant velocity (mm/sec) of the moving

plate and H is the sample thickness (mm) between moving

plate and stationary plate. The shear stress can be

obtained from

F

where F is applied shear force (i.e. the weight in Kg

multiplied 9.8 m/sec2 to obtain Newton) and A is the surface

area (rtf) of the contacting plate.

3.5.1.2 Cone-Plate Rheometer

A cone-plate mode rotational rheometer (Rheometrics,

RMS-800, Figure 3.5) was also used to measure shear

viscosity. Viscosity measurements were made over a range of

shear rates of 10~2 to 10c sec’1. A plate of 2.5 cm diameter

and cone angle of 0.1 radian was used for the upper part and

same diameter of plane plate was used for the bottom

portion.


1 0 1

Compounded pellets were molded in a compression mold

developed in our laboratory (Figure 3.6). This has the same

cavity geometry as that required in a cone-plate rheometer.

The Wabash compression molding machine was used at 200 'C,

and pressures of 5 MPa for the PS matrix compound system,

and 5 MPa for the PP matrix compound system at 210 3C.

Nitrogen gas was introduced into the chamber around the

cone-plate to prevent oxidation degradation of the sample.

The shear rate in the cone-plate mode is given by (284,

285)

shear stress is determined from the torque, M, and the cone

radius, R (284, 285)

• Qy = — (3.5)a

where ^ is the rotation rate and a is the cone angle. The

3 M (3.6)


1 0 2

A A A A

\J \l V

T ra n sd u c e r

S ta tio n a ry P a rt

S a m p le

Moving P a r t

Figure 3.5 Schematic diagram of cone-plate rheometer


1 0 3

0.1 Radian

25 I mm

Figure 3.6 Schematic diagram of compression mold forRheometrics


3.5.1.3 Capillary Rheometer1 0 4

An Instron capillary rheometer (Instron 3211, Figure

3.7) was used to measure steady state shear viscosity at

high shear rates. This involved a series of dies with

diameter of 1.6 mm and length/diameter ratios of 9.3, 19.3,

and 28.5. Measurements were made at 200 °C for the PS

matrix system and at 210 VC for the PP matrix system. The

viscosity measurements were made over a range of shear rates

of 10° to 102 s'1.

The shear rate at the wall in the capillary rheometer

is given by (284, 285)

Yv = 3w’+ l ' 4 ri

32 Q

kD (3.7)

where Q is the flow rate and n' is

n,= dln(a]2)vd \ n ( 3 2 Q / x D 3)

(3.8)

The total pressure, p T in the capillary rheometer may be

expressed in the form


1 0 5

T ra n sd u c e r

P lu n g er

S a m p le

C apillary Die

Figure 3.7 Schematic diagram of capillary rheometer


1 0 6

P T ~ ^ P d l e ~*~^P&ncrar.ce * ~ ^ P e x .

~ ^ P d i e ~*~^P ends

p r= 4(tj12)w L_

D ' t ' ^ P e n d s

(3.9a)

(3.9b)

where D is the diameter of the capillary, and L the length

of the capillary. Equation (3.9) suggests the Bagley plot

(269) where p r is plotted as a function of L/D and (ai:)w

determined from the slope and ^per.ds from the intercept.

3.5.2 Elongational Flow Measurements

we studied uniaxial extension using a uniaxial

rheometer developed by Yamane and White (283) . It consists

of an isothermal silicone oil bath, a force transducer, and

a take-up system (see Figure 3.8).

Samples were prepared using an Instron capillary

rheometer (Instron 3211) at 200°C for PS matrix system with

the diameter of 1.6 mm and the length/diameter of 28.5 was

used.


1 0 7

Constant extensional strain rate measurements were

made. Extruded samples were placed in the silicone oil bath

between a pair of gears on one end and a force transducer at

the other end. The sample is then pulled by the rotating

gears which move at constant angular velocity. The distance

between the gears and the force transducer is 20 cm.

A 1/15 HP B&B electrical motor with rotor diameter 10.9

cm was used to draw out the sample in the range of 0.36 to

1.62 rpm. A force transducer with a maximum capacity of 400

gmf was used. It was connected to a chart recorder for

readout analysis. The elongational viscosity was determined

as a function of time in a range of elongation rates from

0.0005 to 0.0023 sec"1 which corresponds to 0.36 to 1.62

3m.

The elongation rate is given by

1 dL RQ.

r = 7 * ‘ ~ T (3'10:

where R is roll radius, ^ the angular velocity, and L the

sample length. The elongational stress is obtained through


1 0 8

thermocouple

LVDT

1/thermostatic fluid bath

Figure 3.8 Schematic diagram of silicone oil bathelongational rheometer


1 0 9

cru ( 0 =F {t) F ( t )

A (t) A0exp(/£0

where F is the elongational force, A the cross-sectional

area, A0 the initial cross-sectional area, and t the time.

Measurements at very low stretch rates were made in the

creep mode. For measurements of the yield value, we used

the same sandwich rheometer chamber (Figure 3.9).

Elongational flow yield values were measured in the nitrogen

gas filled chamber(NCM). We measured only yield values.

Samples were clamped on one end and a weight applied on the

other end. We measured the displacement after various

periods up to 2-3 hours. When there was no change in the

displacement reading at low stresses we considered an

elongational yield value to exist. When there was a change

in displacement reading, the sample generally failed by

necking. The stress where these first occurs is the yield

value.


3.5.3 Oscillatory Flow Measurements1 1 0

The complex viscosity was measured using a parallel

plate mode rotational rheometer (Rheometrics, RMS-800,

Figure 3.10) at 210 °C for the PP matrix system.

Measurements were obtained over a range of frequencies of

10"" to 10" rad/sec. The strain amplitude was maintained

constant at 1% for all measurements.

The shear stress for sinusoidal oscillatory flow

experiments has the form

cr12( 0 = G '(a))y sin art + G"(co)y coscot = G 'y sm (c o t + <5) ( 3 . 1 2 )

where Y is the shear strain, G' is the storage modulus, G''

is the loss modulus, G* is the complex modulus, 03 is the

frequency, and 5 is loss angle. The torque M is related to

the shear stress M at the outer radius by

G'(co) = G * cosS = c o s8 n 1 3 ]V I n R *Q I J . I J J


Figure

Thermometer Temperature Sensorn i

Isothermal Chamber

Stationary Clamp

Uniaxial Sample

Moving Clamp

' i !

0Displacement Gauge

(0.001 mm)

Weight

.9 Scheme of elongation rheometer formeasurement yield value


1 1 2

A A A A

V V U

T ra n sd u c e r

S ta tio n ary P a rt

S am p le

Moving P a r t

Figure 3.10 Schematic diagram of parallel platerheometer.


1 1 3

G"(co) = G* s in ^ = a>rj' =2 M H .— 7— siinice

sine) (3.14)

n* = yl(n')2 + (n")2 = -J{G"loo)2 +(n")2 = —CO

(3.15)

The strain Y at the outer radius is

where M is the torque, R is the plate radius, H is the gap

3.6 Processing Studies and Flow Geometries

We have chosen several experimental geometries to

characterize the flow of these particle-filled compounds.

We gave particular attention to particle orientation

distributions through cross-sections of different processing

geometries.

The reason we have chosen these geometries is to see

the orientation and array behavior of the talc and mica

particles.

height, and ^ is the shear angle.


3.6.1 Extrusion Through Dies1 1 4

The primary industrial processing operation studied was

extrusion through dies. We made studies through dies with

circular cross-sections and with rectangular and annular

cross-section. In addition we studied converging flow into

a die entrance.

3.6.1.1 Capillary Die

We investigated talc particle flow using various

different capillary dies with different capillary die

diameters (0.8, 1.6, 2.4, 3.2 mm), and capillary L/D ratios

(9.3, 19.3, 28.5 for the 1.6mm diameter die).

3.6.1.2 Rectangular Dies

Specially fabricated rectangular and slit dies were

attached to an Instron capillary rheometer (Instron 3211) to

obtain extruded sheet samples. The slit die thickness was

1mm, 0.6mm, and 0.3mm, respectively. We investigated the

effect of aspect ratios of the slit dies (1:2, 1:10, 1:20).


1 1 5

3 . 6.1.3 Annular Die

A specially fabricated annular die was attached to the

Instron capillary rheometer to obtain annular die extrusion

samples. The annular die had a length of 35.6 mm, an inner

diameter of 6.1 mm, and an outer diameter of 7.6 mm.

3.6.1. 4 Converging Flow

We observed converging flow from a cylindrical

reservoir (D = 9.5 mm) into a capillary die. An Instron

capillary rheometer (Instron 3211) was used to investigate

flow from reservoir to capillary entrance (45J). The

investigation of talc particles' capillary entrance flow

using SEM was our point of interest.

Special attention was given to die entrance pressure

losses.

3.6.2 Compression Molding

Molding operations were represented by compression

molding. A Wabash hot press (20-1212-2TMB) was used for


1 1 6

preparing compression molded samples. A mold with

dimensions of 15x15 cm was used.

This flow is a squeezing flow.

Table 3.5 summarizes various processing geometries and

condition in PS matrix system.

3.7 X-ray Characterization of Fabricated Parts

3.7.1 Orientation Studies from Wide Angle X-ray

Diffraction (WAXD)

We determined the orientation of talc particles from

various fabricated parts by wide angle x-ray diffraction.

3.7.1.1 WAXD Bragg Angle Scanning

X-ray diffraction Bragg angle(2®) scans of talc and

calcite powders were made using a 12 kW Rigaku Denki x-ray

generator with Ni-filtered Cu-Ka radiation. The operating

voltage and current were 40 kV and 150 mA, respectively. A

reflection technique was used.


1 1 7

Table 3.5 Various processing geometries and condition in PS matrix system

Processing Variables DimensionCapillary die (a) capillary die 45°, 135°

extrusion entrance angles(b) capillary die 0.8, 1.6, 2.4, 3.2

diameter mm(c) capillary L/D 9.3, 19.3, 28.5

ratios D=1.6 mmSheet die (a) slit die area 2.0, 3.9, 1.95 mm'

extrusion (b) aspect ratio of 1:2, 1:10, 1:20slit dies

Annular die Di=6.1 mmextrusion Do=7.6 mm

L=35.6 mmConverging flow Entrance angle

45'Compression 5 MPa

molding 15x15 mm


3 . 7 .1.1.1 Amorphous Halo1 1 8

If a completely crystalline filler is added to an

amorphous polymer system, we can consider filler portion as

the crystalline portion and amorphous polymer as an

amorphous portion. The amorphous intensity of polystyrene

was measured using a Bragg angle scan of talc and calcite.

The relative intensity of the amorphous halo of a

compound represents the concentration of amorphous polymer

itself (182, 183). We may conclude that measuring the

amorphous halo's relative intensity gives the amorphous

content in a binary mixture system. This method is

convenient and simple for the determination of the

crystalline fraction (filler fraction) in amorphous polymers

and does not require correction for the Lorentz-factor,

polarization or incoherent radiation.

In a polymer crystal the distances between bonded atoms

and second nearest neighbors are subject to little

variation, and furthermore the distance of closest approach

of a neighboring chain is a vector distance with a high

probability of occurrence. These modes of quasi-short-range


1 1 9

order are responsible for the interference halos observed in

the diffraction patterns of amorphous polymers.

3. 7.1.1.2 Particle Size

Particle sizes of the mixture components affects the

accuracy of x-ray intensity measurements because of the

microabsorption (or particle-absorption) phenomena (181).

To minimize microabsorption effects, the particle diameter D

should be proper for quantitative x-ray analysis. For fine

(micron) particle samples, using (//D<0.01) is recommended

(181) where M is the linear absorption coefficient.

However, when the particle diameter D' is much less than

optimum size i.e. D' « D, there is an intensity loss (181)

due to the presence of an amorphous surface layer on each

particle. Furthermore, in comparison to a powder-powder

mixture (181), a particle filled polymer matrix system

should have much less free volume. Thus it is considered

that this compounded sample gives more accurate intensity

data than a powder-powder mixture system (181).

When we add crystalline filler into an amorphous

polymer matrix, the intensity of the amorphous halo doesn't


1 2 0

change proportional to the filler content because each

material's density and mass absorption coefficient (182,

183) is different. When we specify the x-ray's polarization

factor, the Lorentz factor and absorption factor (x-ray wave

length, sample thickness and shape), a quantitative analysis

is possible for a flat specimen with known density, weight

(or volume) fraction, and mass absorption coefficient (/*,)

of each material.

3.7.1.2 WAXD Flat Film Measurements

X-ray diffraction patterns were obtained using a

General Electric x-ray XRD-6 generator with a copper target

and N i - P filter (*-=1.54 A) . The operating voltage and

current were 30 kV and 30 mA, respectively. A transmission

technique was used. The film used was Kodak Scientific

Imaging Film Direct Exposure 12.5x12.5 cm.

3. 7.1.3 WAXD Pole Figure Measurements

The degree of particle orientation for each compound

was represented by using the pole figure method. We


1 2 1

determined biaxial orientation factors also using the pole

figure method. The biaxial orientation factors represented

on White and Spruiell orientation triangle (Figure 2.6).

In our investigation, the effect of isotropic particle

on the orientation of anisotropic particles was

investigated. All the measurements on the degree of

orientations were done quantitatively by WAXD method. X-ray

diffraction patterns were obtained using a General Electric

x-ray XRD-6 generator with a copper target and N i - P filter

(^•=1.54 A) . The operating voltage and current were 30 kV

and 30 mA, respectively. A transmission technique was used.

1.6x1.6x1.6 mm cubic size sample was mounted on a goniometer

and rotated $ angle 3 60 degree and X angle 90 degree while

the x-ray was positioned on the sample. Transmitted x-rays

were detected by photon counts/sec unit as a function of

rotation angle ^ and X and recorded in a connected computer.

Plotting was done by using commercial software Surfer. X-

rays (40KV and 150 mA) with CuKa radiation were generated

using a Rigaku x-ray generator.


3.7.1.3.1 Uniaxial Orientation1 2 2

Equation (2.12) was used to characterize uniaxial

orientation of the talc particles. We characterized

uniaxial orientation function fi. We conducted quantitative

orientation studies by using the pole figure method.

Orientation factors were represented on the White and

Spruiell orientation triangle.

3.7.1.3.2 Biaxial Orientation

Using Equations (2.19a) and (2.19b) for biaxial

orientation, we characterize biaxial orientation functions

fa,jr fBzj for the talc particles quantitatively by using the

pole figure method. These again were represented on a White

and Spruiell orientation triangle.


1 2 3

3.7.2 X-ray Intensity Studies for Composition

Analysis of Particle Filled System

3. 7. 2.1 Introduction

A quantitative analysis of particles in a filler

composite were performed for one filler (isotropic or

anisotropic) system and two fillers (isotropic plus

anisotropic) system in thermoplastics to determine the

amounts of particles in a binary (182) and ternary system

(186) using the amorphous intensity of polystyrene.

In this dissertation, we describe a new approach to the

investigation of composite of inorganic filler in an

amorphous thermoplastic matrix (PS/Talc, PS/Calcite,

PS/talc/calcite). The wide angle x-ray diffraction(WAXD)

intensity method for a binary mixture system was used. X-

rays (40KV and 150 mA) with CuKa radiation were generated

using a Rigaku x-ray generator. The Bragg angle scanning

range was from 5° to 45°.


3.7.2.2 Binary Mixture (Single Particle) System1 2 4

The x-ray intensity depends on the position of the

atoms relative to a given set of planes.

Iihki. = P’L'A-IfI2 (3.18)

where Irh is the structure factor that depends on the atomic

scattering factor, P is the polarization factor (incoherent

radiation) that depends on the Bragg angle, L is the Lorentz

factor that depends on reflecting (exposure) time, A is the

absorption factor(transmission factor) that depends not only

on its elemental composition and the wave length of the x-

rays but also on the size and shape of the specimen.

Alexander and Klug represented the absorption of a flat

specimen as:

K|X|li = r , . r ‘ , T~T (3.19)

where


1 2 5

1,2,3 = uppercase subscripts designating components of a

powder mixture

M = subscript referring to he "matrix", that is, the sum of

all the components other than 1

II = subscript referring to line I of component 1

P: = density of (solid) component 1

Xi = weight fraction of component 1 in a mixture

‘K = volume fraction of component 1 in a mixture

= linear absorption coefficient of (solid) component 1

for the x-ray wavelength used

P:* = M-: /Pt = mass absorption coefficient of component 1 for

the x-ray wavelength used

M = linear absorption coefficient of a sample consisting of

several components

IlL = intensity of line i of component 1 of a mixture

(Iii) a = intensity of line i of pure component 1

11 = intensity of component 1 of a mixture

In the case of mixture of 2 components, when Ai

for the pure first component (^m = ^), from Equation (3.19)


while for a mixture containing a weight fraction Xi of the

first component and Xz=l-X2 of the second component.

. . . K,x, (3.21)

More generally

In = K|ixiP\M

(3.22)

where M-* is mass absorption coefficient of a sample

consisting of several components.

Dividing Equation (3.21) by Equation (3.20) gives

_ *iM\(i \ ~ f • • \ * (3.23)v I 70 X|(^l -P2)+ P2

The quantity Xi and ‘K is related to the volume fraction by


1 2 7

x. = — P

so, 1 - / . . \ , , . (3.24)(p \ ~P\ )P\4l +PP2

3.7.3 Scanning Electron Microscopy (SEM)

3.7.3.1 Introduction

The scanning electron microscope (SEM) is a powerful

instrument which permits observation and characterization of

heterogeneous organic and inorganic materials and surfaces

on a local scale. The area to be examined is irradiated

with a finely focused electron beam, which may be static or

swept in a raster across the surface of the specimen. When

the electron beam hits the surface of the specimen, signals

such as secondary electrons, backscattered electrons,

characteristic x-rays, and photons of various energies are

produced. These signals are detected from specific emission

volumes within the sample and can be used to examine many

characteristics of the sample such as surface topography,

crystallography, etc.


1 2 8

In the scanning electron microscope (SEM), the signals

of great interest are secondary and backscattered electrons,

since these electrons vary according to the differences of

the specimen's topography as the electron beam scans across

the specimen. Secondary-electron emission is confined to a

volume near the beam's impact area, permitting images to be

obtained at relatively high resolution. Other signals are

available, which are similarly useful in many areas.

The SEM is one of the most versatile instruments

available for the examination and analysis of the

microstructural characteristics of solid objects. The

primary reason for its usefulness is the high resolution

that can be obtained when bulk objects are examined; our

laboratory's SEM achieved resolutions up to 1 run (10 A) at

200,000 magnification under normal operating conditions.

Another important feature of the SEM is the three-

dimensional appearance of the specimen image, a direct

result of the large depth of field, as well as to the

shadow-relief effect of the secondary and backscattered

electron contrast.


3. 7. 3. 2 Experimental1 2 9

Two scanning electron microscopes (ISI-SX40 and Hitachi

S-2150) were used to investigate the phase morphology of a

cross section of the talc compounds. The scanning electron

microscope (SEM) of Hitachi s-2150 was used to investigate

high magnification purposes that magnification up to

200,000. This computer was connected to scanning electron

microscope (SEM) to obtain digital signals from SEM. The

SEM image data were saved in computer. Nonconducting

samples need coatings before they can be examined and

analyzed in electron-beam instruments that rely on emitted

signals to provide information. Electron charge build up

rapidly in a nonconducting specimen when it is scanned by a

beam of high-energy electron. Before investigation under

scanning electron microscopes, we coated gold on the

specimens to prevent image distortion, as the primary beam

causes thermal and radiation damage, which can lead to a

significant loss of material from the specimen.

The ISI-SX40 and Hitachi S-2150 SEM were used at 20KV

and 80 ^A and 25KV and 100 ^A respectively. SEM film used

was Polaroid Positive/Negative 4x5 Instant Sheet Film T-55


1 3 0

for ISI-SX40 and GE Electronics Inc. Color Printer Papers

B/W Model# UPC-1020 for Hitachi S-2150.


C H A P T E R I V

RHEOLOGICAL MEASUREMENTS IN STEADY AND OSCILLATORY

SHEAR FLOW

4.1 Introduction

In this chapter, we describe an experimental study of

the rheological properties of talc, calcite and mixed

particle compounds. Our study includes (i) steady shear

flow, (ii) uniaxial extension and (iii) oscillatory flows.

The studies presented in this chapter include results

for both polystyrene(PS) based compound and IUPAC Working

Party 4.2.1 polypropylene(PP)-particle filled compounds.

131


4.2 Results1 3 2

4.2.1 Steady Shear Flow Measurements

Figure 4.1 represents the steady shear viscosity as a

function of shear rate as determined from sandwich, cone-

plate, and capillary rheometers for polystyrene (PS) and

talc filled PS compounds (0.05, 0.1, 0.2 0.4 volume

loadings) at 200 °C. The data is replotted as a function of

shear stress in Figure 4.2. Generally, the viscosity

decreases with increasing shear rate. As particle loading

increases the shear viscosity increases with the greatest

increases occurring at low shear rates and shear stresses.

There are zero shear viscosities for the PS, and the

PS/talc 0.05 and 0.1 volume loading compound systems. At low

shear rates and shear stresses the shear viscosity becomes

increasingly high for the PS/talc 0.2 and 0.4 compounds.

There are stresses below which there is no flow for the

PS/talc 0.2 and 0.4 loading compounds. The yield values

which were determined from the sandwich creep instrument are

36-82 Pa for the 0.2 and 290-100S Pa for the 0.4 PS/talc

compounds.


1 3 3

Figure 4

M i n ing i i ninn 1 1 m iiq l i n ing i i iiiii i i i mij Hi i nq 1 1 nmij 11 mill] r umuj i i n i j

ncdL

DDJn

10°

O PS I~1 PS/TALC (95 05)

A PS/TALC (90 10) 3PS / TALC (80 : 20)

O PS/TALC (60:40)

O san d w ich v isco m e te r O c o n e -p la te v isco m e te r • cap illary rh e o m e te rm J i 11 mill i i mini iiimij iiimij iiiiJ ill ■ i mini ■ i irmil i ! mini in

10-7 10-6 10-5 10-4 10-3 10-2 10- ’ 10° 101 102 103 104- 1 .

SH E A R RATE (se c )

Shear viscosity as a function of shear rate for talc filled system at 200°C


1 3 4

1010

109

108cnCD 107 a£ 106COOco 105 >

104

103

102

“ I "I 11 lllii i i iTim

\

r m i ni|— I i i i iuij— r rnnn]— i i i i iuij— i i t ht s

O ps□ PS/TALC (95 : 05) 1

A PS/TALC (90 10) :

V PS / TALC (80 : 20) 1O PS / TALC (60 40) =

I P san d w ich v isco m eu IO c o n e -p la te v isc o m e te r1

I papillary rh eo m e te r "S fti i i mnl i i i mill t Miiml i i_mml i ... . ml i i 11 mil i i i mu

10° 101 102 1 03 1 04 1 0s 106 107 108

SH E A R S T R E S S (P a)

Figure 4.2 Shear viscosity as a function of shear stressfor talc filled system at 200°C


1 3 5

This is shown in Figure 4.3 where we plot creep as a

function of time for different applied shear stresses. To

determine the low shear stress behavior of the 0.2 volume

loading compound we had to introduce a compensation

procedure for the weight of the inner member. This was

discussed in Section 3.5.1.1.

It should be seen in the shear viscosity-shear stress

plots shown in Figure 4.2 for the 0.2 and 0.4 volume loading

talc compounds that there are plateau viscosities just above

the yield values. These are in the range of 5x10' to 5x10“

(Pa.sec).

Figure 4.4 represents the steady shear viscosity for PS

and calcite filled PS compounds (0.05, 0.1, 0.2, 0.4 volume

fraction) as a function of shear rate at 200 3C. The

results are similar to the PS/talc compounds with the shear

viscosity decreasing with shear rate and increasing with

particle loading, especially at low shear rates. The PS and

PS with 0.05 and 0.10 loadings clearly exhibit zero shear

viscosities. The data is replotted as a function of shear

stress in Figure 4.5.


1 3 6

Figure 4

2.0

7165 Pa

6

OJ<D 2265 Pa

0.51375 Pa

1009 Pa > 292 Pa0.0

4 0 0100 200 3 0 0

T im e (min.)

3 Shear strain creep as a function of time at200°C for various creep levels for PS/talc 0.4 volume loading compound


1 3 7

Figure 4.

0)CD3_

f)0Jn

01' |iniiiiij iiiiiiu) 11inwj~ 'mm^ i iniii~i nniij 11mm iiiimii 11limn i iimiir rrnr

o 10

o9

O ps□ PS / CALCITE (95 A PS / CALCITE (90 V PS/CALCITE (80 O PS/CALCITE (60

02

08

07

06

0s

°4^ sa n d w ic h viscometer*"

° 3 b O c o n e -p la te v isco m ete rE ♦ , cap illary rh e o m e te r . . . . _ ,

i mi nd i 11 nirf i i mud i n mil i i mi r d i i i m i l i i n i i r i t i m u t l L i i m d i h i ^ E i i mud

10'7 10-6 10-5 10-4 10*3 10’2 10*1 10° 101 102 103 104

SH E A R RATE ( s e c 1)

Shear viscosity as a function of shear rate for calcite filled PS system at 200°C


1 3 8

1010

109

108'cnaj 107

£ 106 CO OCO 105 >

104

103

10210° 101 102 103 104 10s 106 107 108


Figure 4.5 Shear viscosity as a function of shear stressfor calcite filled PS system at 200°C

= i i 111:ii( I rTTTTTTj 11 {I ll!l| I 1 r lllllj ill miij I I ! I llll| I I 11 llllj I TTTTTH

O ps□ PS/CALCITE (95 A PS/CALCITE (90 V PS/CALCITE (80 O PS/CALCITE (60

05) = 10)20) _ 4 0 ) !

^ san d w ich v iscom e'0 c o n e -p la te v isco m e te ♦ .capillary rh e o m e te r1 11 mill i. Lniml L i n u n L u m u t i_ iim C -L L liilU I I HUH L i n a


1 3 9

At low shear rates and shear stresses the shear

viscosity of many compounds becomes increasingly high.

There are indeed stresses below which there is no flow for

the PS/calcite 0.4 loading compounds. The yield values are

229-428 Pa for the 0.4 PS/calcite compound. This is shown

in Figure 4.6 where we plot creep as a function of time for

different applied shear stresses.

It should be noted that while the 0.2 and 0.4 loading

talc compounds exhibit yield values, only the 0.4 loading

calcite compound clearly exhibits yield value.


function of shear rate for PS and calcite/talc mixed

particle filled PS compounds (0.05:0.05, 0.04:0.12,

0.10:0.06, 0.10:0.12, 0.20:0.20 volume loadings) at 200 °C.

The data are represented as a function of shear stress in

Figure 4.8. Figure 4.7 shows the viscosity level of the

talc/calcite mixed system was lower than the talc filled

system and higher than the calcite filled system. In Figure

4.9 we plot creep in the sandwich viscometer as a function

of time for different applied shear stresses.


Figure 4

1 4 0

3.0

2 .5

~ 2.0JDP-s 1.5 n032 1.0 n

0 .5

0.00 100 2 0 0 3 0 0 4 0 0

Tim e (min.)

6 Shear strain creep as a function of time at200°C for various creep levels for PS/calcite 0.4 volume loading compound

8063 Pa

1074 Pa

239 Pa 194 Pa82 Pa

36 Pa


1 4 1

Figure 4

1 0 i°

109

1087)(o 107 L= 106 n D» 10s >

104

103

10210-7 10-6 10-5 10^ 10-3 10-2 10-1 10° 101 102 103 104

SH E A R RATE ( s e c -1)

7 Shear viscosity as a function of shear ratefor talc/calcite filled PS system at 200°C

Hllll l l l j IlllllUj l l l l l l j I l l l U j I i I l l iU| I m i i l l j I I l l l l llj l l l l l l ll ] I 11 M b

PS / TALC / CALCITE (60 : 20 : 20) \ PS / TALC / CALCITE (90 : 05 : 05)

PS / TALC / CALCITE (84 04 12) ! PS / TALC / CALCITE (84 : 10 : 06) I PS / TALC / CALCITE (78 1 0 : 12 n PS

^ sandw ich v isco m ete r r O co n e -p la te v isc o m e te r

♦ capillary rh e o m e te ri iiimil i n i i i n l i imml i i i i n i J i i n i i i J i i n i i i i ) iiiiiiiI


1 4 2

Figure 4

1010

109

108

7)CD 107 r“ 106 7)Di 10s >

104

103

10210° 101 102 103 104 105 106 107 108


8 Shear viscosity as a function of shear stressfor talc/calcite filled PS system at 200°C

E i i i mi l l | | | nnil" i i i ii r r m n i|— i i iimi|— i 11 iinij— i 11 niiij t t t t t t b

O PS / TALC / CALCITE (60:20:20)= □ PS/TALC/CALCITE (90:05:05)- A PS/TALC/CALCITE (84:04:12)1 V7 PS / TALC / CALCITE (84:10:06)= <5> PS/TALC/CALCITE (78:1012)

PS

^ O O C C b c ^ sandwich viscometer0 cone-plate viscometer ^ capillary rheometer

1 i m i n i i i m i n i i—l 11ititi L i - l l i t i l l mi l t m i l l


1 4 3

c(0cnCO<1>x :

C/3

51520 Pa

4 514 Pa

3

A 239 Pa2

101 Pa1+ 37 Pa

0

0 100 2 0 0 3 0 0 4 0 0 500

T im e (min.)

Figure 4 . 9

(a) 0.78/0.10/0.12

Shear strain creep as a function of time at 200°C for various creep levels for PS/talc/calcite (a) 0.78/0.10/0.12 (b) 0.60/0.20/0.20 volume loading compounds


JO,

cCO•*-*COu_CDCDszCO

53 5 6 2 P a

4 <> 2 9 5 0 P a

31 646 P a

2 1208 P a

1 ^ 9 5 8 P a

282 P a H

0

100 2 0 0 3 0 0 4 0 0 5 0 00

T im e (min.)

(b) 0.60/0.20/0.20

continuedFigure 4.9 Shear strain creep as a function of time

200°C for various creep levels for PS/talc/calcite (a) 0.78/0.10/0.12 (b) 0.60/0.20/0.20 volume loading compounds


1 4 5

In Figure 4.8 talc/calcite (0.05:0.05, 0.04:0.12,

0.10:0.06, 0 .10:0 .12) systems do not exhibit a yield value

and a low shear stress constant viscosity plateau at 2x10°

Pa. The high particle loading 0.20/0.20 talc/calcite mixed

particle compound system exhibits yield values. Figure 4.8

shows the viscosity level of a talc/calcite mixed system

depends on the volume fraction of loaded particles.

In Figure 4.9 we present creep data for the 0.10/0.12

and the 0.20/0.20 samples. We see that the yield value from

0.20/0.20 appears to have a magnitude between 280 and 960

Pa.


function of shear rate for polypropylene (PP) and calcite,

talc, and calcite/talc filled (6743/1, 6743/2, 6743/3,

6743/4, 6743/5, 6743/6) PP compounds (0.25 volume loading)

from a IUPAC Working Party 4.2.1 study at 210 JC. These are

discussed in Section 3.3. Compounds 6743/1, 6743/2, 6743/4

are uncoated particle filled system, 6743/3, 6743/5, 6743/6

are stearic acid coated particle filled system, 6743/1,

6743/6 are talc/calcite mixed particle filled systems,

6743/2, 6743/3 are talc particle filled system, and 6743/4,

6743/5 are calcite particle filled system.


1 4 6

toCL<0Ooco

1011

1Q10

109

108

107

106

105

104

103

102

101

; 11 i iiiiij iT i nuij i i i iiiih iiiiu i^ i i i iiii 11 imiij ' i i imiij m i uni) 11 imuj 11 miiij l u n g

% 6743/0 (PP)o 6743/1 (PP/Talc/Calate. uncoated) ~~

□ 6743/2 (PP/Talc, uncoated)

A 6743/3 (PP/Talc, coated) y 6743/4 (PP/Calcite, uncoated)

< 0 6743/5 (PP/Calcite, coated)

O 6743/6 (PP/Talc/Calcite. coated)

10° iJ i i mini i 11 mill iiiimJ iiiiiJ iimJ miiiihI i minil in I mhhhi Mind

10'7 10-6 10*5 10"4 10-3 10-2 10-1 10° 101 102 1 03 1 04

S h e a r R a te ( s e c ’ )

Figure 4.10 Shear viscosity of PP/fillers as a functionof shear rate at 210°C


1 4 7

Measurements as with the polystyrene compounds were made at

high shear rates in a capillary rheometer (Instron),

intermediate shear rates in a cone-plate rheometer

(Rheometrics) and lower rates (sandwich creep rheometer).

The data are presented again as a function of shear stress

in Figure 4.11.

The polypropylene (PP) exhibits a shear viscosity which

decreases with increasing shear rate and plateaus at low

shear rate.

The shear viscosity of PP and its compounds orders as;

Y = 100 sec'1 6743/(4 ^ 1 ^ 2 ^ 3 ^ 6 >5) > PP(capillary)

Y = 0.1 sec’1 6743/(2 - 3 > 1 > 4 > 6 >5) > PP(cone-plate)

Y = 0.01 sec'1 6743/(2 > 3 > 1 > 4 > 6 >5) > PP(cone-plate)

Y = 0.00001 sec'1 6743/(2 ^ 3 ^ 1 > 4 > 6 > 5 ) » P P (sandwich)


1 4 8

Figure

COcoCLc/)ooCO

1010

109

108

107

106

10s104

103

102

101

11 i iiiiuj i i mi

10°

inmii| iiiiiiii| iiiinii| i i iinii| • i iiiniij i i imiij i i iiiiii| 'i i itti # 6743/0 (PP)O 6743/1 (PP/Talc/Calcite, uncoated)

□ 6743/2 (PP/Talc, uncoated)A 6743/3 (PP/Talc, coated)

SJ 6743/4 (PP/Calcite. uncoated)

0 > 6743/5 (PP/Calcite, coated)0 6743/6 (PP/Talc/Calcite. coated)

-3i mi"! il ill iiimiil i i mini i i mini i i mini immil Liimnl inline

10° 101 102 103 104 105 10s 107 10® 109 1010

S h e a r S tre s s (P a )

l.11 Shear viscosity of PP/fillers as a function of shear stress at 210°C


1 4 9

From Figure 4.11 viscosity shows greater increases in

the low shear rate region. The viscosity level of the

talc/calcite mixed system was lower than the talc filled

system and higher than the calcite filled system. The

surface coated filler system showed lower viscosity than the

uncoated filler filled system. Only the three talc filled

systems (0.25 volume loadings) exhibit yield values. The

other systems do not exhibit yield values.

In Figure 4.12 we present creep data for the

talc/calcite uncoated samples. We see that yield value

appears to have a magnitude between 40 and 100 Pa.


1 5 0

JOCtok _

COi_(0d)-C

CO

4

4 28 P a

2 40 P a3

2101 P a

13 7 P a

0

100 2 0 0 3 0 0 4 0 0 5 000

T im e (m in.)

Figure 4.12 Shear strain creep as a function of time at210°C for various creep levels for PP/talc/calcite 0.75/0.13/0.13 volume loading compounds


4.2.2 Oscillatory Flow Measurements1 5 1

Oscillatory measurements may be interpreted to yield

the dynamic viscosity and storage modulus.

4.2.2.1 Dynamic Viscosity

Figure 4.13 shows dynamic viscosity 7 (^) measurements

at 1 % strain as a function of frequency 03 for pure PP, 25

volume! uncoated talc, 25 volume! coated talc, 25 v%

uncoated calcite, 25 v% coated calcite, 25 v% uncoated

talc/calcite, 25 v% coated talc/calcite compounds in PP at

210 °C. It may seen that talc, calcite, talc/calcite

particles increase the level of the viscosity especially in

the low frequency region.

Surface treated particles compounds have lower dynamic

viscosity. This includes talc, calcite and talc/calcite

filled polypropylene.


1 5 2

cotOcu

10® E— T T T T

10® -

104 -

103 r

102 r

101 -

TTTTI 1 I I m r i l -------1—I I I lllll I TTTTTTT1 I I I I ITTT1 I TTTTTS

10° t i t m i l l t I 1 m i l

# pp

O 1x Calcite,Talc(uncoated) E□ 2xTalc(uncoated)A 3xTalc(coated)

4xCalcite(uncoated) 1<^> 5xCalcite(coated) -

0 6xCalcite,Talc(coated)I I I I I m i l ....................Ill____ I I I ! m i l ____ |__ I I Mi l l ;

10-3 10-2 10-1 10° 101 102 103

co (rad/s)

Figure 4.13 Dynamic viscosity of PP/fillers as aof frequency at 210oC

function


1 5 3

Talc particle compounds exhibit higher dynamic viscosity

than calcite particle and talc/calcite particle compounds at

the same 0.2 5 volume loadings. The data orders as 5743/(2 >

3 > 1 > 6 > 4 > 5 ) for rate sweep dynamic viscosity

measurements. This is seen in Figure 4.13. As we increase

the strain amplitude the dynamic viscosity and storage

modulus decreases as the strain amplitude increases. The

data tend to become independent of strain at strains below

2% for PP and below 1% for particle filled systems.

The dynamic viscosity of the uncoated talc compounds is

slightly higher than the coated talc compounds. The

viscosity of the uncoated calcite compound is significantly

higher than the coated calcite compound. The viscosity of

uncoated talc/calcite mixed particle compound is higher than

the coated talc/calcite mixed particle compound.

4.2.2.2 Storage and Loss Modulus

As noted in the previous section, Figure 4.14 shows the

storage modulus G' f03) as a function of frequency for pure

PP, 25 volume% uncoated talc, 25 volume% coated talc, 25

volume% uncoated calcite, 25 volume% coated calcite, 25


1 5 4

volume% uncoated talc/calcite, 25 volume% coated

talc/calcite at 210 °C. The presence of particles increases

the level of H' f03) and G' (£°) especially in the low

frequency region. Figure 4.15 shows the loss modulus,

G" I0*} as a function of frequency for pure PP, 25 volume%

uncoated talc, 25 volumes coated talc, 25 volume? uncoated

calcite, 25 volume% coated calcite, 25 volume% uncoated

talc/calcite, 25 volume% coated talc/calcite at 210 °C.

For the pure PP, when 63 decreases toward zero, the

storage modulus G' f03) goes to zero. For the pure PP, when

03 decreases toward zero, loss modulus G" f03) also goes to

zero.

Figure 4.16 and Figure 4.17 show the storage modulus,

G'i03) and loss modulus G" (°3) as a function of strain (?)

for pure PP, 25 volume% uncoated talc, 25 volume% coated

talc, 25 volume% uncoated calcite, 25 vclume% coated

calcite, 25 volume% uncoated talc/calcite, 25 volume% coated

talc/calcite at 210 °C. The storage modulus G' i03) and loss

modulus G" (co) of particle filled systems are higher than

pure PP. In Figures 4.16 and 4.17 as we increase the strain


1 0 6 — I l- l I I lll | I TTTTTTTj I I i I 11!i| I TTTTTTTj I TTT7TTT| i i I I 111±

10s

0

3 104i—iDno . S 103

<Dtn

2 102O-PU)

101

# ppO 1x Calcite,Talc(uncoate«) O 2xTalc(uncoated) “A 3xTalc(coated) _

4xCalcite(uncoated) E<3> 5xCalcite(coated) E

, O 6xCalcite,Ta|c(coated)m l t i t i n i t ) i t t i m i l i i i i f i m

10-3 10-2 10-’ 10° 101 102 103

0) (rad/s)

Figure 4.14 Storage modulus (G' ) of PP/fillers asfunction of frequency at 210°C


1 5 6

1 06 E 1 I I I ITI1| 1 I I I I ITT] [“ "TTTTTTTj 1 I I I llllj T I ITTrilj I I I I 11 U

uCO3

105 -

104 -

3T3 103OscoCO 102 o►3

10i -

w {+}wct) y <+>

❖f S * ^ °

<£>v O

O pp@ 1x Calcite,Talc(uncoate<) 0 2xTalc(uncoated)A 3xTalc(coated)^ 4xCalcite(uncoated)<+> 5xCalcite(coated)

(+) 6xCalcite,Ta|c(coated)i N n m i l i i i m i l l i » t i f n i

10*3 10-2 10'1 10° 101 102 103

co (rad/s)

Figure 4.15 Loss modulus (G") of PP/fillers as aof frequency at 210°C

function


1 5 7

amplitude the storage modulus decreases as the strain

amplitude increases. The data tend to become independent of

strain at strains below 2% for PP.

At low frequencies, in Figures 4.14 and 4.15 it is

found that in the compound system G' f63) and G" i03) remain

finite as 03 goes to zero. For 25 volume% filled talc,

calcite, and the talc/calcite particle filled system, G' i03)

and G" f03) are almost independent of frequency at low

frequencies. The data orders as 6743/(2 > 3 > 1 > 6 > 4 >

5) for rate sweep storage modulus G't03) and 6743/(2 > 3 > 1

> 6 > 4 > 5) for rate sweep loss modulus G" f03) . The data

orders as 6743/(2 > 3 > 1 > 6 > 4 > 5 ) for strain sweep

storage modulus G' f03) and 6743/ (2 > 3 > 1 > 6 > 4 > 5 ) for

strain sweep loss modulus G" f03) .


1 5 8

1 0 5 E— 1— i i 1 1 m i --------1— i i 11 m i ------- 1— r~i 1 1 rrn------- 1— i i 111 ill-------1— t t t t t o

104 =-CD

COZ>_lZ>QOLU 0 < QI O I— CO

103 =-

102 -

101 r

10°

O C X D O O O q Ih wo w o o o o H a

V „

0 5

: • PP ;

= O 1x Calcite,Talc(uncoated) -

- □ 2xTalc(uncoated)

=- A 3xTalc( coated) -

: V 4xCalcite(uncoated) 1: O 5xCalcite(coated) -

' 01 !6xCaldte,Talc(coated)

i i i ml i i i i i ml i i i Mini i I I-J—L1 U_1— i » ........

10-2 10-1 10° 101 102 103

STRAIN (%)

Figure 4.16 Strain(%) sweep of PP/fillers as a functionof storage modulus G' at frequency lrad/sec and 210°C


1 5 9

10s

104

<n 103 iz>G O 2 102COCOO—I

101

10°10-2 10-1 10° 101 102 103

STRAIN (%)

Figure 4.17 Strain(%) sweep of PP/fillers as a functionof loss modulus G" at frequency 1 rad/sec at 210°C


=— i— i i m ii[--1— i i m m|-- 1— ri 11 i'i11---1— i i 11 iiij---1— i rTTTTj

0 0 0 fV

V V v ^ V v 0 a A a Ao o o o o o o o o o S

O ppO 1x Calcite,Talc(uncoated) [ j 2xTalc(uncoated)A 3xTalc(coated)V7 4xCalcite(uncoated)<(^ 5xCalcite(coated)

Q 6xCalcite,Talc(coated)I I I I 1 Mil I I I t I I III I I . I M I 111 I I I I I I Ml I I I I I l i t

4.3 Discussion1 6 0

4.3.1 Particle Loading Dependence of Shear Viscosity

4.3.1.1 PS Matrix System

Figures 4.1 and 4.2 for the talc filled compound system

and Figures 4.4 and 4.5 for the calcite filled system showed

that shear viscosity increases with increasing particle

loadings and the shear viscosity increases with decreasing

shear rate as noted by various other studies on PS-CaCOj

compounds (120, 133, 232). As the shear stress decreases to

very low levels the shear viscosity was found to exhibit a

plateau as had been previously observed in our laboratories

by Osanaiye et al (136) and Araki and White (257). At still

lower shear stresses, many of the compounds exhibit yield

stresses. The viscosity increases were highest for the talc

compounds and lowest for the calcite compounds. In Figures

4.18 through 4.20 we compare the viscosity nifa/) / 7(^X)

increases at different shear rates with the well established

1 n(0) correlation for Newtonian fluids.


1 6 1

105

104o§- 103

•I 102ooCO> 1010.>3s 1 0 °0tx

= I I I lllllj 1 I I 1111!| 1 I I I 11 ll| 1 TTTTTTT] i TTTTTTT] TTTTTTTl

10 •1

10-2

□ PS / TALC (95 : 05)

A PS/TALC (90 : 10)

V PS/TALC (80 :20)

O PS/TALC (60 :40)

i i » i »ni l i i m m l i i i i m u I I m i l l ] 1 1 1 1 Lilli 11 in ii i . i . m i

10-3 10-2 10‘1 10° 101 102 103 104

Shear Rate (sec1)

Figure 4.18 Relative viscosity as a function of shearrate for talc-PS compounds


I I I

llffl

1 6 2

□ PS / CALCITE (95 : 05) IA PS/CALCITE (90: 10) T

V PS / CALCITE (80 : 20) :

O PS / CALCITE (60 : 40) _

1•2 1■3

Shear Rate (sec'1)

Figure 4.19 Relative viscosity as a function of shearrate for calcite-PS compounds


1 6 3

10s

104

? 103

— 102 co luooCO> 101 <D >JO0) 10° a:

10-1

io-210-3 10'2 10'1 10° 101 102 103 104

S h e a r R a te ( s e c -1)

Figure 4.20 Relative viscosity as a function of shearrate for talc/calcite-PS compounds

O PS / TALC / CALCITE (60 : 20 : 20) :V PS / TALC / CALCITE (78 : 10 : 12 )_A PS / TALC / CALCITE (84 : 10 06)□ PS / TALC / CALCITE (84 04 12)O PS / TALC / CALCITE (90 05 05) -


1 6 4

b8 7Welt©g6©g/Q©o;=t ? s A L> a 2??

pr-©*

£•c/ioow>a>>iH0cc

T—I I IlirTj I 1 I I llllj I 1 1 11II!| I M I llllj I i I 11 ni| I i l i n o

O 6743/1 (PP/Talc/Calate, uncoated) : nS nTi! C 2©tCS-W= \ j 6743/2 (PP/Tafc, uncoated)A 6743/3 (PP/Talc, coated)V 6743/4 (PP/Calcite. uncoated)

O 6743/5 (PP/Calcite, coated)

0 6743/6 (PP/Talc/Calate, coated)

10s■

104

103

102

101

10°

10-1

^ q - 2 I i i m i n i t » t 111 nl i i I Mi n i i i i i m i l i i m i n i i i i 11 m l i i i i m i l

10-3 10-2 10*1 10° 101 102 1 03 1 04

S h e a r R a te (s e c ’ )

Figure 4.21 Relative viscosity as a function of shearrate for talc/PP, calcite/PP, and talc/calcite/PP compounds


1 6 5

Figure 4.18 presents the viscosity ratios H (<t>) Z1! (0) of

talc-PS compounds system as a function of shear rate. The

ordering of the relative viscosity is talc-PS 5 < 10 < 20 <

4 0 v% compounds.

Figure 4.19 exhibits the order of relative viscosity of

the calcite-PS compounds system. The ordering of the

relative viscosity is calcite-PS 5 < 10 < 20 < 40 v%

compounds.


the talc/calcite-PS compounds system. The ordering of the

relative viscosity is talc/calcite-PS 05/05 < 04/12 - 10/06

- 10/12 < 20/20 v% compounds.

4.3.1.2 PP Matrix System

Figures 4.10 and 4.11 for talc, calcite, and

talc/calcite filled compound indicate the shear viscosity of

particle filled compounds exhibit higher shear viscosity

than PP. Shear viscosity increases with decreasing shear

rate. As shear stress decreased the viscosity showed a

plateau region and below this an apparent yield value.


1 6 6

We consider the behavior of relative viscosity

/ 7(0’?') for these compounds in Figure 4.21


talc-PP, calcite-PP, and talc/calcite-PP compounds system.

The ordering of the relative viscosity is 6743x 2 > 3 > 1 >

4 > 6 > 5 compounds.

4.3.2 Yield Values

Figures 4.2, 4.5, 4.8, and 4.11 showed plateau near to

yield point below where there were no flow for PS/talc,

PS/calcite, PS/talc/calcite, PP/talc, PP/talc coated, and

PP/talc/calcite system respectively.

4.3.2. 1 PS Matrix System

Figure 4.2 shows at 20 v% and 40 v% loadings of talc

particle filled system. Figure 4.5 shows 40 v% loadings of

calcite particle filled system. Talc and calcite particles

have approximately the same particle size.


167

Table 4.1 Shear and threshold yield values of particlefilled PS at 200 3C

Compounds/(Composition)

Shear Yield Value

Ys(Pa)

Threshold Yield Value

(Plateau Region) Ys,acc (Pa)

PS/Talc no no(95:05)PS/Talc r.o no(90:10)PS/Talc 36-82(flow) 245(80:20)PS/Talc 292-1009(flow) 5121(60:40)

PS/Calcite no no(95:05)


PS/Calcite 7 no• Q O • ° n ' V O u . u /

PS/Calcite 239-428(flow) 2378(60:40)

PS/Talc/Calcite no no(90:05:05)

PS/Talc/Calcite 7 no(84:04:12)



PS/Talc/Calcite 282-958(flow) 3150(60:20:20)


1 6 8

Talc has larger BET surface area than calcite, and the yield

value of talc filled system, was higher than calcite filled

system at same volume loading (0.4). At the 20 v% loadings

of talc and calcite particle filled system, the talc filled

system exhibited yield stress but calcite filled system did

not.

4. 3. 2.2 PP Matrix System

Figure 4.11 also indicate the existence of yield values

from talc particle filled system in polypropylene (PP) at 25

v%. However we did not observe yield values from calcite at

25 v%. We could see only plateau region from that

experiment which indicates there might exist a yield value

at lower shear stresses than we might measure. Our sandwich

viscometer can not detect yield values less than 30 Pa due

to machine limit. There may exist yield values at 20 v%

filled calcite particles less than 30 Pa area but our

instrument could not detect below that area. Yield values

for PP matrix system are summarized in Table 4.2.


4. 3. 2.3 Comparison To Earlier Literature1 6 9

Earlier studies on small particle filled thermoplastic

melts have also suggested the existence of yield value and

estimated their values. We have summarized reported yield

values of thermoplastic compounds loaded with different

particles such as titanium dioxide, calcite, carbon black

etc. in Table 4.3. It is clear from Tables 4.1, 4.2, and

4.3 that the yield value increases with decreasing particle

size. Yield value also depend upon the particle and

thermoplastic used.

In almost all cases the earlier reports in the

literature are 'apparent' yield values determined by

extrapolation from higher shear stress data. They have

similar values to our 'threshold' yield values. Exceptions

are the work of Osanaiye et al. (127, 136), Li and White

(270) and Araki and White (257). They used creep

measurements. Apparent yield values significantly

overestimated true values as pointed out by Osanaiye et al.

(136) .


170

Table 4.2 Yield values of particle filled PP at 210 3C

Compounds Shear Yield Threshold YieldSurface Treatment value Value(Composition v%) (Pa) (Pa)PP/Talc/Calcite 37-101 239

uncoated(75:12.5:12.5)

PP/Talc 42-101 683uncoated(75:25)PP/Talc 37-101 428coated(75:25)

PP/Calcite no nouncoated(75:25)

PP/Calcite no nocoated(75:25)

PP/Talc/Calcite no nocoated

(75:12.5:12.5)


1 7 1

Table 4.3 Yield values of particle filled thermoplastics

Filler Size(Mm)

Matrix Vol%

Temp(°C)

Yield Y3 (KPa)

Reference

T.O; 0 .18 LDPE 25 180 2 . 5' Minagawa and White

t,o2 0.18 HDPE 25 180 0.5' Minagawa and White

T.02 0.18 PS 25 180 1' Minagawa and White

t,o2 0.18 PS 30 180 2 .2' Tanaka and White

CaCOj 2 LDPE 30 200 0 .12' Kataoka et al.

CaC03 0.5 PS 30 180 12' Tanaka and White

CaC03 3 PS 30 180 1.5' Suetsugu and White

CaC03 0.5 PS 30 180 10' Suetsugu and White

CaC03 0.07 PS 30 180 40' Suetsugu and White

CaC03 0.8 PP 30 180 7.0' , 1.08-1.23"

Araki

CarbonBlack

0. 025 PS 20 170 12' Lobe and White


1 7 2

continuedTable 4.3 Yield values of particle filled thermoplastics

Filler Size Matrix Vol Temp Yield Ys Reference( m) % (°C) (KPa)

Carbon 0.025 PS 25 170 60' Lobe andBlack WhiteCarbon 0.045 PS 20 180 25' Tanaka andBlack WhiteCarbon 0.045 PS 30 180 9' Tanaka andBlack WhiteCarbon 0.047 LDPE 20 150 15' Ma et al.BlackCarbon 0. 032 LDPE 20 150 20' Ma et al.BlackCarbon 0.029 LDPE 20 150 30' Ma et al.BlackTalc — PP 18 200 0 . 12' Chapman and

LeeCaC03 0.8 PS 40 200 2.4' ,

0.24-0.43"Present work

Talc 0.9 PS 20 200 0.24', 0.04-0.08"

Present work

Talc 0.9 PS 40 200 5.1' , 0.29-1.01"

Present work

Talc/ 0 .8/ PS 20/ 200 3.1', Present workCalcite 0.9 20 0.28-0.96"' threshold (apparent) yield value from extrapolation. " yield value from creep experiment.


1 7 3

They carried out creep experiments of carbon black filled ethylene-propylene terpolymer (EPDM) at 100 "C using sandwich viscometer at very low shear stress. Our yield values as summarized in Tables 4.1 and 4.2. The talc particle filled system exhibit higher yield values compared to the calcite filled system.

4.3.3 Viscosity-Shear Stress Plateau

Figures 4.2, 4.5, and 4.11 exhibited a plateau near to

the yield point below where there was no flow. We name the

shear stress at the upper end of the plateau the 'Threshold

Yield Stress' . This threshold yield stress is very close to

the real yield value. Araki (257) described viscosity-shear

stress plateaus in calcite filled PP system, carbon black

filled EPDM systems, and PP-EPDM systems.

Earlier yield values were determined from extrapolation

(compare Table 4.3). Osanaiye and White (127, 136), Li and

White (270, 271) used creep experiments. The papers of

Osanaiye and White (127, 136) detected yield values in

carbon black compounds and indicate the existence of

plateaus. Later Araki and White (257) used same creep

experiments and observed yield values experimentally and


1 1 A

found a plateau region. They (257) found yield values and

high viscosity plateaus from higher rubber content TPE(TPE-

2) and ABS(ABS-2) This plateau region corresponds to the

high stress limit of threshold stress in our experiments.

The mechanism of yield values in particle filled

compounds is of interest. It was found by Osanaiye and

White (136) that replacement of EPDM rubber with paraffin

oil at constant carbon black level in compounds leads to a

reduction of yield values. This suggests that the mechanism

of yield values involved particle-polymer networks and not

simply particle-particle compounds.

The speculation for the existence of threshold yield

value is interaction between particle-particle and particle->->/-> "1 t rrr* ea v


1 7 5

4.3.4 Comparison Between Single Particle Filled System

And Mixed Particle Filled System

4.3.4.1 PS Matrix System

Figures 4.7, and 4.8 suggest 0.2/0.2 loading system

exhibit highest viscosities while 0.05/0.05 loading system

exhibit low viscosity level. The viscosity level of

0.04/0.12, 0.10/0.06/, and 0.10/0.12 loading system

apparently located lower than 0.2/0.2 loading system and

higher than 0.05/0.05 loading system however they are close

to each other. So the main conclusion is the viscosity

level mainly depends on volume loadings and then particle

shapes. The anisotropic particle increases the viscosity

level.

We compared at the same volume fraction for different

compounds. Figure 4.22 show 10 volume percent PS/talc,

PS/talc/calcite, and PS/calcite compound systems. Figure

4.23 show 40 volume percent PS/talc, PS/talc/calcite, and

PS/calcite compound systems. Figure 4.22 compare the order

of viscosity level on 10 volume percent particle filled

system talc = talc/calcite > calcite the low stress region.


1 7 6

Figure 4.22 compares the order of viscosity level on 40

volume percent particle filled system talc > talc/calcite =

calcite at low stress region. The viscosity level of the

talc/calcite filled particle system is lower than the talc

filled system and higher than the calcite particle filled

system at the same volume loadings. This represents calcite

particle contribute to lower the viscosity level while the

talc particle contributes to raising the viscosity level for

both the 10 v% and 40 v% system. This seems more clear in

the 10 volume percent compound. The 40 volume percent

system seems more complicated.

4. 3. 4.2 PP Matrix System

Figures 4.10 and 4.11 exhibit the order of viscosity

level on the uncoated particle-filled system talc >

talc/calcite > calcite and also exhibit the identical order

viscosity level on a coated particle-filled system as

talc>talc/calcite>calcite. The viscosity level of the

talc/calcite filled particle system is lower than the talc

filled system and higher than the calcite particle filled

system at the same volume loadings.


1 7 7

COroCL

COooCO>

TTTT1

PS/TALC (90 : 10) PS/CALCITE (90 :10) PS/TALC/CALCITE (90:05:05)

108

10° 101 102 1 03 1 04 1 05 1 06 1 07


Figure 4.22 Viscosity as a function of shear stress for10 v% talc, calcite, and talc/calcite filled PS system at 200°C


1 7 8

Figure

O PS / TALC (60 : 40 ) <3• PS / CALCITE (60 : 40) !© PS/TALC/CALCITE (60:20:20)


.23 Viscosity as a function of shear stress for 40 v% talc, calcite, and talc/calcite filled PS system at 200°C


1 7 9

This indicates calcite particle contribute to lower the

viscosity level while talc particle contribute to raise the

viscosity level for both coated and uncoated system.

4.3.5 Comparison Between Stearic Acid Treated Particle

Filled System And Untreated Particle Filled System

4.3.5.1 PP Matrix System

Surface treatment of the reinforcing fillers is of

importance in industrial practice. Reductions in viscosity

by surface treatment have been reported by several

investigators (105, 273). It would appear that melt flow

properties of suspensions of different types are in large

part due to different levels of inter-particle rather than

purely hydrodynamic considerations. Adding stearic acid to

calcite substantially reduces the yield values of molten

polymer compounds (133, 272). Suetsugu and White (133)

investigated stearic acid effect on calcite filled system.

They found the order of reduction increases with decreasing

particle size and decreasing shear rate. At the shear rate

of 0.063 (sec"1) and 0.16 (sec"1) the order of reduction was


1 8 0

0.7 6 and 0.64 for the 0.5 M-m and 30 volume percent calcite

particles. They presented reduction function as

tr, , rj(y ,<f>, uncoated) - rj(y,<p, coated)H( y) = ---------------------------------- (4.1)

t](y,<p, uncoated)

Tanaka and White (272) investigated stearic acid effect on

calcite filled system. The order of reduction at the shear

rate of 0.001 (sec*1) and 0.1 (sec"1) the order of reduction

was 0.92 and 0.83 for the 0.5 1% and 30 volume percent

calcite particles.

Figures 4.10 and 4.11 exhibit the order of viscosity

level on uncoated talc (x2), calcite (x4), and talc /

calcite (xl) particle filled systems and coated talc (x3),

calcite (x5), and talc / calcite (x6) filled systems. All

systems showed higher viscosity level for the untreated

system i.e. xl>x6, x2>x3, and x4>x5. The talc particle

filled system didn't exhibit large differences between

surface untreated system and stearic acid treated system.

However the calcite particle-filled system did show

considerable differences between surface untreated system

and stearic acid treated system. Stearic acid coated


1 8 1

calcite particle filled system lowered viscosity level

considerably compared to talc treated system i.e. stearic

acid effect is higher on calcite than talc particle. Our

system shows the order of reduction at the shear rate of

0.01 (sec"1) and 1 (sec’1) the order of reduction was 0.85

and 0.67 for the 3.5 and 25 volume percent calcite

particles. For the talc particles the order of reduction

was 0.23 and 0.04 for the 2.5 and 25 volume percent talc

particles at the shear rate of 0.01 (sec L) and 1 (sec ') .

For the talc/calcite particles the order of reduction was

0.73 and 0.32 for the 25 volume percent talc/calcite

particles at the shear rate of 0.01 (sec *) and 1 (sec *) .

Table 4.4 summarize the reduction function for each systems.

Surface treating agents seem to reduce particle-

particle, attraction. Stearic acid emulsifies the

individual calcite particles resulting in the reduction of

particle-particle bondings.


1 8 2

Table 4.4 Viscosity reduction by stearic acid coating oftalc, calcite, and talc/calcite particles in PP at 25 v%

Compounds Shear Rate (see’*) Reduction Factor

PP/Talc 0 . 01 0.23

1 0.04

PP/Talc/Calcite 0.01 0.73

1 0.32

PP/Calcite 0 .01 0.85

1 0. 67


1 8 3

4.3.6 Comparison Between Complex Viscosity And Shear

Viscosity

We compared the complex viscosity with the steady

shear viscosity for polypropylene from Figure 4.24. It was

found that

n'(a) = n(y) (<» = /) (4.n

This is the well known rule of Cox-Merz (263) established

for polystyrene (PS).

For the filled compounds this is generally not the

case. Rather

n'(co)>rj(y) (a = r) (4.2)

For the pure polypropylene melts, the agreement is

quite good. However, the complex viscosity n'i0*) is much

greater than the shear viscosity in the 25 v% PP/talc,

PP/talc/calcite, PP/calcite filled system. For our talc and

calcite filled system, the Cox-Merz relation fails.


Figure

102

101

10°

O pp o0 1x Calcite,Talc(uncoated)Q 0 2xTalc(uncoated)A 3xTalc(coatecl)V 4xCalcite(uncoated)< 0 SxCalcite(coated)

I O Steady Shear Viscosity q 6xCalcite,Talc(coated)

E O Complex Viscosity

ill i i i i i ml i i i i i ml » » mil t i i i mil | [ 1 j llll10-3 10-2 10-1 10° 101 102 103

co (rad/s ) /Shear Rate (sec ~)

1.24 Comparison between complex viscosity andshear viscosity of PP/fillers as a function of frequency/shear rate at 210°C


1 8 5

The Cox-Merz relation also fails in the stearic acid added

talc, calcite, and talc/calcite filled system. The failure

of the Cox-Merz relation for small particle filled polymer

melts was first reported by Nakajima et al. (274, 275).

Later Suh (6i5) reported the failure of the Cox-Merz relation

from 40 v% talc-PP and talc-PPS compounds.

Clearly, the resistance to flow for small strains is

much larger than for large amplitude flows. It is clearly

associated with forces between the particles of the talc,

calcite, and talc/calcite network.

4.3.7 Comparison Between Talc Particle Filled System and

Calcite Particle Filled System

Figure 4.25 exhibited the comparison between talc and

calcite particles at the same loadings in a polystyrene (PS)

filled system. The talc particle exhibited higher viscosity

level than the calcite at low shear stress range but

exhibited a lower viscosity level at high shear stress

range.


1 8 6

1010 |-rr rmnj— i i rmi— i i i iimii— i i i niiij— i i i unij— i i mm|— mrrr

COCDCL

COooCO>

109

108

107

106

105

104

103

102

□ 95 :05A 90: 10 V 80:20 O 60 :40

0 PS (200°C)I □ PS/TALC■ PS / CALCITE1 i i mill I i i mill i ' ' mill i i i mill i i i i mill I I I null

10° 101 102 103 104 105 106 107SH EA R S T R E S S (P a)

Figure 4.25 Viscosity as a function of shear stress fortalc and calcite filled system at 200°C


1 8 7

M e c h a n i s m

The mechanism of yield value in particle filled

compound melts is considered to be particle-particle

interaction, which leads to agglomeration and formation of

3-dimensional network structures. Similar explanations are

widely discussed in the literature (108, 114, 120, 129, 230,

232) also. These compounds form such structures due to

particle-particle interaction above critical concentration.

The 3-dimensional network structures of talc compounds

should depend upon direction. This anisotropic

characteristics of the talc particle leads to different

yield values with stresses being applied to different

directions.

Direction dependence of yield values for plastic

deformation of anisotropic solids has been reported in the

literature for metals and solid polymers (259-262) . The

results indicate the high dependence of yield values with

direction. Figure 4.25 may represent above phenomenon for

talc and calcite compounds.


CHAPTER V

ELONGATIONAL FLOW RHEOLOGICAL MEASUREMENTS

5.1 Introduction


the elongational rheological properties of talc, calcite and

mixed particle compounds of polystyrene. Our uniaxial

extension flow study includes (i) elongational flow in a

silicone oil bath (SBM), (ii) elongational flow in a heated

chamber containing nitrogen gas (NCM).

The studies presented in this chapter are based upon

the polystyrene(PS) compounds described in Chapter 4.

188


5.2 Results1 8 9

5.2.1 Silicone Oil Bath Elongational Flow (SBM)

5.2.1.1 Polystyrene (PS)

The elongational viscosity of PS system is shown as a

function of (a)log time/(b)linear time at various elongation

rates in Figure 5.1a,b. For the system Figure 5.1a the

elongational viscosity was independent of time at long

times. The steady state asymptotes of the values of

elongational viscosity are considered to be the steady state

elongational viscosity.

The transient elongational viscosity increases and

reaches a steady state and then decrease with time at low

stretch rate. The decrease of elongational viscosity

behavior is due to the exponential reduction of filament

cross-section area at constant stretch ratio. After the

steady state, in the long time, the values of elongational

viscosity seem to decreases. This behavior probably means

the beginning of filament failure.


Visc

osity

(P

a.s)

V

iscos

ity

(Pa

s)

1 9 0

103

10210-1

1 0 7 I — ' - r i-Tn n i : r i i . m f

106

105

104

10°

mi| i tii i:u| :— t i i rtty

O 5.038x1 o'4 (s’1) 3r i -4 -1 i^ 7.832x10 (S ) IA -3 -1^ 1.076x10 (V 2.320x1 O'3 -0 -3 -13.950x10 (S )

I i(s'1) 1

101 102

(a) Time (sec)

103 104

107

106

10s

104

1030 200 400 600 800

(b) Time (sec)

7.832x10 (s )1.076x1 o’3 (s'1) -2.320x1 o'3 (s'1) :

-3 -1 ■3.950x10 (S ) -

Figure 5.1 Elongational viscosity measurements of PSsystem at 200°C


5. 2.1.2 Calcite Compounds1 9 1

The elongational viscosities of 5, 10, 20, 40 v%

calcite filled PS compounded systems are shown as a function

of (a)log time, (b)linear time at various elongation rates

in Figures 5.2a,b, 5.3a,b, 5.4a,b, and 5.5a,b. For the

system Figures 5.2a, 5.3a, 5.4a, and 5.5a the elongational

viscosity was independent of time. The steady state

asymptotes of the values of elongational viscosity are

considered to be the steady state elongational viscosity.

The elongational viscosity increases and reaches a

steady state and then decreases with time at low stretch

rate.

Figures 5.6 and 5.7 summarize the elongational

viscosity as a function of elongational rate/stress for the

calcite filled systems. The steady state elongational

viscosity for the compounds usually decreases with increases

in elongation rate. The elongational samples of 40 v%

breaks before the elongational viscosity reaches a steady

state.

R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission

1 9 2

Figure 5.2

C0<0CL‘358(0>

5.038x10 (s )□ -4 -17 .8 3 2 x 1 0 (S )

A - 3 - 1“ 1 .076X 10 (S )

V 2.320x10"3 (s'1)O 3.950x1 O'3 (s'1)

106

-3

10210- 10° 101 102

(a) Time (sec)

103 104

COCOCL

CO8 S2 >

5.038x10 (s ) 7.832x10-4 (s'1) i Sxio ts'1) 2.320x1 O'3 (s'1) 3.950X10"3 (s '1)

10®

r

200 400 600(b) Time (sec)

800

Elongational viscosity measurements of PS/calcite (95/05 v%) system at 200°C


Figure 5.3

» 104 >

103

O - 4 - 1& 5.038x10 {s )n -4 -1U 7.832x10 (S )A 1.076x10‘3 (s’1) 1

- 3 - 1 1V 2.320x10 (s ) 1O a.osoxiois'1) :

102 10-1 10° 101 102

(a) Time (sec)

103 104

10®

^ 5.038x10 IS )— -4-1^ 7.832x10 (s )A -3 -1** 1.076x10 (S )

O 3.950x1 O' (s’ )

103 600 800200 4000(b) Time (sec)



Figure 5.4

CO8CO5 104

103

10210-

□t, o

10°

G□AVo

5.038x1 O'4 (s'1) 7.832x1 O'4 (s*1) 1.076x10"3 (s"1) 2.320x10*3 (s"1) 3.950x1 O'3 (s’1)

101 102

(a) Time (sec)

103

CO<0

CO8CO5

10®

200 400 600(b) Time (sec)

800



1 9 5

Figure 5.5

107

106

c/>« 10s■S'<n8 104

103

102

TTTTTTp

o

oV

o

5.038x1O'4 (s*1) 7.832x10"4 (s'1) 1.076x10*3 (s ')

V 2.320x1O'3 (s '1) 3.950x1 O'3 (s '1)

_1_■ ""ill__1 1 Li

o□A

o

10-1 10° 101 102 (a) Time (sec)

103 104

107

106

rr

<0CL105

104

103

Q

1

5.038x10-4 (s'1) □ 7.832x10-4 (s '1)^ 1.076x1 O'3 (s'1) V 2.320x1 O'3 (s'1) O 3.950x1 O'3 (s'1)

200 400(b) Time (sec)

600 800



1 9 6

Figure 5.

109# PS□ PS / CALCITE (95 : 05 V%) A PS / CALCITE (90 : 10 V%) V PS / CALCITE (80 20 V%) <3> PS / CALCITE (60 40 V%)

106

10°10-6

ELONGATION RA TE ( s e c '1)

6 Elongational viscosity as a function ofelongational rate for calcite filled system at 200°C


1 9 7

C O

C L

U J

109

108

=— i—i i~rm rj----- 1—i ii i ni|----- 1—i i 11 nij i i rn ni| i r r m i

C O 107OoC O > 106 _l < z oF 105 <CD

104

103

E E J L

PS□ PS/CALCITE (95 A PS/CALCITE (90

PS/CALCITE (80 <$> PS/CALCITE (60

05 V%)I 10 V%L_ 20 V%) \40 v%):

■ I I I I m l I I m i n i i i i i i m l i i i l i i i i I i i i m i l l

10° 101 102 1 03 1 04 1 05

ELONGATION S T R E S S (P a)

Figure 5.7 Elongational viscosity as a function ofelongational stress for calcite filled system at 200°C


198

Table 5.1 Elongational yield values of particle filled PS at200 °C

Compounds(Composition)

Silicone Bath 'Apparent'

Elongational Yield value (SBM) Yei.apo

Nitrogen Bath Creep

Elongation Yield value

(NCM) YeiPS/Talc no no(95:05)PS/Talc no no(90:10)PS/Talc < 287 221-487(80:20)PS/Talc < 1946 2977-10864(60:40)




PS/Calcite < 1900 770-2961(60:40)





PS/Talc/Calcite < 1939 2682-6486(60:20:20)

R eproduced with perm ission o f the copyright owner. Further reproduction prohibited without perm ission

1 9 9

The result for the silicone oil bath method (SBM)

suggests by extrapolation an elongational flow yield value

for 0.4 volume loading of calcite was 1900 Pa. Table 5.1

summarizes the elongational yield values.

5 . 2 .1. 3 Talc Compounds

The elongational viscosities of the 5, 10, 20, 40 v%

talc filled PS compounded systems are shown as a function of

(a)log time, (b)linear time at various elongation rates in

Figures 5.8a,b, 5.9a,b, 5.10a,b, and 5.11a,b respectively.

The elongational samples of the 40 v% breaks before the

elongational viscosity reaches a steady state. For the

system Figures 5.8a, 5.9a, 5.10a, and 5.11a the elongational

viscosity was independent of time at long times. The long

time asymptotes of the values of elongational viscosity are

considered to be the steady state elongational viscosity.


viscosity as a function of elongational rate/stress for talc

filled system.


200

Figure 5 .8

107

106

W«S 10sQ_

v>OOcfl 104

103 r

10210-1

□ <#

o□AV

3-i

45.038x1 o '4 (s'1) 7.832x1 O'4 (s’1)1.076x10*3 (s"1) -= 2.320x10*3 (s'1)

O 3.950x1 O'3 (s'1)">»ll i- ' ' »»»»< '

10° 101 102 (a) Time (sec)

103 104

cn(OQ.£coooCO

10s

w 5.038x10 (s )Q 7.832x10"4 (s'1) A - 3 - 1^ 1.076x10 (s )V 2.320x1 O'3 (s'1)

- 3 - 1V 3.950x10 (s )

800600200 4000(b) Time (sec)

Elongational viscosity measurements of PS/talc (95/05 v%) system at 200°C.


Figure 5.9

v O -4 -1 |^ 5.038x10 (s )— i - 4 - 1 5u 7.832x10 (s ) ^^ 1.076x1o'3 (s'1) ;V 2.320x1 o'3 (s'1) _ / \ -3 -1 =<y 3.950x10 (s ) :

' » ' - ' i l i i i t iLJnl I I I f l l l l i I— i—I 11111

10-1 10° 101 102 103 104 (a) Time (sec)

COCO

Q_

Q 7.832x10 (s'

O 3.950x1o'3 (s '1) -

103 8006004000 200(b) Time (sec)

Elongational viscosity measurements of PS/talc (90/10 v%) system at 200°C.

CO

§ 104

103


103

10210-1 10°

□□o

5.038x10 (S ) 37.832x10 '4 (s"1) ]

-3 -1 |1.076x10 (S ) J

- 3 - 1 3 2.320x10 (s ) 33.950x10-3 (s '1) 1

101 102 (a) Time (sec)

103 104

107 T

co0.

CO8CO>

106

£ 10s

104

103

□o

-4 -15.038x10 (S j

-4 -17.832x10 (S )1.076x1 O'3 (s '1)2.320x10‘3 (s '1)3.950x1 o"3 (s '1)

200 400 600(b) Time (sec)

800

Figure 5.10 Elongational viscosity measurementsPS/talc (80/20 v%) system at 200°C.


2 0 3

e-|| *?£££▼ LaS-H-AS©^*;©^?©©1

107 F

106

m 10s a.i

i 104 >

103 k-

102

Q

V

i i i m p 1 t i i i mi j i i m mj |

A

- 4 - 1U 5.038x10 (s )r i - 4 - 1^ 7.832x10 (S )^ 1.076x1 O'3 (s'1)V 2.320x1 O'3 (s'1)O 3.950x10‘3 (s '1)

10-1 10° 101 102 103(a) Time (sec)

i

j104

£ 105

-4 -1^ 5.038x10 (S )r-l -4 -1^ 7.832x10 (S lA - 3 - 1 - s^ 1.076x10 (S ) 3V 2.320x10'3 (s '1) jO 3.950x1 O'3 (s '1) "

200 400 600(b) Time (sec)

800

Figure 5.11 Elongational viscosity measurements ofPS/talc (60/40 v%) system at 200°C.


2 0 4

The results of the silicone oil bath method (SBM)

measurements 'suggest' apparent elongational flow yield

measurements for 0.2 volume loading of talc of order 290 Pa,

and for 0.4 volume loading of talc was the larger of order

1950 Pa. Table 5.1 summarizes the 'suggest' elongational

yield values.

5.2.1.4 Talc / Calcite Compounds

The elongational viscosities of 05/05, 04/12, 10/06,

10/12, 20/20 v% mixed particle talc/calcite filled PS

compounded systems are shown as a function of (a) log time,

(b)linear time at various elongation rates in Figures

5.14a,b, 5.15a,b, 5.16a,b, 5.17a,b, and 5.18a,b. The

elongational viscosity increases and reaches a steady state

and then decrease with time at low stretch rate.

For the systems of Figures 5.14a, 5.15a, 5.16a, 5.17a, and

5.18a the elongational viscosity was independent of time at

long times. The long time asymptotes of the values of

elongational viscosity are considered to be of steady state

elongational viscosity.


2 0 5

The steady state elongational viscosity for the

talc/calcite compounds usually decreases with increases in

elongation rate. The elongational sample of 0.2/0.2 volume

loading of talc/calcite filled system breaks before the

elongational viscosity reaches a steady state. This

behavior implies the filament failure.


viscosity as a function of elongational rate/stress for talc

filled systems.

The silicone oil bath method (SBM) elongational flow

measurements suggest apparent yield values for the 0 .2/0.2

volume loading of talc/calcite of 1900 Pa. The steady state

elongational viscosity for the talc/calcite compounds

decreased as elongation rate increases. Again Table 5.1

summarizes the elongational yield values.


2 0 6

Figure

□ PS / TALC (95:05 v%) -A PS/TALC (90 : 10 v%) IS? PS / TALC (80 : 20 v%) -<£> PS / TALC (60 : 40 v%)

CO(6

EE □ □

10°

ELONGATION R A T E (S '1)

.12 Elongational viscosity as a function ofelongational rate for talc filled system at 200°C


2 0 7

1010

109

108

COa 107

£ 106COOGO 105 >

104

103

102

£ r r i i t iiti— i i i i inij— i i i i iuij— i 11 n n i |— i i im r i ] i i 11mij i i m i ?

03

□ PS/TALC (95 A PS/TALC (90 S-/ PS/TALC (80 <3> PS/TALC (60

05 v%)10 v%) - 20 v%)40 v%)

I I I mill i I I I i l l mil i i l 'Hill i i i mill i i I I I I mil

10° 101 102 1 03 1 04 1 05 1 06 1 07ELONGATIONAL S T R E S S (P a)

Figure 5.13 Elongational viscosity as a function ofelongational stress for talc filled system at 200°C


2 0 8

107 - IT] ! I I 1 III]

(0(0Q.inoo(0

106 r

10s

104

103

10210-

o

10° 101 Time (sec)

0 5.038x1 o"4 (s'1)□ 7.832x1 o"4 (s'1)□ 1.076x1 O'3 -1

(S )V 2.320x1 O’3 -1

(S )o 3.950x1 O'3 -1

(S )! J mi 1 I 1 1 Ultl :

102 103 104

toCL

tnooin

107

106

2* 10s

104

103

^ O O r

200 400Time (sec)

5.038x1 O'4 (S*

7.832x1 o"4 (S* 3 1.076X1 O'3 (s'V 2.320x10*3 (s' O 3.950x1 O’3 (s'

600

Figure 5.14 Elongational viscosity measurements ofPS/talc/calcite (90/05/05 v%) system at 200°C.


8 io4 </>

103 r

102IQ- 100

0□AVo

5.038x1 o"4 (s '1) 7.832x10"”* (s '1) 1.076x10"3 (s '1) 2.320x10*3 (s '1) 3.950x10"3 (s'1)

1 0 1 102

Time (sec)

103 10“

1e+7

1e+6'35*(0a

1e+5tnootn>

1e+4

1e+30 200 400 600

Time (sec)

mV

o 5.038x10 (s" ) .S 7.832x1 o"4 (s"1)A - 3 - 1^ 1.076x10 (s )T77 “3 *1V 2.320x10 (s )

-3 -1 V 3.950x10 (s



210

107

t106

CO

s. io=CO8 104OT

103

102 aulL10- 10°

"T TTllip'

o

.038x10 (s )□A

7.832x10"4 (s’’)1.076x10"3 <s’1)_3 -y _

V 2.320x10 (s’ ) j O 3.950X10’3 (s’1)

101 102

Time (sec)103 104

107

COreo.COoo(0

106

£ 10s

104

103

M

oO□AVo

-c -1 5.038x10 (s )7.832x1 O’4 (s*1) '1.076x1 O*3 (s’1)2.320x1 O'3 (s’1)

-3 -1 3.950x10 (s )I ■ ' ' '200 400Time (sec)

600

Figure 5.16 Elongational viscosity measurements ofPS/talc/calcite (84/10/06 v%) system at 2 00°C.


211

r r 11 h i m i i i rrmj- t—r r i m i j i—rr rm T j-

g 105 >*S 104 fern p>

103

102

o V

n - 4 - 1U 5.038x10 (S ) 3r*l -4 -1^ 7.832x10 (S ) JA - 3 - 1^ 1.076x10 (S )V 2.320x1 O'3 (s'1)O 3.950x1 O'3 (s'1)

"' li «tmi___ L.,1 { 11

10-1 10° 101 102 1 03 1 04

Time (sec)

1e+7 e i r

1e+6

~ 1e+5

1e+4

1e+3

COCO

*c758CO>

Q q 23SG

I- Srs - 4 - 1- 5.038x10 (S )

2 7.832x1 O'4 (s '1) A 1.076x1 O'3 (s’1) V 2.320x1 O'3 (s '1) 0 3.950x1 O'3 (s '1)

200 400

Time (sec)

600



212

107 e-r-

106

<n« 10s Q_

CO8 104

103 -

102

t t t i iii "~i—r-r 11 n n 1 i m i mi ( i i 11 mi

oV□VA

- 4 - 1^ 5.038x10 (s )n - 4 -1u 7.832x10 (s )A 1.076x10"3 (s ')V 2.320x1 O'3 (s‘1)O 3.950x1 O'3 (s '1)

■ i mil ■ i i ■ < ■ i ml

10-1 10° 101 102 103 104 (a) Time (sec)

106

3 1V 2.320x10' (s' ) j/S -3 -1 fV 3.950x10 (s ) ]

8006004002000(b) Time (sec)

Figure 5.18 Elongational viscosity measurements ofPS/talc/calcite (60/20/20 v%) system at 200°C .


2 1 3

COCOQ_

COOOCO>

<ozo—ILU

109

10®

107

10®

10s

104

= I— 1 | | 11 Uj I I I I I 1111 I I I T 11111 i i I i 11111 i i i i t i II j i i t 1 11 d

□ PS / TALC / CALCITE (90:05:05 V%)A PS/TALC/CALCITE (84:04:12 V%) -^ PS/TALC/CALCITE (84:10:06 V%) ^<3> PS/TALC/CALCITE (78:10:12 V%) E0 PS/TALC/CALCITE (60:20:20 V%)

103

00

i i i 11 m l i i i 11 ml i i i 11 m l i i i i m i l i i i 11 m l i i i i m i

10-e 10-s 10-4 10-3 IQ-2 10- 10°

ELON G ATIO N RATE (s e c )

Figure 5.19 Elongational viscosity as a function ofelongational rate for talc/calcite filled system at 200°C


2 1 4

109

S 108

C O 107ooC O> 106 _l < z op 10s <CD

3 104LU

10310° 101 102 1 03 1 04 1 0s

ELO N G A TIO N S T R E S S (P a)

T— TTTTTTT]--------- 1— TTTTTTTj 1 I I I I 1111 I I l I I II11 i 1 i m i l

□ PS /TALC /CALCITE (90:05:05 V%) ;A PS / TALC / CALCITE (84:04:12 V%) -^ 7 PS / TALC / CALCITE (84:10:06 V%) -<0> PS / TALC / CALCITE (78:10:12 V%) :0 PS / TALC / CALCITE (60:20:20 V%) ;

i i i i 11 i l l i i i i i m l i i i i i m l i i t i u n i i i i i n n

Figure 5.20 Elongational viscosity as a function ofelongational stress for talc/calcite filled system at 200°C


5.2.2 Nitrogen Bath Elongational Flow (NCM)2 1 5

5.2.2.1 Polystyrene (PS)

We could not make measurements of the elongational

behavior because the PS filament samples failed in all the

experiments, no matter how small the applied load. This

indicates that polystyrene does not exhibit a yield stress

in elongational flow.

5.2.2.2 Calcite Compounds

The nitrogen gas chamber method (NCM) elongational flow

yield studies indicates that filament samples with 5, 10,

and 20 volume percent calcite fail as did the polystyrene.

However the 40 volume percent sample behaved as if it was a

solid at low applied stresses.


measurements indicated that for the 0.4 volume loading

calcite sample, the yield stress was 770-3000 Pa (see Table

5.1) .


5 .2.2.3 Talc Compounds2 1 6

The 0.05 and 0.10 volume loading talc compounds behaved

as did the similar low concentration calcite compounds.

They failed in all experiments.

The 0.2 and 0.4 volume loading compounds exhibited

different behavior. They responded as soft solids at low

stresses.


measurements indicated that for the 0.2 volume loading talc

sample, the yield stress was 221-487 Pa and for the 0.4

volume loading talc it was about 3000-10,864 Pa (see Table

5.1) .

5.2.2.4 Talc/Calcite Compounds

The mixed particle compounds with composition

0.05/0.05, 0.04/0.12, 0.10/0.06, and 0 .10/0.12 all failed in

all elongational flow experiments. These materials would

seem not to have yield value.


yield measurements indicated that for the 0 .2/0.2 volume


2 1 7

loading talc/calcite the elongational yield stress was about

5400-6500 Pa (see Table 5.1).

5.3 Discussion

5.3.1 Polystyrene (PS)

5.3.1.1 Comparison To Shear Viscosity And Earlier

Investigation

From Figure 5.21 for the PS melt, the ratio [ ei/ s] is

about 3 at low deformation rates and increased at higher

rates.

Experimental studies of uniaxial elongational flow

behavior of polymer melts in which stable elongational flow

is found generally show that at low stretch rates the

elongational viscosity goes asymptotically to three times of

shear viscosity (263, 265-267). This is identical to

Trouton' theoretical and experimental result for Newtonian

fluids (268). Ide and White (263), Munstedt (264), and

Vinogradov (266, 267) investigated PS melt systems and found

them to exhibit this behavior. Our results indicate an


2 1 8

elongational viscosity which is three times higher than

shear viscosity. It has a value of 30xl03 Pa.S as opposed

to a shear viscosity of 9xlOJ which shows good agreement

with the previous researches cited above.

5.3.2 Talc Compounds

5.3.2.1 Estimation Of Yield Values From Nitrogen Bath

Method (NCM)

Batchelor (94) and Goddard (103) explained that the

elongation viscosity function decreases as a function of

extension rate. In elongational flow, the fibers are

parallel to each other. They move past each other as the

filament is stretched, creating a shearing flow between the

parallel fibers, which are sliding each other.


2 1 9

<Zof-<CDzo_lLLJXsXCO

106 F-CO(dCL

CO 10s O O CO>

104 -

103 -

— i i m 111 i— i— i i i 1111 i i i i i i rri i i i i t 11,

o % © o

o O o o oo o

; O PS Shear Viscosity

O PS Elongational Viscosity(SBM)

102 I I I I I I III L I L1 I f i l l I I I I I I I I I______ I I I 1 I t It

10° 101 102 103 104

SH EAR/ELON GATIO NAL S T R E S S (P a)

Figure 5.21 Shear/elongational(SBM) viscosity as afunction of shear/elongational stress rate for PS at 200°C


220

The elongational flow of polymer melts filled with

small particles have been investigated by White and his

students (106, 135, 272). In studies of carbon black (106,

272)r calcite (135, 272), and titanium dioxide (135) filled

melts, the elongational viscosity function was found to

exhibit a yield value. Lobe and White (106) found Yei is

1.2Ys for their carbon black filled polystyrene melt. The

studies of Tanaka (272) and Suetsugu (135) with White find

that Yel is about 1.8 Ys for several compounds that they

studied.

We compared the nitrogen gas filled chamber method

elongational yield stress and the shear yield stress. When

we compared elongational yield values measured from the

nitrogen gas bath method and shear yield values from

threshold values, the values of Yei/Ys at 0.2 volume loading

talc compound system gives 9.8 and Yei/Ys at 0.4 volume

loading talc compound system gives 10.0. The values of

Yei/Y3 for talc filled systems are higher in the 0.4 volume

loading than the 0.2 volume loading.

Table 5.1 summarizes elongational yield values.


2215.3.2.2 Comparison Of Silicone Bath Data To Shear

Viscosity

We plot the elongational (SBM) and shear viscosity

variation with talc volume loadings as a function of

shear/elongational rate/stress in Figure 5.23 and Figure

5.24 using the traditional method (silicone oil bath

elongational method) . The values of at a stretch and

shear rate of 0.001 (sec-1) are 4.8 at 0.05 volume loading,

3.6 at 0.1 loading, 0.9 at 0.2 loading, and 0.2 at 0.4

loading talc. The elongational viscosity exhibit unusually

lower values than shear viscosity especially at higher

loadings (0.2, 0.4). This peculiar behavior suggested

further investigation of the talc particle's absorption of

silicone oil.

We also compared the apparent yield stresses determined

by extrapolation. The values of Yei,app/Y3,app at 0.2 volume

loading talc compound system gives 0.4. The value of

Yei,app/Ys,app at 0.4 volume loading talc is 0.8. These are

also anomalously low.


222

5.3.2. 3 Investigation Of Silicone Oil Absorption

We immersed talc compounds into 200 °C silicone oil for

three minutes and measured the sample's weight changes.

Talc compounds absorbed silicone oil up to 18.5 wt%.

Calcite compounds absorb oil up to 9.6%. And talc/calcite

compounds absorb oil up to 14.5%. Table 5.2 summarizes the

talc, calcite, and talc/calcite compounds' silicone oil

absorption.

This absorption of silicone oil seems to be the reason

why the talc compound viscosity exhibited the low values of

rlel/rl3 based upon silicone bath measurements.


2 2 3

CO(0

CL

COOOCO>

oH<oZo—IUJQCsXCO

o11O1009

08

07

06

05

04

o3o2o10°

11 nuiij ~i i imuj "ninifl| imiu~i iinnj lining i iiinii|' i iiinii| iTiitiiq lining lima□ PS/TALC (95 : 05 V%) _j A PS/TALC (90:10V% ) \ V PS/TALC (80 :20V % )1 O PS / TALC (60 : 40 V%) -

" □ Shear Viscosity

- □ Elongational Viscosity(SBM)

i i mini i i niial i i mill i i mill iimJ imJ i mini iiimnl iniiiiil i i iiniJ iiimh

10’7 10"6 10'5 10"410'3 10‘2 10'1 10° 101 102 103 1 04SHEAR/ELONGATIONAL R A TE ( s e c '1)

Figure 5.23 Shear/elongational(SBM) viscosity as afunction of shear/elongational rate for talc filled system at 200°C


2 2 4

COCOQ.

COOOCO>_l<zoI-<CDzo—ILUi r

xCO

1010

109

108

107

106

105

104

= i 111mi|— r m u ii|— i 11 iiiiii— i 11 niiij— r r r m n j — i 11 niiij i 11 unij m riia

□ PS / TALC(95:05)A PS/TALC(90:10)V PS / TALC(80:20) o PS / TALC(60:40)

a 103

102

=_ A Shear Viscosity

A Elongational Viscosity(SB' I I mill i i I mill i i m i n i i i i mill i l m i n i i ll ll ll 1 I I mill— I LI l ll lt

10° 101 102 1 03 1 04 1 05 1 06 1 07 1 08

SHEAR/ELO N GATIO NA L S T R E S S (Pa)

Figure 5.24 Shear/elongational(SBM) viscosity as afunction of shear/elongational stress for talc filled system at 200°C


2 2 5

Table 5.2 Silicone oil absorption from compounded material

Material Weight Increase (%)PS/Talc 3.7(95/05)PS/Talc 4.9(90/10)PS/Talc 11.8

(80/20)PS/Talc 18 . 5(60/40)

PS/Calcite 3.1(95/05)

PS/Calcite 3.9(90/10)

PS/Calcite 6.2

(80/20)PS/Calcite 9.6(60/40)

PS/Talc/Calcite 4.3(90/05/05)


PS/Talc/Calcite 7 . 6(84/10/06)

PS/Talc/Calcite 8 . 9(78/10/12)



2 2 6

5.3.2.4 Shear Flow Characterization of SBM Elongational

Flow Specimens

We carried out shear flow measurements using

elongational specimens to investigate silicone oil

absorption effect on the rheological behavior. We ploted

the elongational (SBM) and shear viscosity measured from the

elongational flow specimens as a function of


5.26. We see that shear viscosity shift downward by about

one decade.

In this system, elongational viscosity exhibits a

higher viscosity level than shear viscosity. From Figure

5.25 for the talc-filled compounded systems the values of

^ei/^s =2.2 for 0.2 talc loading system and =1.8 for

the 0.4 talc loading system. These values are close to that

found for Polystyrene and what would be expected for a

system exhibiting a von Mises yield value.


2 2 7

COcdCL

<Zo

108

107

coOo 106 co>

105

<o 104

LU£ 103 <LU X CO

102

I I I I llllj I I I Mlllj 1 I I 11II1J 1 I I iilJIJ TTTTTTTT] I T'l JIIH

v PS/Talc (80:20 v%) I

O PS/Talc (60:40 v%) 1

% 0

V ^7 OV v o

oV v O

V < > /N

E V Shear Viscosity of SBM Samples

o

- V Elongational Viscosity(SBM)i i i mill i i i i mil ml ' ' ' "ml I I I I lllll I -LI I III

10'5 10-4 10-3 10-2 10-1 10° 101

SHEAR/ELONGATIONAL RATE ( s e c 1)

Figure 5.25 Shear(SBM)/elongational(SBM) viscosity as afunction of shear/elongational rate for talc filled system at 200°C


2 2 8

cocda.

108

107

=” “ l— I I I l l l l | " I I l 11 M!j I I I M 1111 i i I i u i i j i ' i" i i i i i i j I TTTTTS

coO0 106 co>1 105o

g 1040—ILU

1 103LU

W 102

$

v PS/Talc (80:20 v%) - O PS/Talc (60:40 v%) 1

oV v £ v O

%

V Shear Viscosity(SBM) =

V Elongational Viscosity 'i i i i mil i i i i mil i i i i mil i ii mill i i i mill I I I I 111!

101 102 103 104 10s 106 107 SHEAR/ELONGATIONAL STR ESS (Pa)

Figure 5.26 Shear(SBM)/elongational(SBM) viscosity as afunction of shear/elongational stress for talc filled system at 200°C


2 2 9

We compared silicone oil bath apparent elongational

yield stresses and the apparent shear yield stress from

elongation specimens. The values of Y el,app /Ys ,SBM 3 t 0 . 2

volume loading talc compound system gives 1.3 and Yei.app/Y3,SBM

at 0.4 volume loading talc compound system gives 0.5

respectively. These extrapolated results determined from

apparent yield stresses should not be considered

particularly accurate.

5.3.3 Calcite Compounds

5.3.3.1 Estimation Of Yield Values From Nitrogen Bath

Method (NCM)


elongational yield stress and the previously determined

shear yield stress. The values of Yei/Ys at 0.4 volume

loading calcite compound system gives 2.4. Comparing with

silicone oil bath method, 0.4 volume loading calcite system

did not change in Yei/Y3 ratio considerably.


2 3 0

5.3.3.2 Comparison of Silicone Bath Data to Shear

Viscosity

We plot the elongational (SBM) and shear viscosity with

calcite volume loadings as a function of shear/elongational

rate/stress in Figure 5.27 and Figure 5.28.

From Figure 5.27 for the calcite-filled compounded

systems the values of ^ei/^s are 10 at 0.05 loading, 10 at

0.1 loading, 0.5 at 0.2 loading, and 0.6 at 0.4 loading of

calcite particle. High loadings of calcite (0.2, 0.4)

compounds showed an elongational viscosity lower than the

shear viscosity. This result suggests investigation of

silicone oil absorption of calcite particles..

We also compared silicone oil bath apparent

elongational yield stress. The values of Y ej.,app/Y3,app at 0 . 4

volume loading calcite compound system gives 0 .8 .


2 3 1

coCDCL

C/DOoC/D>

oH<oZo—IUJXsXCO

o11o 10

o90so7o6o5o4

o3

o2

o1

rnimij— n m ;i iiiimij lining lining i 11 iiiii i riiiiiij i iimiij i niiii n.iuiij i hub

0°

□ PS/CALCITE (95 A PS/CALCITE (90 V PS/CALCITE (80 O PS/CALCITE (60

05 V%) -j 10 V%) : 20 V%) 1 40 V%)

□ Shear Viscosity

□ Elongational Viscosity(SBM)i mini i "'miill I III Mill i 11 mill i 11 mil I 11 mill i miinl i 11 mnl i i iimJ iniiiiil i mi

10-7 10-6 10-5 10-4 10-3 10-2 10-1 10° 101 102 103 104-1.

SH EAR/ELO NGA TIO NA L RATE (se c ')

Figure 5.27 Shear/elongational(SBM) viscosity as afunction of shear/elongational rate for calcite filled system at 200°C


2 3 2

COcoCL

1010

109

108

£ 107

b i i i mill— i i i'i nn|— tt

COOoCO><Zo

CDzoUJX

106

10s

104

fi 1°3XCO

102

TTTTTJ I ITI IlIIJ l I 11 mij TTTTTTTTj TTTTTTH

□ PS / CALCITE (95:05) A PS/CALCITE (90:10)- V PS / CALCITE (80:20): O PS / CALCITE (60:40).!

□ Shear Viscosity

□ Elongational Viscosity(SBM)i i 11 hkI i iitmil i iiiiiiiI i i i ttttil i i i mill K4 ii mill I II III)

10° 101 102 1 03 1 04 1 05 1 06 1 07

SHEAR/ELONGATIONAL STRESS (Pa)

Figure 5.28 Shear/elongational(SBM) viscosity as afunction of shear/elongational stress for calcite filled system at 200°C


5.3. 3.3 Comparison To Earlier Investigations2 3 3

Our results ( Y e,app/Y3,ap p = 0 . 8 ) from traditional

measurements showed considerable disagreement with earlier

investigations (1 0 7 , 1 3 8 ) of elongational flow of calcite

compounds whose values are close to the von Mises yield

surfaces {Ye/Ys= ^ ) (237) .

Calcite filled PS data from previous Tanaka and White's

(107) result (Ye/Y3=1.8), and Suetsugu and White's (138)

result (Ye/Y3=1.5). Even calcite particles' silicone oil

absorption effect is very small we believe they still lower

down the viscosity levels.

5. 3.3. 4 Investigation of Silicone Oil Absorption

We immersed calcite compounds into 200 °C silicone oil

for 3 min. and measured the sample's weight changes.

Calcite compounds absorbed silicone oil up to 9.6 wt%.

This seems the reason for the calcite compounds

viscosity order being reversed compared to shear (NCM)

viscosity measurements. This is again silicone oil affect

on the particles.


2 3 4

5.3.3.5 Shear Flow Characterization Of SBM Elongational

Specimens

We plot the elongational and shear viscosity with

calcite volume loadings as a function of shear/elongational

rate/stress in Figure 5.29 and Figure 5.30. Elongational

specimens were modified to cone-plate samples using a

compression mold (see Figure 3.5). Then we investigated

shear flow measurements using elongational specimens.

From Figure 5.29 for the calcite-filled compounded

systems, the ratio of the apparent rlel/Tls are 2.2 at 0.2

loading, and 1.8 at 0.4 loading calcite particles.

We compared the silicone oil bath elongational yield

stress and shear yield stress of the samples produced in the

silicone oil bath Yei,app/Y3,sEM at 0.4 volume loading calcite

compound system gives 1.9. The shear yield value was

estimated for elongational flow specimens.


2 3 5

CO(0

CL

10®

107

=””I—MM lllj “I—t “TTTTirj I i i 11 i i 11 i i i uiii| i i l 111H j I i i i i fb

COoa io6 >

2 1050

1 wOLU| 103LUXCO

102

□ PS/Calcite (80:20v%) A PS/Calcite (60 :40v% )^

A A

A□ A a A A

□ D □ A□ □ Ad d

E □ SBM Sample Shear Viscosity

- □ Elongational Viscosity(SBM)I i i i mil I I l l I i i mill I i i i mil I I II mil I I i I m i l

10-5 10-4 10-3 10-2 10-1 10° 101SHEAR/ELONGATIONAL RATE (se c 1)

Figure 5.29 Shear(SBM)/elongational(SBM) viscosity as afunction of shear/elongational rate for calcite filled system at 200°C


_ 109 co

£ 108 £8 107 o co><zo

106

10s

< 10"

103o—I LUX2 102XCO

101

i i i m iij— i i i n iiij— i r1 1 in ij— i T m T n j— i i i i i i i i |— i i i i i i i i |— r r T r r r e

□ PS / Calcite (80 : 20 v%) :A PS/Calcite (60:40 v% )l

&&

V

^ □ SBM Sample Shear Viscosity

□ Elongation Viscosity(SBM)I i ' mill i i ' mill i ' I i mil i I I ' i ' : mil I I 1 mill LI 11II

10° 101 102 103 104 105 106 107

SHEAR/ELONGATIONAL STRESS (Pa)

Figure 5.30 Shear(SBM)/elongational(SBM) viscosity asfunction of shear/elongational stress for calcite filled system at 200°C


5.3.4 Talc/Calcite Compounds2 3 7

5.3. 4.1 Estimation of Yield Values from Nitrogen Bath

Method (NCM)


elongational yield stress and the shear yield stress. When

we compare elongational yield values measured from nitrogen

gas bath method (NCM) and shear yield values from minimum

threshold values, the values of Yei/Ys for 0.2/0.2 volume

loading talc/calcite compound system gives 9.5.

Table 4.1 and Table 5.1 summarizes shear and

elongational yield values.

5.3.4.2 Comparison of Silicone Bath Data to Shear (NCM)

Viscosity

We plot the elongational and shear viscosity of the

talc/calcite 0 .2/0.2 volume loadings as a function of


5.32 using traditional method.


2 3 8

When we compare elongational (SBM) viscosity and shear

viscosity at high volume loadings (0.2/0.2), the value of

Hei/Tls is 0.3. Similar behavior was found earlier for the

calcite and talc filled systems. This resulted in

investigations of silicone oil absorption on talc and

calcite particles.

We compared silicone oil bath apparent elongational

yield stress and the apparent shear yield stress, Ye:,app/Y3,acP

for the 0 .2/0.2 volume loading talc/calcite compound system.

The value is 0.6. Talc/calcite data shows lower than

calcite result.

5.3.4.3 Investigation of Silicone Oil Absorption

We immersed talc/calcite compounds into 200 °C silicone

oil for 3 minutes and measured sample's weight changes.

Talc/calcite compounds absorbed silicone oil up to 14.5 wt%.

Table 5.2 indicates talc particle compounds absorb

silicone oil more than talc/calcite particles and calcite

particle absorb less than talc/calcite particle compounds.


2 3 9

o PS / TALC / CALCITE (60:20:20 V%)

_J<z

zo_lLU £§ 104

XCO103

£ Shear Flow © Elongational Flow(SBM)

10°10-1

-1.SHEAR/ELONGATION RATE (sec )

Figure 5.31 Shear/elongational(SBM) viscosity as afunction of shear/elongational rate for talc/calcite filled system at 200°C


240

COCOCL

COOC_>CO><zoi-<o

UJa:<LUXCO

1 09 £ 1—I I rmi| 1 I I I l ll l j 1— I I i ' t l l l j 1— TTTTTTT]-------!— TTTTTTT] I I I I I l'(io PS / TALC / CALCITE (60:20:20 V%) :

108 t-

107 U

10® —

1 0 s -

104 -

° V

• •

0 Shear Row

© Elongational Flow(SBM)

103 i i i h i i i I i > i m i n i i i i i mi l i i i i i m l t _ i i li_li

101 102 103 104 105 10® 107

SHEAR/ELONGATION STRESS (Pa)

Figure 5.32 Shear/elongational(SBM) viscosity as afunction of shear/elongational stress for talc/calcite filled system at 200°C


2 4 1

5.3.4.4 Shear Flow Characterization of SBM Elongational

Specimens

We plot the elongational (SBM) and shear viscosity

(SBM) with talc/calcite 0.2/0.2 volume loadings as a

function of shear/elongational rate/stress in Figure 5.33

and Figure 5.34. Elongational specimens were modified to

cone-plate samples using a compression mold (see Figure

3.5). We investigated shear flow measurements using

elongational specimens.

From Figure 5.33 for the talc/calcite-filled compounded

systems, the ratio nel (*t*) /'Hg (§) is about 7.1 for 0.2/0.2

talc/calcite particle system. This system shows values

higher than von Mises theory.

We compared the silicone oil bath apparent elongational

yield stress and silicone oil bath method shear yield stress

Yei.app/YSlsBM at 0.2/0.2 volume loading from Figure 5.34. The

talc/calcite compound system gives 3.8.


2 4 2

COCOCL

107

C0o2 106 >z 10soh-<§ 104 oUJ£ 103sXCO

102

o PS/TALC/CALCITE (60:20:20 V%) :

oo

£ Shear Flow(SBM) :

- O Songational Flow(SBM)i i i i mil i i i 11 ml i i i 11 ml i i i i mil i i i 11 ml i i i 11 in

10-5 10 10-3 10-2 10-1 10° 101

-1,SHEAR/ELONGATION RATE (sec )

Figure 5.33 Shear(SBM)/elongational(SBM) viscosity as afunction of shear/elongational rate for talc/calcite filled system at 200°C


</)CD

CL

1 0 s e — i m i n i i |— i m n i t]— i i i i t t i i j— i "i 1111fT|— r n n n q — i i i I 'l iu

o PS /TALC /CALCITE (60:20:20 V%) I

1 0 7 lr

COO% 106 >

10s rO

<2 104

LU X 103

o

t^ E £ Shear Flow(SBM)

XCO102

. Q Elongational Flow(SBM)i i I ..... ill i i i i mil i i i i mil i i i 11 ml i i i i mi

10° 101 102 1 03 1 04 1 05 1 06

SHEAR/ELONGATION STRESS (Pa)

Figure 5.34 Shear(SBM)/elongational(SBM) viscosity asfunction of shear/elongational stress for talc/calcite filled system at 200°C


2 4 4

5.3.5 Conclusions

Because of silicone oil absorption we could not measure

the elongational viscosity behavior of talc, calcite, and

talc/calcite compounds using conventional instrumentation.

Measurements of elongational yield values for sure of the

compounds could be made in a chamber containing nitrogen

gas.

We estimated elongational yield values in two different

experiments. One is from a traditional silicone oil bath

filled elongational apparatus. The other measured

elongational creep as a function of applied force (tensile

stress) .

Previous researches (95, 106, 107, 114, 138) obtained

shear yield values from extrapolation using cone-plate (RMS)

and elongational yield values from silicone oil bath method

(SBM). Cone-plate shear yield values from extrapolation are

very close to high threshold yield values in our system.

Earlier investigation did not realize there could be

silicone oil absorption of calcite particles. The Ye/Ys

ratio of Tanaka and White (107) shows 1.8 for calcite filled


2 4 5

PS system. However the Ye/Y3 ratio of Suetsugu and White

(138) ranges from 0.25-1.53 for calcite filled PS system

which is low compared to von Mises yield ratio. However if

they knew the existence of minimum threshold stress their

ratio will be raised further.

0.4 volume loading talc filled system investigated in

the nitrogen bath method gave much higher elongational yield

values than 0.2 volume loadings of talc and same content of

calcite compound i.e.

for talc compounds

Y Y(4 0v%) ;2 . 9 - 10 a (2 0v% ) ;2 . 8 ~ 10 » V3Ys Ys

for calcite compounds

* S ~ 3Ys

The mechanism of the yield value seems to be particle-

particle attraction, which leads to aggregation and the

formation of gel structures.


2 4 6

Talc has higher BET surface area (16.5 m2/g) than

calcite (7 m2/g) at same average particle size. Higher BET

surface area gives higher contacting surface area to

polymer. So the high loading gives a higher yield value

than low yield value.

The particle loading dependence of elongational

viscosity indicates it increases with increasing loading and

decreasing elongational rate/stress.


C H A P T E R V I

WIDE ANGLE X-RAY DIFFRACTION (WAXD) CHARACTERIZATION

6.1 Introduction


talc and calcite compound composition analysis and talc

particle orientation using the WAXD technique. Composition

analysis was carried out using the Bragg angle x-ray

intensity method. The concentration of talc and calcite in

polystyrene were represented using the Alexander-Klug

equation (182) which is being applied to a mixed

crystalline particle and amorphous polymer system

apparently for the first time in our research. A

qualitative analysis of particle orientation was carried

out using the flat film method. A quantitative analysis of

particle orientation was determined using the pole figure

analysis method.

247


6.2 Results2 4 8

6.2.1 Composition Analysis of Particle Filled System

Using Bragg Angle X-ray Intensity

6.2.1.1 PS / Calcite System

Figures 6.1 to Figure 6.6 show the x-ray intensity

distribution of compounds of 0, 5, 10, 20, 40, and 100v%

calcite in a PS matrix. Figure 6.1 represents the

intensity distribution of PS as a function of 2®. Figure

6.7 summarizes the intensity distributions of calcite-PS

compounds with various loadings of calcite. We see in

Figure 6.7 the intensities of the (110), (211), (101 ),

(210) , and (200) crystallographic planes of calcite

particles for various calcite particle loadings. The

scattering intensity of the polystyrene is reduced with

increasing calcite loading.


20000PS

15000

o<uCO

c3

COca)

5000

i

10 20 30 40 50

29

Figure 6.1 Intensity distribution of polystyrene


2 5 0

20000PSCALCITE 5V% PS * 0.33

15000'oa>co"coc§ 10000

&coc<D *—* c5000

10 20 3020

40 50

Figure 6.2 Intensity distribution of PS and PS/calcite(5 v%)


2 5 1

2 0000

o0)to

c3ootocd)

PSPS/CALCITE (10 V%) PS*0.23

15000

10000

5000

40 5020



Inten

sity

(cou

nts/

sec)

2 5 2

Figure

20000 PS PS / CALCITE (20 V%) PS*0.14

15000

10000

5000

L.4j

403020 50

26

6.4 Intensity distribution of PS and PS/calcite(20 v%)


lity (c

ount

s/se

c)

2 5 3

20000

15000

10000

COc0)c5000

00


PSPS / CALCITE (40 V%) PS’0.06

4030 5020


Inte

nsity

(c

ount

s/se

c)

2 5 4

Figure

20000

(211)

15000

10000

5000 (210)(200)(101)

(110)

403020 50

20

6.6 Intensity distribution of calcite powder


Inten

sity

(cou

nts/

sec)

2 5 5

20000

15000

10000

5000

00

Figure 6.7 Intensity distribution of various calciteloadings

PS05% CALCITE10% CALCITE 20% CALCITE 40% CALCITE

16279 PS

4987 5%

30 40 5020


6.2.1.2 PS / Talc System2 5 6

Figure 6.1, Figure 6.8, Figure 6.9, Figure 6.10,

Figure 6.11, and Figure 6.12 show x-ray intensity

distribution of compounds of 0, 5, 10, 20, 40, and 100v%

talc in a PS matrix. Figure 6.13 summarizes the intensity

distribution of talc with various loadings of talc. We see

the intensities of the (001), (002/020), (003), (200/i^l),

(131/131), and (004) crystallographic planes of the talc

particles for various calcite particle loadings in Figure

6.13. The scattering intensity of the polystyrene is

reduced with increasing talc loading. As talc is added

into polystyrene (PS) the scattering intensity of the

polystyrene is modified as shown in Figure 6.13. Figure

6.8 shows the scattering intensity of 100% polystyrene

reduced to 55% at 5 v% talc-PS filled compound. Figure 6.9

shows the scattering intensity of 100% polystyrene reduced

to 40% at 10 v% talc-PS filled compound. Figure 6.10 shows

the scattering intensity of 100% polystyrene reduced to 23%

at 20 v% talc-PS filled compound. Figure 6.11 shows the

scattering intensity of 100% polystyrene reduced to 17% at

40 v% talc-PS filled compound.


2 5 7

20000 PS 100% PS/TALC 5V%

PS* 0.55

15000

o 10000

5000

50403020100

2 0

Figure 6.8 Intensity distribution of PS and PS/talc(5 v%)


2 5 8

20000 PS 100% P S/TALC 10V% PS ' 0.4

15000

oa>in«c38. 10000

c©c5000

—-'CL.50403020100

2 6



Inte

nsity

(c

ount

s/se

c)

2 5 9

2 0 0 0 0

PS 100% PS/TALC 20V%

PS * 0.23

15000

10000

5000

5020



2 6 0

20000 PS 100% PS/TALC 40V% PS *0.17

15000

o a> (n"35c3Oo 10000

</>c0)c5000

6050403020



2 6 1

30000(003)(001)25000

o 15000

£ 10000

(002+020)(131+131)5000

(200+131,(004)

40 503010 200

20

Figure 6.12 Intensity distribution of talc powder


2 6 2

80000PS

-to

c3outoca>

PS/TALC (5v%) PS/TALC (10v%) PS/TALC (20v%)

PS/TALC (40v%)

70000

60000

50000

40000

30000

20000

10000

300

4020 50

20

Figure 6.13 Intensity distribution of various talcloadings


6.2.1.3 PS / Talc / Calcite System2 6 3

Figure 6.22 through Figure 6.27 show x-ray intensity

distribution of compounds of PS/talc/calcite 90/05/05,

85:04:11, 54:03:43, 85:10:05, 78:10:12, 53:05:42, and

60:20:20 v% which has weight fraction of 88:12:14,

88:12:30, 88:12:178, 77:23:14, 77:23:30, 77:23:178, and

61:39:32 wt% each. Figure 6.28 summarizes the intensity

distribution of various loadings of PS/talc/calcite for

talc compounds 100:00:00, 88:12:00, 88:12:14, 88:12:30,

88:12:178 and Figure 6.29 summarizes 100:00:00, 77:23:00,

77:23:14, 77:23:30, and 77:23:178. The crystallographic

planes of the talc/calcite mixed particle occur in the

sequence of talc (001), talc (002/020), calcite (110), talc

(003), calcite (211), calcite (10^), calcite (210), and

calcite (200) with various loadings of talc/calcite

particles in Figure 6.28. The scattering intensity of the

polystyrene is reduced with increasing talc/calcite

loading. As calcite is added into PS/talc system the

scattering intensity of the polystyrene is modified as

shown in Figure 6.28 and Figure 6.29.


2 6 4

o<u10c3oo

25000

20000

15000

£ 10000©c

5000 \cah;lte (110V

PS/TALC/CALCITE(88:12:000 wt%)

PS/TALC/CALCITE(88:12:13.6 wt%)

PS/TALC*0.7

Iclte

10 20

calcite calcite calcite (101) (210) (200)

40

2 6

Figure 6.14 Intensity distribution of PS andPS/talc/calcite (90/05/05 v%)


Inte

nsity

(c

ount

s/se

c)

2 6 5

25000

20000

15000

10000

5000

PS/TALC/CALCITE (88:12:000 wt%) PS/TALC/CALCITE

(88:12:29.9 wt%)PS/TALC-0.4

t001 1003

t020

c 2 1 1

f" cm C101 c 2 1 0 C 2 p 0

40302020

Figure 6.15 Intensity distribution of PS andPS/talc/calcite (84/04/12 v%)


Intensity (

counts

/sec)

2 6 6

25000

20000

15000

10000

5000

PS/Talc/Calrite (88:12:000 wt%) PS/Talc/Calcite (88:12:177.9 wt%) PS/Talc'0.1

Icite11)

tali: calcite calcite calcite(1 0 1) (2 1 0) (2 00)

catch talc (110

(002/ 020 )

4535 403025

20

Figure 6.16 Intensity distribution of pS andPS/talc/calcite (54/03/43 v%)


Intensity (

counts

/sec)

267

25000

20000

15000

10000

5000

00

Figure 6.17

PS/TALC/CALCITE (77:23:000 wt%) PS/TALC/CALCITE (77:23:13.6 wt%) PS/TALC'0.50

talc(003)talc

(001)

calcite(211)

(002/II20)

calcite calcite calcite (10T)taic<210> <200>

(004)_

:alcite talc KiO) (112)

4540353025

29

Intensity distribution of PS and PS/talc/calcite (85/10/05 v%)


Inten

sity

(cou

nts/

sec)

2 6 8

25000

20000

15000

10000

5000

00

Figure 6.18

PS/TALC/CALCITE (77:23:000 wt%) PS/TALC/CALCITE (77:23:29.9 wt%) PS/TALC*0.39

calcite(211)

I20)calcite calcite calcite

(lOTjtalc*210) (200) ,(004)|-

ilcKe talc TO) (112)

4535 4030

20



Inten

sity

(cou

nts/

sec)

2 6 9

25000

20000

15000

10000

5000

00

Figure 6.19

5 10

talc(002/020)

talc(003)

-salcfte

calcite(211)

PS/TALC/CALCITE (77:23:000 wt%)PS/TALC/CALCITE (77:23:177.8 wt%)PS/TALC-0.18

calcite calcite calcite< 1 0 T ) t a l c « 2 1 0 ) ( 2 0 0 )

f (0°4),\wiT35 40 45



Inten

sity

(cou

nts/

sec)

25000

20000

15000

10000

5000

00

Figure 6.20

2 7 0

— PS— PS/Talc/Calcite

(88:12:00 wt%)— PS/Talc/Calcite

(88:12:13.9 wt%)— PS/Talc/Calcite

(88:12:29.9 wt%)— - PS/Talc/Calcite

(88:12:177 9 wt%)

calcite calcite calcite (101) taldt210> <200>

35 40 45

Intensity distribution of PS and various PS/talc/calcite (88:12: wt) loadings

talc (002/020)

/ • \

calcite

25 30

20


Inten

sity

(cou

nts/

sec)

2 7 1

25000

20000

15000

10000

5000

00

Figure 6.21

talc (002/020)

talc 1 (003)|J

calcite(211)

calcite' r , V o ) ( 1 1 2 )

PSPS/Talc/Caldte (77:23:00 wt%) PS/Talc/Calcite (77:23:13.6 wt%) PS/Talc/Calcite (77:23:29.9 wt%) PS/Talc/Caldte (77:23:177.8 wt%)

calcite calcite calcite(1 0 T )ta l< i(2 1 0 ) (2 0 0 )

(«*♦)-;-- — r

10 15 20 25 30 35 40 45

20

Intensity distribution of PS and various PS/talc/calcite (77:23: wt) loadings


4

2 7 26.2.2 Flat Film Measurements of Particle Orientation

6.2.2.1 Uniaxial Extrudates

Figure 6.22 shows x-ray film patterns of a 20v% talc

particle filled polystyrene system which has been extruded

from a 1.6 mm diameter capillary die (L/D=28.5). The

positions of the (001), (002 + 020), (003), (200 + 13]jf

(131+131), and (004) planes of talc particles on the film

patterns indicate the direction of orientation of the talc

particles relative to the flow direction '1'. The normals

to the surfaces of the talc particles are in the radial

direction and the talc particles are circumferentially

arranged.

Figure 6.23 shows typical x-ray film patterns of a

20v% calcite particle-filled polystyrene from the capillary

die extrudate. The (110), (211), (10^), (210), and (200)

planes of the calcite particles show no sign of

orientation.

Figure 6.24 shows a x-ray film pattern based on a beam

normal to a 10% PS/talc/calcite (90/05/05) capillary

extrudate.


2 7 3

(001)

(002)

(003)

Figure 6.22 Typical x-ray pattern of 20v% talc particlesfrom capillary extrudate (D=1.6mm, L/D=28.5)


2 7 4

«

X-ray

•t'=»- ND (3)

NO (3)

Figure 6.23 Typical x-ray pattern of 20v% calciteparticles from capillary extrudate(D=l.6mm, L/D=28.5)


2 7 5

— 0-X-ray "■ •0-.

FD(1)

-2»- ND (3)

ND (3)

Figure 6.24 X-ray pattern of PS/talc/calcite (90:05:05v%) system from capillary die extrusion (D=1.6mm, L/D=28.5)


2 7 6Other compositions (84:04:12, 84:10:06, 78:10:12,

75:19:06, 69:17:14, 60:20:20) were similar. They show the

mixture of the (001), (002/020), (003), (200 + 1

(131+131), and (004) planes of talc particles and the

(110), (211), (10l), (210), and (200) planes of the calcite

particles. It is noted that talc particle planes are not

clearly shown on the film due to calcite particle planes

intensity.

6.2.2.2 Compression Molded Sheets

Figure 6.25 shows x-ray pattern of the talc particle

for compression molded sheets for the 5, 10, 20, 40 v%

compounds. The x-ray beam is directed towards the edge of

the sheet. The normals to the (001), (002), and (003)

plane of the talc particles are concentrated in the

direction perpendicular to the surface of the molded sheet.

This indicates the discs are parallel to the direction of

flow in forming the molded sheet. The (002/020) plane

appears at Bragg angles intermediate between the (001) and

(003) planes. We can also see the (200/1 3l) and (131/131)

planes near the (002/020) planes.


(b) 10 v% (d) 40 v%

FD(1)

ND (3)

FD(1)

X-ray

Figure 6.25 Flow direction x-ray pattern of talcparticle filled system from compression molding (a) 5 v%, (b) 10 v%, (c) 20 v%, (d)40 v%


(a) PS/talc/calcite (90:05:05)

(b) PS/talc/calcite(84:04:12)

(c) PS/talc/calcite (d) PS/talc/calcite(84:10:06) (78:10:12)

Figure 6.26 X-ray pattern of PS/talc/calcite system fromcompression molding (a) 90:05:05 v%, (b)84:04:12 v%, (c) 84:10:06 v%, (d) 78:10:12v%, (e) 75:19:06 v%, (f) 60:20:20 v%


(e) PS/talc/calcite (75:19:06)

(f) PS/talc/calcite(60:20:20)

continued Figure 6.26

X-ray

FD (1)

ND (3)

FD (1)

X-ray pattern of PS/talc/calcite system from compression molding (a) 90:05:05 v%, (b)84:04:12 v%, (c) 84:10:06 v%, (d) 78:10:12v%, (e) 75:19:06 v%, (f) 60:20:20 v%


2 8 0Figure 6.26 shows x-ray patterns of PS/talc/calcite

compounds formed by compression molding. These are: (a)

90:05:05 v%, (b) 84:05:12 v%, (c) 84:10:06, (d) 78:10:12,

(e) 75:19:06, and (f) 60:20:20 using the WAXD flat film

method. We see the oriented (001), (002/020), (003),

(200 + 1 ^i) / (131+131), and (004) planes of talc particles

clearly.

6.2.3 Pole Figure Measurements

6.2.3.1 Capillary Die Extrudat.es

The flow direction (FD), normal direction (ND), and

transverse direction (TD) of capillary die extrudates

samples are equivalent to a flow direction (1-direction),

and two normal directions (3-direction) due to the symmetry

of the capillary extrudate and the flow.

A pole figure of the (001) plane for the talc compound

from the capillary extrudates is shown in Figure 6.27.

This pole figure indicates that the c-axis of talc

particles orient along the radial direction normal to the

extrudate surface. The symmetry axis of the capillary

extrudates is the flow direction.


TD2 8 1

(a)

Figure 6.27 The pole figures for the (001) plane of the5 v% talc compound from the capillary die extrusion experiment


6 . 2 . 3.2 Rectangular Die Extrudates2 8 2


transverse direction (TD) of rectangular extrudates samples

are equivalent to flow direction (1-direction), the

direction of velocity variation direction (2-direction),

and the transverse direction (3-direction).


from the rectangular extrudates is shown in Figure 6.28.

This pole figure indicates that the normals to the (001)

plane of talc particles are concentrated in the direction

perpendicular to the rectangular die wall. The discs, not

the normals, are parallel to the flow direction.

6. 2. 3.3 Slit Die Extrudates


transverse direction (TD) of the slit extrudates samples

are equivalent to the flow direction (1-direction), the

direction of velocity variation direction (2-direction),

and the neutral direction (3-direction).


from the slit extrudates is shown in Figure 6.29.


(b)

Figure 6.28 The pole figures for the (001) plane of the5 v% talc compound from the rectangular die extrusion experiment


2 8 4

ND

(a)

FD

(b)

Figure 6.29 The pole figures for the (001) plane of the5 v% talc compound from the slit die extrusion experiment


2 8 5This pole figure indicates that the normals to the (001)

plane of talc particles are concentrated in the direction

perpendicular to the slit die wall. The discs are parallel

to the flow direction.

6.2.3.4 Annular Die Extrudates


transverse direction (TD) of the annular extrudates samples

are equivalent to flow direction (1-direction), the

direction of velocity variation direction (2-direction) ,

and the normal direction (3-direction).


from the annular extrudates is shown in Figure 6.30. This

pole figure indicates chat the normals to the (001) plane

of talc particles are concentrated in the direction

perpendicular to the annular die wall and perpendicular to

the flow direction.


2 8 6

TD

(b)

Figure 6.30 The pole figures for the (001) plane of the5 v% talc compound from the annular die extrusion experiment


6.2.3.5 Compression Molding287


transverse direction (TD) of compression molded samples are

the flow direction (1-direction), a second flow direction

(2-direction), and normal direction (3-direction). A pole

figure of the (001) plane for the talc compound from the

compression molding sample is shown in Figure 6.31. This

pole figure indicates that the normals to the (001) plane of

talc particles are concentrated in the direction

perpendicular to the compression mold wall and the talc

particles are parallel to the flow direction.


Figure

2 8 8

NP

\I

FD

(a)

FD

cn

(b)

5.31 The pole figures for the (001) plane of the 5 v% talc compound from the compression molding experiment


6.3 Interpretation2 8 9

6.3.1 Composition Analysis of Particle Filled System

Using Bragg Angle X-ray Intensity

6.3.1.1 Theoretical Background

The x-ray scattering intensity from PS decreases as

calcite and talc particle increases in calcite-PS and talc-

PS compound systems. The PS scattering intensity decreases

more than proportionally as particle content increases.

The x-ray diffraction intensity from crystalline

material depends on the position of the atoms relative to a

given set of planes.

I,,*,, = P-L'A'IfP (6.1)

where IfI2 being the structure factor that depends on atomic

scattering factor, P being the polarization factor

(incoherent radiation) that depends on Bragg angle. L is

the Lorentz factor that depends on reflection (exposure)

time. A is the absorption factor (transmission factor) that


2 9 0depends on the elemental composition, the wave length of

the x-rays, and the size and shape of the specimen.

Alexander and Klug (182) represented the diffraction

from a mixture of compound specimen as:

K.x,I i - r . . .1 ( 6 . 2 )

A l[x i(A i ~ Am> + A m ]

where

I: = intensity of scattering from component 1 of a mixture

^ , function of the nature of the component 1 and

the geometry of the apparatus

M = subscript referring to the "matrix"

P: = density of (solid) component 1

x. = weight fraction of component 1 in a mixture

Pi = linear absorption coefficient of (solid) component 1

for the x-ray wavelength used

Pi* = Pi /Pi = mass absorption coefficient of component 1 for

the x-ray wavelength used


2 9 1Consider the case of a mixture of 2 components, when

M\

For the case when M m is zero, from Equation (6.2)

(:) = (6-3:

while for a mixture containing a weight fraction Xi with

mass absorption of component Mi of the first component and

a second component with mass absorption of component Mz

Ti = r~ / - K^ -rr-— ri (6.4:Pilx i\Mi ~ Mz) + M z J

For pure material 1

K 1x l(I:): = (6.51

PiMz

Dividing Equation (6.4) by Equation (6.5) gives

I i _ *iM\ „ _(6 .6)W o x i(^i “ Ml) + Ml


292

Converting to volume fractions ‘K and 2

x = — <t>- xt p v..

( //; - u \ ) P i<!>2 + p p \so, ~ 1 . . \ , . (6.7)

where

= volume fraction of component i in a mixture

Using Equation (6.6) gives the theoretical intensity

ratio of a binary mixture material. For example calcite 40

v% (x=0.37 wt%) , the absorption coefficient of PS MPS* is 8

and calcite M-calclLe* is 70.87 (cf. Mta>c* is 31.06). This

gives IPS.4a,t>/(I?s) 0 ratio 0.062 which is represented in Figure

6.32 point '(f)' solid line. The real Ifs,4o*/ (I?s) 0 ratio

data from experiments shown on Figure 6.5 is 0.06. The mass

absorption coefficients Mi* of MPS*, Mcaicice*, and Mtalc* were

determined from chemical composition, molecular weight, and

mass absorption coefficients M/P of the elements for a CuKa

wavelength (188). The examples are shown on page 69 of

reference (18 8). Table 6.1 summarizes the mass absorption

coefficient of elements for CuKa at ^-=1.5418 A.


293

Table 6.1 Mass absorption coefficient of elements for CuKa at *-=1.5418 A.

1

Ho. 4 35

2

Heo.38 3

3 4 5 6 7 8 9 10

Lie.-i6 Be:, so B2 .J5 C4 .sc N7.52 On .5 Fl£.4 Ne2;.9

11 12 13 14 15 16 17 18

Na3o.: Mg3a.€ A I 48.6 S iso. 6 P-4.1 Sas.: Cl:>: A r m

19 20 31 32 33 34 35 36

Kus Ca:£; Gao-. 3 Ge-5.6 As 5 3.4 S e 01.4 Brso.s Kr:;e


6. 3.1.2 Ternary Mixture System294

Lennox (184) presented an 'Internal Standard Method' to

analyze a binary particle mixture system in 1957. To

analyze an unknown component p in a binary mixture (p+q), we

may add a known weight of the unknown (yF) and do

experiments to determine the unknown composition (xp) . Let

the original weight fraction xF be unknown. Suppose yF

grams of p (per gram of sample) be added. The new weight

fraction of p and q are

xp + y t i + y D and

x„Xq =

1 + Yc (6 .8 )

The new intensity ratio from at scattering angle is

K o :< + vip _ ipr q p I p

kq K<qPp

= const * ( xp + yp. ) (6.9)


295Using different compositions yp we can measure the

intercept and the absolute value xp can be determined.

6. 3.1.3 PS / Calcite System

The relative intensities Ips (<!>) / (Ips) o may be read from

Figure 6.1 to 6 .6. For ♦ = 0.05, the ratio is 0.33, for ♦ =

0.10, it is 0.23, for ♦ = 0.20, it is 0.14 and for ♦ = 0.40,

it is 0.06. This relative intensity was plotted in Figure

6.32 as a function of weight fraction of PS. This plot was

represented again as a relative calcite particle intensity

in Figure 6.33 due to relationship

1 - Ips (♦calcite) / (Ips) 0 = Icaic-.te ( ♦ ? » ) / ( Icalcite ) 0 ( 6 . 1 0 )

Figure 6.6 presents the (110), (211), (10^), (210),

and (200) planes of calcite particles. The intensity of

scattering of calcite particle loadings is given in Figure

6.7. The scattering intensity of each plane is reduced as

calcite loading decreases.


296Figure 6.32 contains the calculated Alexander-Klug

(182), Equation (6.2), for PS/calcite (solid line) and

experimental (open circle) relative x-ray absorption

intensity-concentration curves for the calcite-PS compounds

as a function of PS content. The data is replotted in

Figure 6.33 which shows a comparison of theoretical

intensity-concentration curves (solid line) as a function of

calcite content. The PS intensity ratio was determined from

the pure PS amorphous halo. The absorption coefficient of

PS P-ps* is 8 and calcite Pcaic e* is 70.87 (cf. Ptai=* is 31.06)

which is calculated from tables (182) .

The %error from calcite-PS theoretical line is

approximately 0, 3, 1, 3, 5, 0% for the 5, 10, 20, 40, 100

v% calcite filled system. Thus if we multiply the reduced

number from the amorphous halo in Figure 6.32 into pure PS

intensity, we get the PS content within 5% error range

(average 2%). Inversely we can determine the unknown

filler's content from the PS intensity ratio Ips, <t>/ (Ip3) c> as

exhibited on Figure 6.33.

We conclude that intensity ratio I p s . * / ( I Ps) a determine

the composition of PS and calcite from calcite-PS compound

system.


297

coCL

>*.t; °mC Q.

c— CO<D>J5a:

Theoretical Intensity C oncentration

Experimental M easu rem en ts0.8

0.6

0 .4

0.2

0.00.8 1.00.60.0 0.2 0.4

W eight F raction of P S

Figure 6.32 Comparison of theoretical intensity-concentration curves (solid line) and experimental measurements (open circle) for PS/calcite mixtures


298

0.8

0.6GOO o

sS 0 .4

T heore tical Intensity C oncen tration E xperim ental M easu rem en ts

0.2

0.0 0.80.6 1.00 .40.20.0W eig h t F rac tion o f C alc ite

Figure 6.33 Comparison of theoretical intensity-concentration curves (solid line) and experimental measurements (closed hexagon) for PS/calcite mixtures


6.3.1.4 PS / Talc System29S

From Figure 6.1 and Figures 6.8 to 6.12 we may

determine Ips (fy / (IP3) o for the talc-PS compounds . The

relative intensities are 0.55, 0.40, 0.23 and 0.17 for the

= 0.05, 0.10, 0.20 and 0.40 compounds. We plot

I talc (^ ) / ( I e,lc)o in Figure 6.34 as a function of volume

fraction talc. We also compare our data with the Alexander-

Klug equation, Equation (6.2). The calculated absorption

coefficient of PS M'ps* is 8 and talc M-calc* is 31.06 (188) .

Figure 6.34 shows the comparison of theoretical

intensity-concentration curves (solid line) as a function of

talc content. The PS intensity was determined from the pure

PS amorphous halo.

The %error from talc-PS theoretical line is

approximately 7, 4, 5, 4, 3, 0% for the 5, 10, 20, 40, 100

v% talc filled system each. We get the PS content within 7%

error range (average 5%).

We show talc-PS content from PS intensity ratio

Ips,*/(Ips) c on Figure 6.34.


300

0.8

0.6

0010.4

0.2 T heore tica l Intensity C o n cen tra tio n

• E xperim ental M e a su re m e n ts

0 .0 0 .2 0 .4 0.6

W eight Fraction

0.8 1.0

Figure 6.34 Comparison of theoretical intensity-concentration curves (solid line) and experimental measurements (closed circle) for PS/talc mixtures


301We conclude that intensity ratio Ips,*/ (Ip3) a may be

used to determine the composition of PS and talc from talc-

PS compound system.

6.3.1.5 PS / Talc / Calcite System

6.3.1.5.1 Pseudo binary mixture system of PS/(Talc/Calcite)

We determined relative intensity I OS / (Ips) : for

the pseudo binary mixture of PS and talc/calcite compounds

from Figures 6.22, 6.23 and Figure 6.24. This system

consists of PS/talc/calcite (90:05:05 v% (88:12:14 wt%),

84:04:12 (88:12:30), 54:03:43 (88:12:178)) system. The

relative intensities are 0.7, 0.4, and 0.1 for the ^ =

90:05:05, 84:04:12, and 88:12:178 wt% compounds. We also

determined the relative intensities for the systems of

PS/talc/calcite (84:10:06 v% (77:23:14 wt%), 78:10:12

(77:23:30), 53:05:42 (77:23:178)) system. The relative

intensities are 0.50, 0.61 and 0.82 for the 4* = 84:10:06,

78:10:12, 53:05:42 v% compounds. We also compared our data

with the Alexander-Klug equation, Equation (6.2). The

absorption coefficient of PS ^PS* is 8 and talc taic/caicite* is


30245.85, 53.56, 66.31 for talc/calcite 10:05, 10:12, and

05:42 v% (182) . Figure 6.21 shows the intensity

distribution for PS compounds with various talc/calcite

loadings (00:00, 10:00, 10:16, 10:12, 05:42 v%).

Figures 6.35 and 6.36 shows the comparison of

theoretical intensity-concentration curves (line) of mixture

PS as a function of talc/calcite content. The reduced PS

intensity was determined from the PS/talc/calcite amorphous

halo.

6.3.1.5.2 Pseudo binary mixture system of (PS/Talc)/Calcite

We determined the relative intensity

Ips-.aic (♦calcite) / dps-ca.c) u for the pseudo binary mixture of

PS/talc and calcite compounds from Figure 6 . 2 2 through

Figure 6 . 2 7 . This system consists of (PS/talc)/calcite

( ( 9 0 : 0 5 ) : 0 5 v% ( ( 8 8 : 1 2 ) : 1 4 wt%), ( 8 4 : 0 4 ) : 1 2 v% (( 8 8 : 1 2 ) : 3 0

wt%)), ( ( 5 4 : 0 3 ) : 43 v% ( (88:12) : 178 wt%), ( ( 8 5 : 1 0 ) : 05 v%

( ( 7 7 : 2 3 ) : 1 4 wt%), ( ( 7 8 : 1 0 ) :12 v% ( ( 7 7 : 2 3 ) :30 wt%), and

( ( 5 3 : 0 5 ) :42 v% ( ( 7 7 : 2 3 ) : 178 wt%) system. The relative

intensities are 0 . 7 , 0 . 4 , 0 . 1 , 0 . 5 , 0 . 3 9 , and 0 . 1 8 each. We

also compare our data with the Alexander-Klug equation,


303Equation (6.2). The absorption coefficient of PS ps+taic*

is 13.3 and talc ^caicice* is 70.87 (182) .


intensity-concentration curves (line) of mixture PS as a

function of talc/calcite content. The PS intensity was

determined from various PS/talc/calcite (88:12:calcite wt%)

composition.

The %error from PS/talc/calcite (88:12:calcite wt%)

theoretical line is approximately 12, 9, 2 % for the 14, 30,

178 wt% calcite filled system each. We get the PS content

within 12% error range (average is 8%).


intensity-concentration curves (line) of mixture PS as a

function of talc/calcite content. The PS intensity was

determined from various PS/talc/calcite (77:23:calcite wt%)

composition.

The %error from PS/talc/calcite (77:23:calcite wt%)

theoretical line is approximately 12, 6 , 1 % for the 14, 30,


within 12% error range (average is 8%).


intensity-concentration curves (line) of mixture PS/talc as


304a function of calcite content. The PS/talc intensity was

determined from various calcite (88:12:calcite wt%)

composition.

The %error from (PS/talc, 88:12 wt%)/calcite



within 12% error range (average is 9%) .


intensity-concentration curves (line) of mixture PS/talc as

a function of calcite content. The PS/talc intensity was

determined from various calcite (77:23:calcite wt%)

composition.

The terror from (PS/talc, 77:23 wt%)/calcite



within 10% error range (average is 7%) .

We conclude that intensity ratio I ps+taic, (‘t’caicite) / ( Ips-tan) s

determine the composition of PS/talc and calcite in

PS/talc/calcite compound system. The ternary mixture system

exhibited %error result higher than the binary mixture

system. This may due to higher orientation of talc

particles.


305

Relative Intensity vs. Weight Fraction of PS

1.0

0.8

I 0.6

o>.'</)c<Dc0)>rav(X

0.4

0.0

PS/Talc/Calcite (88:12:000) PS/Talc/Calcite (88:12:13.6) PS/Talc/Calcite (88:12:29.9) PS/Talc/Calcite (88:12:177.8)

• PS/Talc/Calcite (88:12:000)■ PS/Talc/Calcite (88:12:13.6)A PS/Talc/Calcite (88:12:29.9)▼ PS/Talc/Calcite (88:12:177.8)

0.0 0.2 0.4 0.6

Weight Fraction of PS

0.8 1.0

Figure 6.35 Relative intensity distribution of varioustalc/calcite mixed particle as a function of PS concentration


306

Relative Intensity vs. Weight Fraction of PS

1.0

o32a

"wO2*V)cQ)<D>

(Dir

PS/Talc/Calcite (77/23:000 wt%) PS/Talc/Calcite (77/23:13.6)

PS/Talc/Calcite (77/23:29.9)

PS/Talc/Calcite (77/23:177.8)

PS/Talc/Calcite (77/23:000 wt%) ■ PS/Talc/Calcite (77/23:13.6)A PS/Talc/Calcite (77/23:29.9)▼ PS/Talc/Calcite (77/23:177.8)

0.4 0.6

Weight Fraction of PS

Figure 6.36 Relative intensity distribution of various talc/calcite mixed particle as a function of PS concentration


307

Relative Intensity vs. Weight Fraction of PS+talc

1.0

^ 0.8 h

0.6

o>.toc£c(1)>raa)a:

0.4 h

0.2

PS:Talc/Calcite (88:12/000 wt%) PS:Talc/Calcite (88:12/13.6) PS:Talc/Calcite (88:12/29.9)

PS:Talc/Calcite (88:12/177.8)

• PS:Talc/Calcite (88:12/000 wt%)■ PS:Talc/Calcite (88:12/13.6)A PS:Talc/Calcite (88:12/29.9)▼ PS:Talc/Calcite (88:12/177.8)

0.00.0 0.2 0.4 0.6

Weight Fraction of PS+talc

0.8 1.0

Figure 6.37 Relative intensity distribution of various(PS/talc,88:12 wt%)/calcite mixed particle system as a function of PS+talc concentration


Rela

tive

Inte

nsity

of

Ips^

foe-

ateW

ps^a

icJo

308

Figure

Relative Intensity vs. Weight Fraction of PS+talc

■▲▼

PS:Talc/Calcite— PS:Talc/Calcite

- PS:Talc/Calcite

— PS:Talc/Calcite

> PS:Talc/Calcite PS.Talc/Calcite PS:Talc/Calcite PS:Talc/Calcite

(77:23/000 wt%) (77:23/13.6)

(77:23/29.9)

(77:23/177.8)

(77:23/000 wt%) (77:23/13.6) (77:23/29.9) (77:23/177.8)

0.00.0 0.2 0.4 0.6

Weight Fraction of PS+talc

0.8 1.0

6.38 Relative intensity distribution of various (PS/talc,77:23 wt%)/calcite mixed particle system as a function of PS+talc concentration


3096.3.1.6 Summary of PS / Talc, PS / Calcite, and PS /

Talc / Calcite System

6.3.1.6.1 PS / Talc, and PS / Calcite System

The first quantitative analysis using x-ray absorption

was done by Clark and Reynolds (178) in 1936 for mine-dust

analysis. Hull (177) pointed out each component in a

mixture exhibited a characteristic absorption intensity and

proportional to the amount present. Alexander and Klug

(182, 188, 189) introduced mathematical relationships

between intensity and absorptive properties of the sample.

Their work was mainly applied to particle-particle mixture

systems. In mixed particle compounds, there were

difficulties in quantitative analysis especially for

anisotropic particles because they easily orient during

packing or processing. The degree of orientation of

anisotropic particles gives different peak intensities.

This creates questions in quantitative analysis of particle-

particle mixed system. We considered the Alexander and Klug

(182, 188, 189) mathematical relationship between intensity

and absorptive properties to still apply.


310The predictions for the binary systems work well

with experiment.

We have investigated the effect of filler content from

various compositions of fillers using WAXD (reflection

technique) and the amorphous halo intensity. Investigation

of filler composition using amorphous halo intensity of PS

is first done in our laboratory. The %error range for

calcite content in the mixture with PS was 5% (average 2 %)

and 7% for talc content (average 5 %). The calcite,

isotropic filler, showed good results in quantitative

analysis because of its isotropy which showed a good

reproduction ability, but in the case of anisotropic filler

talc the measuring of filler intensity from the peak gives

error due to talc particle's orientation which is well known

(183-186, 188, 189) .

6.3.1.6.2 PS / Talc / Calcite System

Using Alexander and Klug (182, 188, 189) mathematical

relationship between intensity and absorptive properties and

pseudo binary mixture method can be applied for calcite-


311talc-PS filled system. There seems no investigation on

systems such as the calcite-talc-PS system.

The %error range for talc/calcite content in the

mixture with PS was 17% (average 9 %).

The talc/calcite, mixed filler, showed good result in

quantitative analysis due to isotropy contribution which

showed good reproduction ability. For anisotropic talc, the

intensity of amorphous halo gives more accurate results than

using anisotropic filler's plane intensity. In order to get

more accurate intensity distribution data from anisotropic

particle filled system one should consider azimuthal angle

intensity and the degree of orientation of anisotropic

particles.

6.3.2 Flat Film Measurements Of Orientation

The WAXD flat film technique was used to characterize

the state of orientation of talc particles. The

transmission method was used. We have presented an

experimental study of the orientation characteristics of

talc, calcite and talc/calcite particle filled compounds in


312capillary die extrudates for talc, calcite, and

talc/calcite, and compression molded samples of talc and

talc/calcite at various volume loadings.

Typical results in the form of WAXD flat film technique

are shown in Figure 6.22-6.26. These WAXD flat film

techniques qualitatively shows the state of orientation.

Figure 6.22 shows talc particles in extrudate orients with

their disc surfaces in the circumferential direction.

Figure 6.23 shows calcite particles do not exhibit

orientation. Figure 6.24 exhibits overlapped peaks

indicating orientation of talc/calcite particle. Molded

sheet samples exhibited sharper arcs compared to extrudates;

i.e. The degree of orientation of the molded sheet sample

showed higher than the uniaxial sample. Figure 6.25

exhibits sharp arc for a beam in the normal direction for

the (001), (002+020), and (003) planes. Figure 6.26 is for

compression molded talc/calcite compound. Due to the

overlap of characteristic peaks we can't see talc particle's

(001), (002+020), and (003) planes. Qualitatively the film

technique easily distinguish degree of orientation for

single particle system. Using the flat film technique is

limited when applied to the talc/calcite system.


313

6.3.3 Orientation Factors And Pole Figure Measurements

Uniaxial and biaxial orientation factors were

determined from the pole figures. Orientation factors were

determined and represented by White and Spruiell's

orientation triangle (163).

6. 3.3.1 Capillary Die Extrudates

Figure 6.31 presents uniaxial orientation factors for

5, 10, 20, 40 v% talc filled system. Table 6.2 summarizes

the orientation factors of capillary extrudates of talc, and

talc/calcite filled systems. The degree of orientation of

talc particle exhibit values at 5 v% of (-0.39) and at 10 v%

(-0.40), at 20 v% (-0.39) and at 40 v% (-0.36). There is a

noticeable decrease at 40 v%.


314

Figure

: B FD

O 5 v% Talc

□ 10 v% Talc

A 20 v% TalcV 40 v% Talc

.39 White and Spruiell orientation triangle for capillary die extrudates


315Table 6.2 Orientation factor for talc, and talc/calcite

filled system from capillary die (L/D=28.5, D=1.6mm) extrudate at Q = 29.9 (mm3/s) 200°C.

PS/Talc (95 : 05 v%)

PS/Talc/Calcite (90 : 05 : 05 v%)


fooi.FD = ~ 0 . 39 fooi.FD = —0 . 37 fool, FD = -0.38

PS/Talc (90 : 10 v%)



f 0 0 I, F D = ~ 0 . 4 0 fcoi.FD = —0.38 fooi.FD = -0.39

PS/Talc (80 : 20 v%)



fooi.FD = -0.39 f 001, FD = — 0 . 3 3 f •• rr = -0.37

PS/Talc (60 : 40 v%)


fooi.FD = -0 . 36 fooi.FD = —0.36


6.3.3.2 Rectangular Die Extrudates316

Figure 6.28 indicates the crystallographic axis of the

normal to the talc particles perpendicular to the surface of

the wall i.e. The talc particles are aligned parallel to the

surface of the rectangular die wall.

6.3.3.3 Slit Die Extrudates

Figure 6.29 shows pole figures for the (001) plane of

talc particles.

Because of the simplicity of the geometry, orientation

factors were determined and represented on White and

Spruiell's orientation triangle in Figure 6.40 for 5, 10,

20, 40 v% talc filled system. Table 6.3 summarizes the

orientation factors of slit die extrudates of talc, and

talc/calcite filled systems. The talc particle's degree of

biaxial orientation for flow (1) direction and transverse

direction of the (001) plane (fB=-D/ f°Tn) is 5 v% (-0.80, -

0.80), 10 v% (-0.82, -0.82), 20 v% (-0.80, -0.80), and 40 v%

(-0.83, -0.83).


317

Figure

f, BFD

(-1, - 1)

5 v% Talc

10 v% Talc

20 v% Talc 40 v% Talc

f. BTD

.40 White and Spruiell orientation triangle for slit extrusion


318Table 6.3 Orientation factor of talc, and talc/calcite

filled system from slit die extrudate (W/T=20,T=0.3 mm) extrudate at Q = 9049.5 (mmVs) 200°C

P S / T a l c

(95 : 05 v%)

P S / T a l c / C a l c i t e

(90 : 05 : 05 v%)


(84 : 04 : 12 v%)

foe:, FD = - 0 . 8 0

foOl.TD = —0 . 7 3

fooi.FD = —0 . 6 2

f 0G1, TD = —0 . 6 3

fooi.FD = - 0 . 4 9

foe 1, TD = —0 . 6 2

P S / T a l c

(90 : 10 v%)


(84 : 10 : 06 v%)


(78 : 10 : 12 v%)

f ooi, ?d = —0 . 8 2

fooi.TD = - 0 . 7 9

f 001, FD = —0 . 64

fooi,TD = —0 . 62

f 001, FD = —0 . 5 0

f ooi, td = —0 . 5 6

P S / T a l c

(80 : 20 v%)


(75 : 19 : 06 v%)


(69 : 17 : 14 v%)

O C\J

CO 00

O O

1

1It

IICl

QIt.

(4

o O

o o

i

f 001, FD = —0 . 7 8

f 001, TD = —0 . 7 7

f 0 0 I, FD = —0 . 7 4

f 001, TD = —0 . 7 0

P S / T a l c

(60 : 40 v%)


(60 : 20 : 20 v%)

f 001. FD = —0 . 8 3

foOl.TD = —0 . 8 1

fooi.FD = - 0 . 7 2

f G J I, TD = —0 . 6 9


319This result represents the talc particle's c-axis. It is

perpendicular to the surface of the slit die wall i.e. The

talc particles are aligned parallel to the surface of the

die wall.

6 .3.3.4 Annular Die Extrudates

The pole figures indicates that the c-axis of talc

particles orient normal to the wall as shown in Figure 6.30.

This result indicates that the talc particle's c-axis

is perpendicular to the surface of the annular die wall i.e.

The talc particles are aligned parallel to the surface of

the annular die wall.

6. 3.3.5 Compression Molded Parts

Orientation factors were represented on White and

Spruiell's orientation triangle in Figure 6.41 for 5, 10,

20, 40 v% talc filled system. Table 6.4 summarizes the

orientation factors of compression molding of talc, and

talc/calcite filled system.


320

FD1

0.5

0.5

-0.

5 v% Talc

10 v% Talc

20 v% Talc 40 v% Talc

(-1.-1)

f, BFD3

Figure 6.41 White and Spruiell orientation triangle for compression molded parts


321Table 6.4 Orientation factor of talc, and talc/calcite

filled system from compression molding at 5 MPacompression (Thickness = 1 mm) at 200 'C

PS/Talc (95 : 05 v%)



f001, FD = “0.90 fooi.TD = —0 . 90

f 001, FD = —0.86fooi, TD — —0.86

fooi.FD = —0.47 f 001, TD = —0.47

PS/Talc (90 : 10 v%)



f001, FD = “0.90 foOl.TD = “0.90

f 00 1, FD = —0.81 foOl.TD = -0.81

fooi.FD = —0.75 f 0 0 1, TD = —0.75

PS/Talc (80 : 20 v%)



f 001, FD = —0.87 fooi.TD = —0.87

f 001, FD = “0.86 fooi, TD = —0.8 6

fooi.FD = —0.87 f 001, TD = —0.87

PS/Talc (60 : 40 v%)


f 001, FD = —0.83 foOl.TD = —0.83

fooi.FD = — 0.86 foOl.TD = —0.86


322The talc particle's degree of biaxial orientation (f ?Eif

f%D3) for flow (1) direction at (001) plane is 5 v% (-0.90,

-0.90), 10 v% (-0.90, -0.90), 20 v% (-0.87, -0.87), and 40

v% (-0.83, -0.83). This result represent the talc

particle's c-axis as perpendicular to the surface of the

mold wall i.e. talc particles are aligned parallel to the

surface of the mold wall or flow direction.

6.3.3.6 Mixed Particle Filled System

6. 3. 3.6.1 Capillary Die Extrudates

Capillary die extrudates for mixed particle system did

not show considerable differences as a function of addition

of calcite particles. As the talc fraction changes as

PS/talc/calcite 90:05:05, 84:10:06, and 75:19:06 v% the

orientation order of talc particles exhibited -0.37, -0.38,

and -0.35, and for PS/talc/calcite 84:04:12, 78:10:12, and

69:17:14 v% fraction the orientation order of talc particles

exhibited -0.38, -0.39, and -0.37.


323

0.0 T T

-0.2 h

-0 .4coro| -0.6

O calc ite 0 vol%

□ ca lc ite 6 vol%A ca lc ite 12 vol%

V ca lc ite 20 vol%-O

-0.8 r

- 1.00 5 10 15 2 0 2 5 30 35 4 0 4 5 50

Talc (vol%)

Figure 6.42 Orientation function of talc as a function ofvolume loading of calcite from capillary die extrudates


324This indicates the talc particle filled capillary die

extrudate system did not show considerable changes (see

Figure 6.42) in talc particle orientation. The 20/20 v%

talc/calcite filled system exhibited -0.36.

6.3.3.6.2 Slit Die Extrudates

Slit die extrudated mixed particle systems show

considerable differences as a function of addition of

calcite particles. Table 6.3 represents the orientation

factor of mixed talc particles as a function of calcite

volume loading from slit die extrudates. As talc fraction

increases from 5 v%~ 20 v% the orientation order of 06 v%

calcite fraction mixed system showed -0.62--0.78, and 12v%

calcite fraction mixed system showed -0.49~-0.74.

This result indicates that as the relative

concentration of calcite particle fraction increases (or

talc particle fraction decreases) in the mixture of

talc/calcite particle filled system the degree of talc

particle orientation decreases (see Figure 6.43).


0.0

-0.2O u_*3 -0 .4c0ro

1 -0 6*L-O

- 0.8

- 1.00 5 10 15 2 0 2 5 30 3 5 4 0 4 5 5 0

Talc (vol%)

i i i ~

O ca lc ite 0 vol%□ ca lc ite 6 vol%

A ca lc ite 12 vol%V ca lc ite 20 vol%

i i i i i i i i

Figure 6.43 Orientation function of talc as a functionvolume loading of calcite from slit die extrudates


6.3.3.6.3 Compression Molding326

Compression molded mixed particle system show

considerable differences as a factor of addition of calcite

particles. Table 6.4 represents the orientation factor of

talc particles as a function of calcite volume loading from

compression molding. As talc fraction increases from 5 v%~

20 v% the biaxial orientation factor of 06 v% calcite

fraction mixed system showed a variation from -0.81 to -

0.86. The 12v% calcite fraction mixed system showed a

variation from -0.47 to -0.87. 20/20 v% talc/calcite mixed

system showed -0 .86.

When calcite particle fraction increases (or talc

particle fraction decreases) in the mixture of talc/calcite

particle filled system, the degree of talc particle

orientation decreases (see Figure 6.44).

6 .3.3.6 Summary

Typical results in the form of WAXD pole figure

technique are shown in Figures 6.27, 6.28, 6.29, 6.30, and

6.31. They indicate that the c-axis of talc particles

orients normal to the walls of dies and molds.


327

0.0

-0.2QLi.

*3 -0 .4co

’•4— *(0.1 '°-6 V-O

- 0.8

- 1.00 5 10 15 2 0 2 5 30 35 4 0 4 5 50

Talc (vol%)

calc ite 0 vol% calc ite 6 vol%

calc ite 12 vol% calc ite 2 0 vol%

Figure 6.44 Orientation function of talc as a function ofvolume loading of calcite from compression molding


328These WAXD patterns show high levels of orientation of

talcs; specifically, the particle normals are perpendicular

(i) to the compression mold surface, (ii) to the slit die

surface, (iii) to the capillary extrudate surface, (iv) to

the rectangular die surface and (v) to the annular die

surface.

The data have been converted to orientation factors,

for the compression molded and in extruded sheets. These

give a better quantitative comparison of the levels of

orientation. It is found that the orientation factors fi=

and f3s are equal and less than -0.90. These indicate the

talc particle surfaces being parallel to the surface of the

sheets. In Figure 6.39, 6.40, and 6.41, we plot the

orientation function for the same process conditions in an

orientation triangle which was developed by White and

Spruiell. The orientation factors for the talc particles in

the extruded filaments are different in Figure 6.39.

Generally fiBis negative and f3Bis zero. These calculations

show the talc particle's c-axis is perpendicular to the

surface of the wall i.e. talc particles are aligned parallel

to the flow direction. This is equivalent to a state of


329uniaxial orientation with the talc particle normals

perpendicular to the axis.

We have also studied the influence of particle loading

on the talc particle orientation in compression molded

sheets, extruded sheets and extruded filaments. The

orientation levels are the highest for the compression

molded samples. We found that for the compression molded

sheets and extruded sheets the degree of orientation

increases with increasing volume fraction as shown in Figure

6.45.

Figure 6.45 shows the fi3orientation factor for the

capillary extrudates. The degree of orientation increases

for the 0.05 and 0.10 volume fraction samples but decreases

for the 0.20 and 0.40 samples which was not observed from

earlier studies in Lim (70, 7_1, 8_0, 8_1) and Suh (82-84) .

This phenomenon which was not observed in the extruded

sheets suggested further investigations using scanning

electron microscope (SEM), where particle orientation

distributions through extrudate cross-section may be studied

more precisely.


330

0 .0

-0.2

-0 .3

-0 .4Capillary Extrudates (Uniaxial)

-0 .5

- -0.6

-0 .7

S heet Extrudates (Biaxial)

-0.8

-0 .9Com pression Moldings (Biaxial)

i - i 1 I L— I I I U

0 .50.3 0.40.20.0 0.1

Volume Loading

Figure 6.45 Orientation function as a function of volumeloading of capillary extrudates, sheet extrudates, and compression moldings


331We investigated calcite/talc mixed particle filled

system. We could not see considerable orientation changes

of talc particles in capillary extrudated samples as shown

in Figure 6.42. However slit die extrusion sample showed

decrease in degree of orientation as increase calcite

particle loadings from 6 v% to 12 v% at 10 v% talc and at 20

v% talc respectively as shown in Figure 6.43. Compression

molding showed decrease in degree of orientation as increase

calcite particle loadings from 5 v% to 10 v% at 10 v% talc

as shown in Figure 6.44. However high loading system

(talc/calcite=20:06, 20:12, 20:20) did not show significant

changes in compression molding system.


CHAPTER VII

CHARACTERIZATION OF LOCAL PARTICLE ORIENTATION

IN PROCESSED COMPOUNDS

7.1 Introduction

In this chapter, we describe an effort to measure

localized orientation of anisotropic particles which arise

in different processing geometries. The primary anisotropic

particles to be studied are talc but investigations were

also made with mica and talc/calcite. Characterization was

carried out using scanning electron microscopy (SEM).

332


7.2 Results333

We inspected fracture surface of compression molded

sheets, slit die extrudates, capillary die extrudates,

rectangular die extrudates and annular die extrudates using

SEM.

7.2.1 Compression Molded Samples

Talc

SEM photomicrographs of sliced compression molded

sheets of 5 and 40 volume percent compounds of talc in

polystyrene at 5 MPa exhibited cross-sections indicating the

talc disc shaped particles were parallel to the mold

surface. These are shown in Figure 7.1.

M i c a

SEM photomicrographs of sliced compression molded mica

sheets with 5 and 40 volume percent of mica in polystyrene

prepared under the same conditions as the talc particle

filled sheet are shown in Figure 7.2. The mica particles

are also parallel to the mold surface.


Figure 7.1 Cross-section of 5 v% and 40 v% talc particle filled compression molded polystyrene sheets


335

(a) 5 v%

(b) 40 v%

Figure 7.2 Cross-section of 5 v% and 40 v% mica particlefilled compression molded polystyrene sheets


7.2.2 Extrudates336

7.2.2.1 Capillary Die

Tal c

Filaments extruded from capillary dies exhibited a more

complex behavior. This is shown in Figure 7.3. For the

0.05 and 0.10 samples, the talc particle discs are oriented

with their long axes tangential to concentric circles whose

center is the filament axes as shown in Figures 7.3 (a)-(f).

However at the 0.20 and 0.40 concentrations, there appear to

be two regions in the extrudate cross-section each with a

different type of structural order as shown in Figures 7.3

(g)-(l). At the larger radii near the filament surface the

talc particles are circumferentially arranged as at lower

concentrations. At smaller radii, the talc particles appear

to be arranged in a radial manner. There is a surface of

separation.


337

Figure 7.3 Cross-section of (a) 5 v%, (b) 10 v%, (c) 20v% and (d) 40 v% talc particle filled capillary die extrudated filaments


338

(g) skin 20 v% (j) skin 40 v%

intermediate 20 v% intermediate 40 v%

(i) core 20 v% continued Figure 7.3

core 40 v%

Cross-section of (a) 5 v%, (b) 10 v%, (c)v% and (d) 40 v% talc particle filled capillary die extrudated filaments

20


339The position of this surface of separation (radial

direction orientation) is at larger radii for the 0.40

volume fraction sample.

We sought to quantify and expand our observations for

the capillary die. We investigated the variation of the

position of separation of the two ordered states with

extrusion conditions for the capillary die. It was found to

occur in 20 and 40 volume percent compounds not in 5 and 10

volume percent compounds which only exhibited a radial

direction orientation.

We plot the radial ratios defined as the ratio of the

diameter 'd' of the region with radial orientations to the

diameter of the die 'D' i.e. d/D versus 32Q/7rD3 in Figure

7.4. Figure 7.4 shows the radial ratio increases with

extrusion rate at volume fractions 0.20 and 0.40.

Figure 7.5 shows the radial ratio d/D of the disordered

radius d increases with volume loading increases at each of

the die wall shear stresses eA p/4L investigated where

has been corrected by the Bagley method (269). Figure 7.6

shows this radial ratio increases with die wall shear stress

with different volume loadings.


340

Figure 7.

• TALC 05 V%

■ TALC 10 V%

- A TALC 20 V%0.8▼ TALC 40 V%

Q■oO

_ i<Q<CC

0.2 -

0.010° 1 0 '

Extrusion R ate (32Q/ttD3)

Dimensionless analysis of radial ratio d/D vs. extrusion rate of capillary extrudates.


341

1.0 r

• 3 2 0 /itD ^ 7 .4 ( s ')■ 32Q/itD3= 74.4 (s ')A 32Q/jeD3=743.9 (s ')0.8

0.4

0.2

0.0 h. 0 10 15 20 25 30 35 40 455

TALC (V %)

Figure 7.5 Dimensionless analysis of radial ratio d/Dvs. volume loadings of capillary extrudates.


342

T5O

1.0 r

0.8

0.6

<CC. 0.4_i<Q< 0.2

TALC 40V%

0.0 -

A TALC 20V% ■ TALC 10V% • TALC 5V%

■m•rn

5.0x10* 10s 1.5x10s 2 .0x10s

DIE WALL SHEAR S T R E SS (P a)

2.5x10s

Figure 7.6 Dimensionless analysis of radial ratio vs.die wall shear stress based upon different volume loadings from capillary extrudate.


343Figure 7.7 shows the die wall shear rate ratio

(compound die wall shear rate-PS die wall shear rate/PS-die

wall shear rate) increases with talc volume loadings with

capillary extrusion rate at 32Q/7lD3=2.2 (sec l) . As talc

volume leadings increase shear rate ratio changes after 10

v% or 15 v% talc compounds.

M ic a

SEM photomicrographs exhibit capillary die mica

extrudates prepared at same condition as talc particle

filled capillary die filament are shown in Figure 7.8. The

capillary extrudates containing mica showed concentric

arrays parallel to the die surface at 5 v% (d/D=0.01). At

40 v% mica compounds had only a skin layer with concentric

mica parallel to the die surface (d/D=0.86). These were

core region exhibiting radial direction orientation as in

talc particle filled capillary die extrudated filament.


344

Figure 7

i

• 32Q/7iD3=2.2(sec'1)

0 5 10 15 20 25 30 35 40 45

TALC (V %)

.7 Dimensionless analysis of shear ratio vsTalc v% (L/D 28.5, D=1.6 mm, 200°C,Capillary).


345

(b) 40 v%Figure 7.8 Cross-section of 5 v% and 40 v% mica particle

filled capillary die extrudated filaments


346T a l c / c a l c i t e

SEM photomicrographs exhibit capillary die talc/calcite

extrudates prepared at same condition as talc and mica

particle filled capillary die filament are shown in Figure

7.9, 7.10, and 7.11. The capillary extrudates containing

talc/calcite showed concentric arrays parallel to the die

surface at 05/05 v% (d/D=0.01). At 04/12, and 10/06 v%

talc/calcite compounds had skin and intermediate layer with

concentric talc/calcite parallel to the die surface

(d/D=0.35). At 10/12, 20/10, and 20/20 v% talc/calcite

compounds had only a skin layer with concentric talc/calcite

parallel to the die surface (d/D=0.85). These were core

region exhibiting radial direction orientation as in talc

and mica particle filled capillary die extrudated filament.

7.2.2.2 Slit Die

T al c

Extrudates of 5 and 40 volume percent from slit dies

with a 20:1 aspect ratio exhibited cross-sections indicating

the talc disc shaped particles were parallel to the die

surface. This is shown in Figure 7.12.


(a) skin 05/05 v% (d) skin 04/12 v%

(b) intermediate 05/05 v% (e) intermediate 04/12 v!

(c) core 05/05 v% (f) core 04/12 v%

Figure 7.9 Cross-section of 05/05 v% and 04/12 v%talc/calcite particle filled capillary die extrudated filaments


(b) intermediate 10/06 v% (e) intermediate 10/12 v%

(c) core 10/06 v% (f) core 10/12 v:



349

(d) skin 20/20 v%(a) skin 20/10 v%

(b) intermediate 20/10 v% (e) intermediate 20/20 v%

(c) core 20/10 v% (f) core 20/20 v%



(c) core 5 v% (f) core 40 v%

Figure 7.12 Cross-section of 5 v% and 40 v% talc particlefilled slit die extrudated polystyrene sheets


351M i c a

Extruded of 5 and 40 volume percent mica compound

sheets prepared under the same condition as talc particle

filled compounds are shown in Figure 7.13. The mica

particles are also parallel to the die surface.

7.2.2.3 Rectangular Die

The results of the above paragraph (capillary die

extrudates) led to studies of other die cross-sections. We

made experiments with a rectangular die with an aspect ratio

of 2 :1 .

T a l c

Filaments extruded from rectangular die (Q/wh"= 2.2

(sec"1) , h=l, w=2, 1=10 mm) exhibited a complex behavior

similar to capillary extrudates. Figure 7.14 shows scanning

electron microscopy (SEM) photomicrographs of cross-section

of rectangular die extrudates with a 2:1 aspect ratio at

volume loadings 0.05 and 0.4.



Figure 7.13 Cross-section of 5 v% and 40 v% mica particlefilled slit die extrudated polystyrene sheets


3 5 3For the 0.05 volume loading samples, the talc particles

are oriented with their long axes tangential to concentric

circles whose center is the filament axes as shown in Figure

7.14. However at the 0.4 loading the talc particle

orientations are complex. There appear to be two regions in

the extruded cross-section each with a different type of

structure order as shown in Figure 7.14. The talc particles

appear to be arranged in a radial manner. Again there is a

tendency for parallel orientation near the wall but random

and radial direction orientations are far from the wall.

There is a surface of separation.

M i c a

Rectangular die extrudates with a 2:1 aspect ratio at

volume loadings 0.05 and 0.4 are shown in Figure 7.15. The

SEM photographs of cross-section of mica particles are

parallel to the die surface at 0.05 the loading. However at

the 0.4 loading the mica particle orientations are complex.

Again there is a tendency for parallel orientation near the

wall but random and radial direction orientations far from

the wall.


354

(a) skin 5 v%

(b) intermediate 5 v%

(c) core 5 v%

(d) skin 40 v%

(e) intermediate 40 v%

core 40 v%

Figure 7.14 Cross-section of 5 v% and 40 v% talc particlefilled rectangular die extrudated filament


3 5 5

(b) 40 v%

Figure 7.15 Cross-section of 5 v% and 40 v% mica particlefilled rectangular die extrudated filaments


7.2.2.4 Annular Die356

T a l c

Figure 7.16 shows SEM photographs of cross-section of

annular die extrudates at volume loadings 0.05 and 0.4. The

talc particles are parallel to annular die surface at 0.05

and 0.4 loadings. The talc particles are parallel to the

die surfaces at 0.05 the loading. However at the 0.4

loading the talc particle orientations are complex. Again

there is a tendency for parallel orientation near the inner

and outer annular walls but random and radial direction

orientations far from the wall.

M i c a

Figure 7.17 shows SEM photographs of mica particles in

the cross-section of the annular die extrudates at volume

loadings of 0.05 and 0.4. The SEM photographs of cross-

section of mica particles are parallel to the annular die

surface at 0.05 the loading. However at the 0.4 loading the

mica particle orientations are complex.


357

(a) skin 5 v% (d) skin 40 v%

Figure 7.16 Cross-section of 5 v% and 40 v% talc particlefilled annular die extrudated sheets


3 5 8

(a) 5 v%

(b) 40 v%

Figure 7.17 Cross-section of 5 v% and 40 v% mica particlefilled annular die extrudates


3 5 9Again there is a tendency for parallel orientation near

the wall but random and radial direction orientations far

from the inner and outer annular walls.

7.2.2.5 Capillary Dies For Various Diameter

The earlier experiments described in section 1.2.2.2

were based on a capillary die of diameter 1.6 mm. We have

looked at other diameters as well.

Figure 7.18 show talc particles' orientation from

capillary die diameter 0.8 mm (0.03 inch, L/D=20) at

32Q/7CD3=17 . 6 (sec"1) . Result shows no considerable difference

compared to capillary die extrudates from die diameter 1.6

mm as shown in Figure 7.2.

Figure 7.19 show talc particles' orientation from

capillary die diameter 4.8 mm (0.18 inch, L/D=20) at

32Q/7CD3=0 . 081 (sec’1) . Result shows no considerable

difference compared to capillary die extrudates from die

diameter 1.6 mm as shown in Figure 7.2. The talc particles

are parallel to the die surface at 0.05 the loading.


3 6 0

(a) skin 5 v%

(b) intermediate 5 v%

(d) skin 40 v%

HHEm

(e) intermediate 40 v%


Figure 7.18 Cross-section view of 5 v% and 40 v% talcparticles from 0.8 mm capillary diameter extrudates


3 6 1

Figure 7.19 Cross-section view of 5 v% and 40 v% talcparticles from 4.6 mm capillary diameter extrudates


362However at the 0.4 loading the talc particle orientations

are random and radial direction orientations far from the

capillary die wall.

7.2.2.6 Capillary Die Entrance Angle 135° Flow

Figure 7.20 shows talc particles' orientation from

capillary die of entrance angle of 135° at 32Q/7CD3= 2 .2 (sec :)

as opposed to the 45° angle of the dies used in the

experiments of sections 7. 2. 2. 2 and 7.2.2.5. Result shows

no considerable difference compared to capillary die

extrudates from die entrance angle at 45° shown on Figure

7.2. The talc particles are parallel to the die surface at

0.05 the loading. However at the 0.4 loading the talc

particle orientations are random and radial direction

orientations far from the capillary die wall.


363

(a) skin 5 v%

intermediate

m

skin 40 v%

intermediate 40 v%


Figure 7.20 Cross-section view of 5 v% and 40 v% talc particles from capillary die entrance 135c


3647.2.2.7 Capillary Die Attached To Twin Screw Extrusion

Machine

Figure 7.21 shows talc particles' orientation from a

capillary die placed at the end of twin screw extruder with

low and high volume loadings. The die contained a

cylindrical hole of diameter 4.8 mm (0.18 inch, L/D=5,

Q=5Kg/hr, 32Q/7tD3=0.0014 (sec"1)). The results are similar

to Figure 7.18 capillary extrudate samples at 32Q/7tD3=2.2

(sec’1) . The talc particles are parallel to the die surface

at 0.05 the loading. However at the 0.4 loading the talc

particle orientations are random and radial direction

orientations in the core region.

7.2.3 Flow into Die Entrance

We also inspected fracture surfaces of the particle

compounds of 20 talc volume percent flowing into the

entrance angle 45° capillary dies.


365

(b) intermediate 5 v% (e) intermediate 40 v%

Figure 7.21 Cross-section view of 5 v% and 40 v% talcparticles from twin screw extruder extrudates


366

(c) plug tip 20 v% (f) plug skin 20 v%

Figure 7.22 Normal direction cross-section view of 20 v%talc particles from reservoir to capillary die entrance at 45°


367Figure 7.22 shows reservoir flow of talc particles

from reservoir to capillary die entrance at entrance angle

45°. The talc particles in the reservoir are oriented only

on the cylinder wall surface as shown in Figure 7.22 (d),

(d) , (f), and (c). This photograph shows the talc particle

normals are perpendicular to the reservoir wall and oriented

to the flow direction. The internal region shows random

orientation of talc particles as shown in Figure 7.22 (a)

and (b) . This photograph shows the talc particles are

oriented randomly in the core region and intermediate

region. As talc particle approaches to capillary die

entrance talc particles orient to flow direction as shown in

Figure 7.22 (c). This photograph shows the talc particles

are well oriented to flow direction as they approach from

reservoir region to capillary die entrance region.


7.3 Discussion368

7.3.1 Summary Of Flow Observation In Long Dies

The main result of the study shows that a careful

investigation of talc and mica particle orientation in a

series of talc-polystyrene, and mica-polystyrene compounds

indicates that in planar geometries such a compression

molding and sheet extrusion, that talc and mica disc

particles are uniformly parallel to the surfaces of the mold

and die. However in extrusion through circular or low

aspect ratio rectangular dies, the talc and mica discs lie

parallel to the die walls only at low particle loadings. At

higher loadings, the particles break down into two regions

one near the walls and a second with radial direction

orientation (see Figure 7.2 and Figure 7.7) in the core of

the die. Variations in the state of orientation of talc

particles in fabricated thermoplastic parts have been

previously noted by Lim and White (7_1) . They found the talc

orientation at the core of injection molded parts was lower

than at the wall region. However there has been no


3 6 9observations of phenomena as striking as what we have

presented here.

7.3.2 Correlation Of Observations From Different

Experiment

7.3.2.1 Feed History Effect

C a p i l l a r y E x t r u d e r

The feed from capillary extrudates at diameter 1.6 mm

which has shear rate 32Q/7lD3=2.2 (sec *) showed in Figure

7.2. Schematic representation in Figure 7.2 was shown in

Figure 7.23. The feed from capillary extrudates at diameter

0.8 mm which has shear rate 32Q/7tD'=17 .6 (sec ') showed in

Figure 7.18. Schematic representation in Figure 7.18 was

shown in Figure 7.23 and Figure 7.25. The feed from

capillary extrudates at diameter 4.8 mm which has shear rate

32Q/7CD3=0.081 (sec*1) showed in Figure 7.18. Schematic

representation in Figure 7.18 was shown in Figure 7.23 and

Figure 7.24.


370

TALC 0 5 V%

0.03(d/D=0.007)1.0(d/D=0.007) 10.0(d/D=0.01)

TALC 10 V%

0.03(d/D=0.007)1.0(d/D=0.007) 10.0(d/D=0.007;

TALC 20 VI

0.03(d/D=0.148)1.0(d/D=0.596) 10.0(d/D=0.7 6)

TALC 4 0 V%

0.03(d/D=0.661)1.0(d/D=0.764) 10.0(d/D=0.88:

Figure 7.23 Summary of schematic observation fromcapillary extrudates with volume and extrusion rate changes


Capillary Die ( D = 0.8, L = 45 mm) Aspect Ratio ( 1 : 1 )Area : 0.46



Capillary Die ( D = 4.8, L = 45 mm) Aspect Ratio (1 : 1)Area : 18.1

Figure 7.24 Geometric Orientation Instability Effecttalc from different capillary dies at 5


372Capillary Die ( D = 0.8, L = 45 mm)Aspect Ratio ( 1 : 1 )A rea: 0.46

Capillary Die ( D = 1.6,L = 45 mm) Aspect Ratio ( 1 : 1 )Area : 2.01

Capillary Die ( D = 3.2,L = 45 mm) Aspect Ratio ( 1 : 1 )Area : 8.04


Figure 7.25 Geometric Orientation Instability Effect oftalc from different capillary dies at 40 v%


3 7 3C a p i l l a r y R e s e r v o i r To D i e E n t r a n c e

In the reservoir (D=9.5mm), the talc particles are

oriented only on the die wall surface region and as they

approach to the capillary die entrance they orient to flow

direction as shown on Figure 7.22c. Schematic

representation of capillary reservoir flow was shown in

Figure 7.26. Figure 7.22c shows plug tip flow at 20 v% talc

particle flow from reservoir to capillary die entrance.

They are well oriented to the flow direction and

circumferential direction on the die wall region and radial

direction in the core. However 40 v% talc filled system

shows radial direction orientation is dominant every where

except on the capillary reservoir die wail surface.

Twin S c r e w E x t r u d e r

The feed from twin screw extrudates at diameter 4.8 mm

which has shear rate 32Q/7tD3 = 1.28xl05 (sec1) showed in

Figure 7.21. Schematic representation in Figure 7.21 was

shown in Figure 7.27.

The results are similar to each other at various shear

rate changes, occurring radial direction orientation.


3 7 4

TALC 5V% TALC 2 0 V% TALC 4 0 V%

Figure 7.26 Summary of reservoir to capillary entranceflow of talc particles


375

5 V% 20 V% 40 V%

Figure 7.27 Schematic representation of twin screwextruder extrudates of talc filled thermoplastics


376It is evident that talc volume loadings are mainly

dependent on occurring radial direction orientation.

7.3.2.2 Dimensionless Correlations

As shown in Figure 7.3 and Figure 7.4 the radial ratio

increases with extrusion rate increases and volume loading

increases. Volume loading seems more effective on radial

direction orientation as shown in Figures 7.3 and 7.4. Die

wall shear stress is also effective on radial direction

orientation, however much less effective on radial direction

orientation than volume loading increases. The critical

point of occurring radial direction orientation was observed

at 10-15 volume percent talc compounds. The n-value of

power law changes as a function of volume loadings as shown

in Figure 7.9. Figure 7.9 also shows the change of n-value

occurs between 10-15 volume percent talc-polystyrene

compound. We plot the changes of shear rates as a function

of volume loadings at constant extrusion rate at 32Q/7lD3 =

2.2 (sec'1) in Figure 7.6. This figure exhibits changes of

curve at 10-15 volume percent talc compounds. This may

related to formation of the liquid crystalline phase.


3777.3.3 Characteristics of Circumferential Arrays

If we imagine the flakes to be arranged

circumferentially with the smallest circumferential array

having six members and being located at the center of the

cross-section as shown in Figure 7.28, for a 0.05 volume

fraction compound the 0.08 Mm thick discs are separated by

1.44 Mm and for a 0.10 volume fraction, the separation

distance is 0.64 Mm. For a 0.20 volume fraction compound

the separation is 0.24 Mm and for a 0.40 volume fraction,

the separation distance is 0.04 Mm. The approximate layer

distance between talc particles in the core is about 0.2

micron and die wall is about 0.03 micron. In the core when

the talc particle distance is less than 0.2 micron there may

exist particle-particle interferences, and on the skin when

talc particle distance is less than 0.03 micron there exists

particle-particle interferences. In compareing 20 v% and 40

v% talc particle distances, calculated 20 v% and 40 v% talc

particle distances are clearly smaller than the talc

distances between six and seven particle rings resulting in

particle interferences. This strongly supports 20 v% and 40

v% talc should have interferences in the core region.


378

▲ (a)

▼ y

(b)

y

i .(c)

’(dj

Talc particle

1.24 micron

a.60

/ \.4"

• . • •• > t ■ • •

• • • •• • • •• • • •••••• •••••

• • • ♦ •

J 0.08 micron

Figure 7.28 Schematic representation of particle-particleangle and their diameter.


7.3.4 Flow Mechanism Hypotheses379

We believe that there is an instability during flow

which breakes up circumferential arrays of disc-like

particles with high radii of curvature into discrete random

groups of small random arrays. Figures 7.29 through 7.31

represent a schematic diagram of the aspect ratio from 1:1

to 1:20 and annular die for 5 v% and 40 v% talc-polystyrene

compounds orientation.

As volume loading and flow rate increase, this breakup

of circumferential arrays occurs up to high radii. As the

aspect ratio of the slit die decreases (10:1~1:1), the

radial direction orientation increases from the core region.

So we conclude talc particles orientation is influenced by

the processing geometry and volume loadings of talc

particles and mica particles (disc particles).

The real average distances observed from 5 v% talc is 1.7

micron (skin), 1.7 micron (core), 10 v% talc is 0.8 micron

(skin), 0.8 micron (core), 20 v% talc is 0.30 micron (skin),

0.23 micron (core), 40 v% talc is 0.20 micron (skin), 0.13

micron (core). The real average distances observed by SEM

show higher than calculated talc particle distance.


Capillary Die ( D = 1.6, L = 45 mm) Aspect Ratio ( 1 : 1)A rea: 2.01

3 8 0

Rectangular Die ( 1 x 2 x 23 mm) Aspect Ratio ( 1 : 2 )Area 2

Rectangular Die ( 0.6 x 6.4 x 15 mm) Aspect Ratio (1 : 10)Area 3.9

Rectangular Die ( 0.3 x 6.0 x 10.7 mm) Aspect Ratio (I : 20)Area 1.952

Figure 7.29 Geometric Orientation Instability Effect oftalc from different aspect ratio dies at 5 v%


381Capillary Die ( D = 1.6, L = 45 mm)Aspect Ratio (1 : 1)A rea: 2.01

Rectangular Die ( 1 x 2 x 23 mm) Aspect Ratio ( 1 : 2 )Area 2

Rectangular Die ( 0.6 x 6.4 x 15 mm) Aspect Ratio (1 : 10)Area 3.9

Rectangular Die ( 0.3 x 6.0 x 10.7 mm) Aspect Ratio (1 : 20)Area 1.952

Figure 7.30 Geometric Orientation Instability Effect oftalc from different aspect ratio dies at 40 v%


3 8 2

Annular Die Talc 5 v% (Di = 6.096, Do = 7.620, t = 0.762 , L = 36 mm)

Aspect Ratio (1 : 21.5) Area : 16.4

tJt

i' I

11 ti

Annular Die Talc 40 v% (Di = 6.096, Do = 7.620, t = 0.762, L = 36 mm)

Aspect Ratio (1 : 21.5) Area : 16.4

Figure 7.31 Geometric Orientation Instability Effect of talc from annular die at 5 v% and 40 v%


We made an empirical equation to relate radial

direction ratio d/D to particle volume loadings $.

3 8 3

dD

[1 +f \ b c

(7.i:

where a is maximum asymptotic radial ratio d / D , b is a

slope parameter, c is value at the inflection point, e is

symmetry parameter makes the curve asymmetric.

Flory (1956) showed the equilibrium degree of disorder

for rod-like particle (1-dimensional particle) as

0'=(-jX l--j) (7.2)

where A is the aspect ratio of a rod-like particle, <t>r is

equilibrium degree of disorder for rod. When A=10, (t>' is

0.64.

For the disc-like particle (2-dimensional particles) we

assume


3 8 4

(7.3)

where $ 2 is equilibrium degree of disorder for disc. When

A= 10, $ 2 is about 0.1, and

(7.4)

where is volume fraction measured and $ 2 is volume

fraction for disc particle. For example, for 0.05, 0.10,

0.20, 0.4 volume fraction talc filled system, d/D values are

0, 0, 0.40, 0.62 each, when A=10, m=0.4. The detail d/D

value may vary with shear rate changes.

It is worthwhile to discuss the mechanisms of particle

orientation in talc-thermoplastic or mica-thermoplastic

suspensions. It should seen that there are different

factors determining the orientation of the talc and mica

particles. First there are Jeffery 'torques' by which the

shear flow rotates the discs into shear planes. This tends

7.3.5 Mechanism of Particle Orientation


3 8 5to flow through a tube to set up a concentric particle

state of orientation. Secondly, by a totally different

mechanism-particle packing at higher loadings, disc

particles orient and arrange in a quasi lattice array to

form a mesophase as occurs in carbonaceous pitches (88-91).

This probably involves a mechanism not unlike that described

by Flory (SJ_) for rigid rods. The layered structure

parallel to the walls of dies and molds involves cooperation

between these two mechanisms.

Particle orientation is unstable in extrusion in some

geometries when the system is concentrated. The curvature

radius effect induced by the capillary walls in the disc

layers would seem to make them unstable at high loadings,

high radii of curvature and high shear rates. The reasons

for this are not completely clear, but one can envisage that

as one moves to increasingly lower radii a concentric disc

configuration becomes more difficult. As the shear

viscosity is highly non-Newtonian and indeed a yield value

exists, there is a very high viscous resistance to the

Jeffery torques which would tend to rotate the disc

particles into the concentric rings. This would tend to

decrease orientation especially in the core where the


38viscosity is the highest and the shear stresses and

torques the lowest.

The question arises as to whether similar phenomena

have been found in other systems. It is to be noted that

radial orientation structures are also observed in carbon

fibers made from disc-like mesophase carbonaceous pitch (87

91) where researchers discuss 'onion-skin' and 'radial'

fiber structures. Honda (^1) indeed has presented cross-

sectional morphologies (see Figure 7.32) for fibers melt

spun from pitch mesophase which are similar to the results

of this paper.


387

-\- \

Radialstructure

Onionskinand

mid-radialStructure

Onionskinand

mid-randomStructure

Figure 7.32 Cross-section texture of pitchHonda

Onion-likeStructure

fibers from H.


C H A P T E R V I I I

ALTERNATE MODELS FOR THE YIELD SURFACE OF

A TRANSVERSELY ISOTROPIC PLASTIC VISCOELASTIC FLUID

8.1. Introduction

Concentrated suspensions of small particles in various

matrices including polymer melts have long been known to

exhibit yield values, i.e. stresses below which there is no

flow (ms, 1H£, H I , 1 2 1 , 1 2 2 , 1 2 2 , 2 2 1 , 2 2 1 , 2 2 1 , 2 2 2 ) ■

This primarily has been discussed in terms of shear flow

experiments (1 0 5 . 1 0 6 . Ill. 1 2 1 , 1 3 6 . 1 3 8 . 2 2 1 , 2 5 7 . 2 6 7 .

2 7 1 . 2 7 2 ) , but evidence also exists for this type of

behavior in uniaxial elongational flow (1 0 6 . 2 7 2 ) . Most

studies simply exhibit shear viscosities which appear to

become unbounded at low stresses. However, more recently

results have been published that actually determine

stresses below which there is no flow (1 3 6 . 2 5 7 , 2 7 1 ) .

388


389There is a long history of efforts to develop 3-

dimensional constitutive equations for small particle

filled suspensions. Bingham (221) and Buckingham (222) in

the 1920s developed a 1-dimensional model of a fluid which

is rigid below a certain shear stress and then exhibits

linear viscous flow above it. This was put into 3-

dimensional form by Hohenemser and Prager (223) and Oldroyd

(227. 228) during the next two decades. The 3-dimensional

character of the yield stress was based upon the von Mises

yield criterion (237) for isotropic perfectly plastic

solids. In 1890 Schwedoff (220) developed a 1-dimensional

model of flow of fluid which was rigid below a critical

stress and behaved as a differentially linear viscoelastic

fluid at high stresses. An isotropic 3-dimensional plastic

viscoelastic model was given by White (231) and

subsequently investigated by this author and his coworkers

(1 2 1 , 220 . , 222 . , 2 2 2 ) .

The above cited investigations were concerned with the

behavior of concentrated compounds of isotropic particles.

However, many particles used in industrial compounds are

not isotropic in character but are instead fibrous and disc

like. Most industrial chopped fibers are made from glass

with dimensions of 10 (am or more, meaning that inter-


3 9 0particle associative forces are small. Compounds based

on such glass fibers do not exhibit yield values in shear

flow. The situation is rather different with particles

based upon minerals. Among these are 2-dimensional

covalently bonded silicate polymer sheets which form the

basis of talcs, micas and clays. They are micron scales in

size, giving rise to strong inter-particle forces and

agglomeration. It is also found experimentally that

particles such as talc and mica strongly orient during flow

in rheometers and geometries used in polymer processing

(71. 8 2 . 8 4 . 2 1 6 ) (see Chapter 6). The representation of

their rheological behavior requires an anisotropic flow

model. A theory of anisotropic and specifically

transversely isotropic plastic viscoelastic fluids has been

developed by White and Suh (240) for this purpose. This

model used an anisotropic yield criterion due to Hill (221.

223., 223) -

In the present paper we describe a new formulation of

the yield surface for this theory of transversely isotropic

plastic viscoelastic materials and contrast it to the

earlier theory.


8.2. Constitutive Relationships391

8.2.1 Three-Dimensional Modeling of Plastic-Viscous

Fluids

A 3-dimensional theory of the rheological properties

of particle-filled fluid including the existence of yield

values, was developed by Hohenemser and Prager (223) in

1932 to represent strain hardening of metals. They

introduced the use of invariants into the theory of non-

Newtonian fluids.

a = - ( t r a) I + T (8.1)3

Their paper builds on the von Mises theory of plastic

yielding. The von Mises yield criterion is based upon the

theory of invariants. The von Mises yield criterion for

isotropic materials is the second invariant of the

deviatoric stress tensor i.e.

tr T2 = 2 Y2 (8.2)


392where T is the deviatoric stress tensor and Y is the

shear yield stress of isotropic materials.

Below a stress field magnitude defined by Equation

(8.2), there is no flow. When yielding occurs in isotropic

materials the deviatoric stress tensor components are set

to the same as the deformation tensor as follows:

T * d (8.3)

2YT = . d (8.4)

v 2 tr d 2

At high stresses Hohenemser and Prager (223) defined the

deviatoric stress tensor T as

T = Y T+2 rig d (8.5)' '1 - — > 2

V2tr T ‘

where trT2 is second invariant.

In 1947 Oldroyd (227) redeveloped Equation (8.5) . He

rewrote Equation (8.5) as

(v/trT7 - J t y J = 47gtrd2 (8.6)


3 9 3

and noted that Equation (8.5) was equivalent to

T = 2Y .v2 tr d * + 277b (8.71

Oldroyd (228) later generalized Equation (8.5) to non-

Newtonian fluids by expressing Hb as a function of trd2.

8 . 2 . 2 Thixotropic Plastic-Viscoelastic Fluids

In 1932 Me Millen (286) and Freundlich and coworkers

(109. 110) and others had associated thixotropy with yield

values. In 1964 Slibar and Pasley (229) modified Equation

(8.7) to include thixotropy in a published paper. They did

this by representing the yield value Y as a function of t r d 2

and time of forms

T =2Y (t , trd2) , ^2 tr d 2

+ 2/7b ( 8 . 8 )


3 9 4

and showed that this equation at least qualitatively

agreed with suspension behavior. A specific form of

Y(t,trd2) was presented and discussed.

Subsequently, White (230) had suggested that Y of

Equations (8.16) and (8.17) should similarly be considered

to depend upon time and deformation history. The

formulation of White and Tanaka (232) and White and Lobe

(233) who used Equations (8.16) and (8.17) seems to be

better in the steady states than in transient flows. This

led Suetsugu and White (137) to propose using Equation

(8.17) with

(t, n d) = Yi(nd) - [ f a e an'J 'Zd z l^ttl1/ 2) - Yf] (8.9)

where Yf is the steady state yield value and Y± the initial

yield value. Yi was taken to be

( 8 . 10 )

where n d is 2trd2. Suetsugu and White represented H as a

single integral constitutive equation.


3 9 5

Montes and White (235) presented a thixotropic-

plastic-viscoelastic fluid model for highly filled small-

particle filled compounds. For highly filled small-

particle filled compounds

2Ya = - p xI + ■ H + H (8.11)

v2 tr H 2

where

H = p n f2{z, </>) [ c x(z) - - (tr c'1 (z) ) I ] dz (8 .12)

Pr = ~ - tr<L (8.13:

(t , n d ) = - f 'Zd z [y^n^2) - y£\ (8.14:

However, Yl was taken to be

yi(u j ) = y/ + / ? ,ny2+ A n ^ (8.15)

which is the same form as Suetsugu and White (137) with a

modified Equation (8.9). Montes and White (235) also

investigated the influence of carbon black on the steady


state and transient rheological properties of gum3 9 6

elastomers.

8.2.3 Three-Dimensional Modeling Of Plastic-

Viscoelastic Fluids

Plastic viscous fluid models are inherently unable to

represent the behavior of particle filled systems with

their inherent complex memories (elasticity). The first

effort to develop a three-dimensional form of a plastic

viscoelastic fluid beyond yield surface was Hohenemser and

Prager (223) who suggested models with Voigt and Maxwellian

behavior. The problems was reconsidered by White (230) in

1979 who wrote

where H is a general memory functional. The matrix is

viscoelastic in character.

Equation (8.6) was shown to be equivalent to

2Y (8.16)T T + HV2 tr T 2

2Y (8.17)T = r H + HV 2 tr H 2


3 9 7

The viscoelastic contribution is specified by H.

A specific simple form for H was proposed by White

(231) for the purpose of illustrating the characteristics

of Equation (8.17). Particular detailed forms of H were

subsequently used by White and Tanaka (232), and White and

Lobe (233) to compare with the experimental data on filled

thermoplastics and elastomers. White and Tanaka (232)

represented H as a single integral constitutive equation

with a Maxwellian relaxation modulus function.

These authors suggested that p. (t ) to a first approximate

could be expressed as

where f (<j>) is a factor that depends upon volume loading and

c ’1 is a Finger deformation tensor (see Equation (2.72)).

This theory was compared to experiments ( 2 2 2 . , 233) on

particle filled polymer melts.

3 (8.18)

(8.19)r


3 9 8More recently Suetsugu and White (133) , and Montes

and White (2 34. 235) presented thixotropic plastic-

viscoelastic fluid models similar to this in which H

depends on time.

8.2.4 Theory Of Transversely Isotropic Plastic

Viscoelastic Fluids

The formulation of transversely isotropic plastic

viscoelastic fluids as developed by White and Suh (jL2.) has

two parts. One of these relates to a yield surface, at

stresses below which there is no flow. The second is a

constitutive relationship between stress and the history of

the kinematics of strain and flow. Both the yield surface

and the constitutive relationship must satisfy the symmetry

of transverse isotropy.

The formulation may be expressed in terms of total

stress a a s :

a = \^ {trq )l + T (8.31)

where / is the unit tensor and T is the deviatoric stress.

The yield surface may be written


3 9 9

/ ( t ) = o (8.32)

The deviatoric stress is related to the history of the flow

kinematics. If this this were to be put in a small strain

form varying linearly with deformation rate we would have

where Y is the yield stress for the particular stress

component, G„kl(t) the relaxation moduli, and d,: is the rate

of deformation tensor. The 81 different Gllkl(t) components

may be reduced to 21 by arguments largely of symmetry.

This is recanted in theory of linear elasticity (240) .

White and Suh (£2) took the yield surface following

Hill's (221. 238. 23 9) treatment for anisotropic materials

to be

(8.33)

(8.34)


4 0 0

For transversely isotropic fluids where '2' is the

symmetry direction this should, according to Hill (221,

238. 239), simplify to

f ( T, ) = /r[<7'» ~ T' ^ +(T* + 2 ^ ] +W{(7'1 " r>J)2 + 4 ^ ] + 2 i ( ^ + 7S) = 1

(8.35)

This reduces the six constants of Equation (8.34) to three

constants. It reduces to the von Mises criteria when F, H,

and L / 3 are the same.

There are similar restrictions on the relaxation

modulus function G,lkt(t) . Symmetry about the '2' axis

requires the 21 independent moduli of Equation (8.35) to

reduce to 5 relaxation moduli. Specifically,

G 3 3 3 3 (t) = Gxm(t)

G 3 3 2 2 (t) = Gxx22 ( t )

G 3 2 3 2 ( t ) = Gx212 ( t )

Gijkm (t ) (k * m) =: 0

Gijkk (t ) (i * j * k) = 0

Gijkm (t ) (i *j) * (k * m)

Gi3i3(t) = — [Gnxi(t) ” Gii3 3 (f)] (8.36)


4 0 1

There are then 5 independent relaxation modulus functions,

G i i i i ( t ) , G 1 1 2 2 ( t ) , G 1 1 3 3 ( t ) , G 2 2 2 2 ( t ) / G 1 2 1 2 ( t ) .

It is possible to develop a simpler formulation of the

yield surface than Equation (8.35) . To this we call

attention to the work of Spencer (243-245) , who proposes

that the yield surface for anisotropic plastic solids with

a preferred direction to be of form:

where nt i s a unit vector which specifies this direction.

This formulation was developed to represent plastic flow in

fiber reinforced composites.

If one presumes the yield surface is independent of

hydrostatic pressure one may introduce the deviatoric

stress Tlf of Equation (8.31) in place of <jq i.e.

8.2.5 New Yield Surface

(8.37a)

F(T„,n,) = 0 (8.37b)


4 0 2

Equation (8.37b) must be valid independent of the sign of

n, . It follows that

F{T^n,n, ) = 0 (8.37c)

The form of Equation (8.37c) must be independent of a

coordinate system. It is argued by Spencer (243-245) that

this equation may be expressed in terms of three invariants

J . = ( r T 2 J - , = n T ~ n J , = t r T 3 (8.38)

If we limit ourselves to quadratic formulations it follows

that we may write Equation (8.37c) in the form

f[T, l ,n,nl ) = CxJ x + C2J 2 - 1 = 0 (8.39a)

or

t r T2 + a [ n - T 2 -nj = f3 (8.39b)

where Ci, C2, a and (5 are constants.

Equation (8.39) may be seen to simplify to the von Mises

criterion when the parameter a (or C2) is set equal to zero.


4 0 3

Clearly T2 must be positive and (3 is positive when a is

zero. It would seem likely that both and a are positive.

Equation (8.39) represents a significant

simplification on Equation (8.35) deriving from the work of

Hill (221. 238. 239). It reduces the number of parameters

of the yield surface from three to two. This is of great

significance from an experimental point of view.

Determination of yield values in shear flow and uniaxial

extension alone can determine the yield surface.

8.3. Application to Shear Flow and Uniaxial Extension

We now consider the application of the two

formulations to simple shear flow and uniaxial extension.

8.3.1 Shear Flow

8. 3.1.1 Simple shear flow parallel to disc surfaces

(CTi 2=CT s 1 / O r 0 ’3 2 = 0 S 3 )

The flow intended is shown in Figure 8.la or Figure

8.1b. It is this type of flow with discs sliding parallel

to each other that occurs in rheometers (22, 24., 240. 276) .


4 0 4

Figure 8.1

2A n

Flow

(b)

Schematic representation of simple shear flow parallel to disc surfaces (a) cri2=crsi (b)< * 3 2 = t f s 3


The stress field which must be applied now is;4 0 5

0 Tr. o ! i 0Tr. 0 o ; n = 10 0 o : 0

Ti:: 0 0I2 = 0 T 2 112 0 (8 .40a,b,c

0 0 0

The primary yield stress Yn or for Hill's

formulation is from Equation (8.35) :

K, ( 8 - 4 1 )

In terms of the model of Equation (8.39b) becomes

1T{2 + ccT{2 =/?

= Y = T■l 12 12 2 + a

(8.42a)

(8.42b)


4 0 6

where Y12 is Ysl the primary yield stress. Clearly

( 3 / ( 2 +a) must be positive.

When a is zero the yield criteria Y12 reduces to

the new yield surface Equation (8.39) may be written

t rT2 + a - n - T 2 n = (2 + a )Y 2{ (8.44)

8.3.1.2 Flow direction shear flow perpendicular to disc

stacking (a13=as2)

If the flow direction perpendicular to disc stacking

as shown on Figure 8.2, the stress field which must be

applied now is;

0 0 0T = 0 0 0 n = 1

T13 0 0 0


4 0 7

Figure 8.2

a n

1

Schematic representation of flow direction shear flow perpendicular to disc stacking( ° ’l 3 = a ’s2 )


4 0 8

T,f 0 0T2 =! 0 0 0 I

! 0 o r „ -(8.45a,b)

The shear stress <t 13 for the Hill's formulation is from

Equation (8.35)

The transverse yield stress Y13 or YS 2 is completely

independent of the primary yield stress Ys l . Only if (F+2H)

is equal to L would Ys2 equal Ys l .

In terms of the model of Equation (8.39b) it becomes

where Ys2 is the transverse shear yield stress. Thus must

be positive.

27jj + an2( T 2 )n n2 =/? (8.47a)

(8.47b)


Clearly4 0 9

(8.48)

and (l+or/2) must be positive. Thus a must be greater than

(-2) . Ys2 is independent of Ys l .

For a von Mises material a is zero and Ys2 and Ysl are the

8.3.2.1 Perpendicular to the Disc Axes (1-direction, cre l l )

Uniaxial extension with the discs parallel to the

surface of the filament being stretched is shown in Figure

8.3. It is this type of orientation which would arise in a

uniaxially stretched filament exiting from a capillary die.

The stress field which must be applied now is;

same . However when a —> oo , we obtain — - —> oo

8.3.2 Uniaxial Extension Flow


4 1 0

Figure 8.3

2' n

Schematic representation of perpendicular to the Disc Axes (1-direction, <Jeii)


4 1 1

T = 0

0

1- T.. 2 * *

0

! °

3 = 1 1 0

T..

! J -, 1II

= I 0

o

- T,a

- T ’4 " I

:8.49a,b)

For Hill's formulation

~ ^ * 1 ~ — — ii ^ 2 2 i 33 — rp— 7 7 (8.50)yj F + H

It can be seen that Hill's criteria gives a tensile yield

stress totally independent of the primary shear yield

stress,

, 8 . 5 1 )i;, \ F + f i

I f Yel l is much larger than Ys l , then L is much greater than

F+H. Yell is related to the transverse shear yield stress

by


4 1 2

& M (8.52)Ys2 V F + H

For a von Mises material F=H and Yeu = ^ 2 • in

addition F is L / 3 , then Yell will also equal \Jj Ys1 .

In terms of the model of Equation (8.3 9b) we obtain

- T 2 + an 2(T222)n2 = /? (8 .53)2 "

The uniaxial elongational stress yield stress is

_ r = 3 = 3 I fi = 3 I Pe l l 11 I I 2 2 11 j | 3 a \ 2 j a

A V + V i +V 2 4 V 6

(8.54)

Clearly /?/(3/2+a/4) is positive and (3 is positive. l + a / 6

must be positive which means that a must be greater than

(-6). This is less restrictive than our previous result.

For a von Mises ( a = 0 ) yield criteria Yei reduces to


Comparing the elongation to the primary shear yield value

g i v e s

Kn _ 3 1(2 + a )

K,

' / 4- n i ,— i ~ (8.56)

Clearly

Making a comparison to the transverse shear yield stress

for this yield criterion gives

YM J i 2Y* 2

l J +

0 +

a4

= V3a

1 +a

(8.57)

Clearly


4 1 4

Figure 8.4 Schematic representation of parallel to theDisc Axes (2-direction, crel2)


4 1 5

8. 3. 2. 2 Parallel to the Disc Axes (2-direct ion, a ei 2)

For uniaxial extension with the discs parallel to the

disc axes of the filament being stretched as shown in

Figure 8.4, the stress field which must be applied now is;

- - T 2 “ 0 0 01 = 0 Tmi 0 n = 1

0 0 _Ir 0

- 7 V 4 "

0 0i

t = 0 T 2’J ° ! (8.58a,b)

0 0 - 7 V j 4 - ■

■111/X X X s fcrmulat ion

This transverse elongational stress is independent of the

primary shear yield stress but related to the primary

elongational stress by


For a von Mises material F=H and Ye22 equals Yen .

For Spencer's yield surface

~ T22 + cm2(T222)n2 = fi (8.6i:

The uniaxial elongational stress yield stress is

3 - _ 3 \JL3

i 2 + a

Kn.=o-22 = r22- r u = - T 22= - ! (a.62)

Clearly a must be greater than (-3/2).

For a von Mises (a=0) yield criteria Ye22 reduces to the

form for Yen and Yel2 is J3 Ysl.

The ratio of the two different elongational yield stresses

is in general

3 a■h2__4+ a

(8.63!


4 1 7

Clearly

Similarly, comparing Yel2 to the primary shear yield stress

gives

‘■el 2 _ 3 2

2 +

2 +

a

a

(8.64!

Clearly

a —> oo —> -y .i 2

8.3.3 Two-Dimensional Shear

8.3.3.1 Shear Flow Parallel To Disc Layers

1-3 flow direction symmetry to 2-direction shear flow

(cy12+ a 32) is shown in Figure 8.5.


4 1 8

Figure 8.5

n

1

Schematic representation of shear flow parallel to disc layers (cr12+cr32)


The stress field which must be applied now is;4 1 9

Tx i:T 12 0

*32

t122 0 Tl2 tJ2

o tI22 + 7y’ o tI2 t32 o t322

This leads

= T 2 + T 2 = cr2 + cr2 =s l 12 ^ 1 12 .2 32 >/2L

In cerms of the model of Spencer's Equation (8.39b)

2 (cr[2 + cr;2) + a(cr22 + cr\2) =

2 _ - . 2 , ~ - 2 _s l 12 + ° ^ 2 2 + a

This indicates stresses in directions 1 and 3 i.e.

a 32 are equally able to produce flow.


8 .65a,b)

8 .6 6 )

we have

8 .67)

8 . 6 8 )

cr12 and

4 2 0Flow will occur when this criterion is achieved and

in a direction defined by it.

8.3.3.2 Two-dimensional shear flow normal to disc layers

(CXi2 + 0 ' i 3 )

Consider 2-3 direction shear flow (cr12+a13) as shown in

Figure 8.6.

The stress field which must be applied now is;

0 Tn Tn 0

z > T12 0 0 n = 1

T13 0 0 o

I 2

r =0 0 ii

0 T 2 12 TvJv,\\(8

0 T T

(8.69a,b)

For Hill's formulation from Equation (8.35) is

2 (F + 2 H ) T 123 + 2LTl2 = 1 (8.70)

Witn^ut knowledge of the relative values of L and F+2H,

this says little.


Figure 8.6 Schematic representation of two-dimensional shear flow normal to disc layers (cr12+ar13)


4 2 2However, if Ys2 is much greater than Ys l , then L is much

larger than F+2H and makes flow more easily in the 1-2

plane. A much larger stress is required from the 1-3

plane.

In terms of Spencer's yield surface

2(7;, + T{i ) JraT{l = P (8.7la)

or

2 + a)a*2 + 2cr = P (8.7lb)

Equation (8.71) appears to mean that if a is positive and

large, a very small stress a x2 can induce flow in the 1-2

plane but a very large stress a 13 is required to induce it

in the 1-3 plane. Flow is then much more likely in the 1-2

plane.


4 2 38.4 Yield Surface Of Anisotropy Parameter a As A

Function Of Various Yield Stress Ratios

8.4.1 Ratio of Uniaxial Yield Stresses Perpendicular to

Disc Axes to Simple Shear Flow Parallel to Disc

Surfaces

The shear flow intended is shown in Figure 8.la or

Figure 8.1b and uniaxial flow in Figure 8.3. It is this

type of shear flow with discs sliding parallel to each

other that occurs in rheometers (22, 24., 240. 276) and

uniaxial flow stretch to 1-direction.

When we consider Yen / Y sl as Xj., a from Equation (8.56)

can be rewritten as follow

x, = *ei: (8.73)

Figure 8.7 represents the yield surface for Yei i / Y sl as

a function of anisotropy parameter a .


-1.5 -1

Figure 8 . 7

! aJ------------------------------------ .— --- ------ ------------- -! : | l l i i i

0 1 2 3 4 5 6 7 8 9 10

Yield surface for yield stress ratio Ye l l / Y sl as a function of anisotropy parameter a


4 2 5When the anisotropy parameter a is positive, the yield

stress ratio Yen / Y slv a . r x e s from -J3 to 3.

8.4.2 Ratio of Yield Stresses Perpendicular to Disc

Stacking to Shear Stress Parallel to Disc

Surfaces

We now consider combined shear flow parallel and

perpendicular to the disc layers. It is this type of shear

flow with discs sliding parallel to each other that occurs

in rheometers {32., 3A, 240. 276) and shear flow

perpendicular to disc stacking.

When we consider Ys2/ Y sl as x2, a. from Equation (8.48)

can be rewritten as follows

a = 2{x\ - 1) (8 .76)

Figure 8.8 represents yield surface for Ys2/ Y sl as a

function of anisotropy parameter a .


Figure 8.8

_j a 10

Yield surface for yield stress ratio Ys2/ Y sl as a function of anisotropy parameter a


4 2 7

When the anisotropy parameter a is positive, the yield

ratio Ys2/ Y si varies from 1 to «.

8.5 Development of Stress Explicit Constitutive Equation

for New Yield Surface

A great advantage of the von Mises yield surface is

the ability to develop following the Oldroyd (227. 228)

constitutive equations which are explicit in the stress.

We will seek to develop a similar formulation here.

Spencer's yield surface can be represented as

2|" a[n ■ T 2 ■ n) nr T 2 1 + -*=— =- — =* = p

t r T(8.77)

We now introduce the parameter M

(8.78)trT"

which is the ratio of the two invariants.

Equation (8.77) can be now written as follows


4 2 8

r T 2 = --- (8.79)1 + cxM 2

Generally, the extra deviatoric stress beyond the

yield surfaces for a transversely isotropic material may be

expressed to start from

a = - (trcr)I + T (8.80)3

when r T 2 > 2Y2

T =

T =

J1-----Tt r T 2V 2

11 P1 1

\l1 + ccM2J.

T + Ht r T '

(8.81)

(8 .82)

We rewrite

1 -

P211 + CXM 2 = H (8.83)

trT'


4 2 9square and take the trace of each side. This gives

1 - - trT 2

1 -

P2

l + 1 aM 2

V2 trT"

1 , - trff2 2

root each sides and solve for Equation (8.84)

Equation (8.85)

1 2 - trT2 = 2 2 tr ff2 +

P 2 11 + aM 2

Introducing Equation (8.85) into Equation (8.1

1 - = f f

to solve for Equation (8.86)

(8.84)

then we have

(8.85)

3) we have

(8 .8 6 )


4 3 0

T = 1 4- H ( 8 . 8 7 )

The final form is represented as

T = H + H ( 8 . 8 8 )

For simple shear flow from Equation (8.42b)

2 = & (8.89)2 + a

P can be eliminated from Equation (8.88) in favor of Ysl.

We obtain


4 3 1

1 + a

T =

or

«1 , 1 !l + aM 2 (8.90)1 ,

t r H 2

Y.,T =

2 + a 2 + aM H + H (8.91)t r H '

8.5.1 M values for Simple Shear Flow

The quantity M is a stress invariant ratios not

constant. It should vary with the type of flow.

For flow parallel to the disc surfaces

T “ =

T 212 0 0= 0 T 212 0 (8

0 0 0

= 2 n= • T12 ' n 2 = 1 (82T,

An equivalent result is obtained for flow in the 3

direction with shear in the 2-direction.


For shear flow perpendicular to the discs4 3 2

. 2 !

^3 0 0 |0 0 0 ' (8.94)0 0 T 213 1

For the reference direction 2 (thickness direction)

n, • 0 • n, . „ „ _,= 2 ’ a = ° 1 8 ' 951Zi13

8.5.2 M Values For 2-Dimensional Flow Parallel To Disc

Layers (cy12+a 32)

T 212 0 T T12 32T 2 = 0 t 22 + t 22 0

T T±12J- 32 0 T 232

For (1+3)-direction shear with reference direction 2

M.shear = 2n. (Tf,

2(T.12

t ;2)t ~;2)

n-,= 1 (8.97)


8.5.3 M Values For Uniaxial Flow433

For 1-direction uniaxial extension

l ’n + 1 ’2 2 + 1 ’33 ~ 0

= -2T„ = —2T.33 1 = AT = A T *’■‘22 3 3

IT 2■‘■11 0 0

0 1 2 - T 4 11 0

0 0 - T 2. 4 lA

For 1-direction extension with reference direction

M.2 (a, n2) _ 2(n2 • T 2, • n2) _ 2(n2 njT 2 + T 2± l l ^ ■‘22 + T,33 (4T 2

For 2 -direction uniaxial extension (normal to

surfaces and parallel to axes)

T11+T22+T22 = 0


(8.98)

(8.99)

( 8 . 1 0 0 )

2

13

( 8 . 1 0 1 )

disc

(8 .1 0 2 )

4 3 4

- 2T,, = T22 = -2T33, IIIf'

1 1 -I - T ‘ ! 4 0 0

T 2 = j 0I1

r 2■*■11 0 !1 ,

° 0

r 2■33 (8.103

(8.104]

For 2-direction extension with disc reference direction 2

M,2-uni2(n, - T,2, • n,)T.2 + T2. + T 2

2(n2 ■ T 2, • n2)T , ,

2(n2 1 r,22 • nj43 r/a)2 4

43

8.5.4 M Values For Biaxial Flow

For 1 and 3 direction biaxial flow

(8.105)

T 1 1 + T 2 2 + T 3 3 = 0 (8.106)

r33 = ri2i rp __ _3 3 _ „ 224

(8.107)


4 3 5

T 2 = j 0

T2-‘■li 0 0

0 4T2 0

0 0 T 2

( 8 . 1 0 8 )

For (1 and 3)-direction flow with reference direction 22

M2(n2 • T 23

b ia x ia l T 2 + r 2 + r 2X 11 ^ 22 ^ 3 3

n.) _ 2 (n2 • 4T,2 • n2) _ 2 (nr 2 -i- 4 r 2 + t 2

t- }4

43

( 8 . 109!

8 .6 . Interpretation of M values

8 . 6 . 1 Simple Shear Flow

The M value of simple shear showed 1 for cr1 2 and cr3 2 and

0 for <t13 at reference direction 2.

0 < M u < 1sh e a r ( 8 . 110 )

This represents 12 or 32 plane direction flow occurs easily

than 13 plane direction flow which imply parallel to

oriented talc particle direction flow occurs easily than


436perpendicular to talc particle direction flow. Rewrite

simple shear flow Ysi from Equation (8.90)

1 + a

T =

S l. 1l + aM

2

f:

ff + ff

t rff‘(8 .111)

When M value is equal to 1, which is the case for

shearing perpendicular to the 2-direction, the anisotropy

term a from Equation (8.111) cancels out and becomes

T = Sl___

1 trff22

f f + ff ( 8 . 112 )

This is the same as for isotropic fluids. For a flow in

which M value is equal to 0, the anisotropy term a Equation

(8.111) remains and T is depend on a as shown in Equation

(8.113) .

T =y“ v1 +

a2 f f + ff

trff'(8.113)


Thus flow becomes more difficult if a is large and4 3 7

positive.

8.7 Discussion and Interpretation

Comparing the transversely isotropic yield surface

formulations of Spencer (243-245) and Hill (221, 23 8 . 239),

we note that the former is more pleasing as being based cn

an invariant formulation as is generally used in continuum

mechanics. It is thus a logical generalization of the

similarly formulated isotropic criterion of von Mises. The

Hill representation though more widely used is an open

question.

An alternate studies of the 1-dimensional transversely

isotropic yield surface formulation of Spencer (243-245.)

have been published by Robinson et a l . (246-252).

The Spencer formulation is based upon two different

parameters which is determinable from creep experiments in

simple shear and uniaxial extension. Hill's criteria

contains additional parameters i.e. three coefficients,

which make it much more difficult to experimentally specify

the yield surface.


4 3 8

The new parameter a or Cx, which enters into the

yield surface of Spencer (243-245) represents the

difficulty of achieving transverse shear as opposed to

inter disc surface shear flow. This is clear from

Equations (8.48) and (8.71). The meaning of the two

parameters F and H of Hill (221. 238. 239) are not clear.

The yield surface, Figures 8.7 through 8.9, showed the

anisotropy parameter a as increasing function on yield

stress ratio Ye l l / Y sl and Ys2/ Y s l . This suggests Yen and Ys2

are an increasing function with anisotropy parameter a .

Experimentally, only Yen / Y sl can be measured from simple

shear Ysl and 1-direction elongation Yen experiments.

Figure 8.7 shows the anisotropy parameter a increases

as a function of Yen / Y si . The anisotropy parameter a

exhibiting infinite at Yel l / Y sl is set equal to 3. The

Yei i /Ysi value of the anisotropic/isotropic mixed particle

filled system exists between the anisotropic and isotropic

particle-filled system at the same content depend on

isotropic particles' concentration. When the isotropic

particle concentration is low in the mixed particle filled

system, the Yen / Y sl value exhibited close to anisotropic

particle filled system at the same concentration. When the

isotropic particle concentration is high in the mixed


4 3 9particle filled system, the Ys l l / Y sl value exhibited close

to isotropic particle filled system which is the same as

the von Mises yield surface at the same concentration.

We have sought a constitutive equation which is

plastic viscoelastic in character and is of the general

type shown in Section 8.5.

The M value, which seems related to the mobility of

the system, is the ratio of normal direction deviatoric

stress invariant versus the other direction stress in the

field of trT2. In shear flow, as M value increases the

memory function H (Hijkm=riBdijkm) which imply deformation rate

of applied stress, increases, which suggests easy mobility

of the system. Comparing the M value of simple shear and

axial extension, the uniaxial direction Muruaxiai showed that

a cerm disappears at 1/3, and the biaxial direction

showed that a term disappears at 1 for and 1 for the simple

shear system. Thus, each system exhibited distinct M

values.

Our model represented as M parameter in Section 8.5

can be well fit for rheometer flow, however it is not good

for varying flow such as converging flow.


CHAPTER IX

A THEORY OF TRANSVERSELY ISOTROPIC PLASTIC VISCOELASTIC

FLUIDS TO REPRESENT THE FLOW OF ANISOTROPIC/ISOTROPIC

PARTICLE SUSPENSIONS IN THERMOPLASTICS

9.1 Introduction

A transversely isotropic yield surface developed by

Spencer (243-245) to represent plastic yielding in fiber

reinforced composites was introduced into the theory of

White and Suh (240) for transversely isotropic plastic

viscoelastic fluids in Chapter VIII. The two yield

surfaces were compared and interpreted for different

applied stress fields.

In this chapter, the transversely isotropic model is

applied to mixed particle filled thermoplastics. We begin

by stating the isotropic plastic viscoelastic model and

440


4 4 1then indicate how the transversely isotropic model may

be considered to merge in to it.

9.2 Linear Transversely Isotropic Plastic

Viscoelastic Fluids

9.2.1 Isotropic Linear Plastic Viscoelastic Fluid

The yield surface of an isotropic plastic viscoelastic

fluid is represented by the von Mises criteria. Equation

(8.35), Hill's criteria for transversely isotropic

materials, simplifies it when it reduces to the isotropic

case. This occurs when

F = H = — L (9.1)3

For the new Spencer yield criteria of Equation (8.39),

isotropy occurs when

a = 0

and the criteria also reduces to the von Mises form.


NOTE TO USERS

Page(s) missing in number only; text follows. Microfilmed received.

UM I


443

T = Y + (J^t - s)[tzd(s) ]dsJr + 2JCG(t - s)d(s)ds (9.4)

where T is deviatoric, trT is zero.

If we are to have incompressibility

r d = dii+d2 2 +d 3 3 = 0 (9.5)

and

/. (t ) —> co

9.2.2 Transition of Transversely Isotropic Linear

Plastic Viscoelastic Fluid

There are five independent moduli (Gu u , G2222, G 1 2 1 2 ,

G 1 3 1 3 , G1122) for a transversely isotropic material and two

moduli for an isotropic material.

We may specify the relationship to isotropy through

three parameters ki(t), k2(t), and k3 (t) . The two

independent moduli are considered as G12i2(t) and GU u(t) .

These become G(t) and X ( t ) in the isotropic theory

G 1 3 1 3 (t ) = ki (t) Gi2 i2 (t) (9.6a)

G2222 (t ) = k2 (t) G i m (t) (9.6b)


444Gll2 2 (t) = k 3 (t) G 1 1 3 3 (t)

= k 3 (t) [Gini (t ) -2 kiG1 2 i2 (t ) ] (9.6c)

where kL(t), k 2 (t), and k 3 (t) independently depend on time.

From Equations (9.4) we may write:

12 = y iz + 2 f - s)d,2(s)ds

3 2 = ^ 3 2 + 2 Gl2ia(t - s)d3 2(s)ds

13 = F 13 + 2 L klG,212 ~ Steads

11 = Yn + f d i l u t e " ^ + k2d22^ + d J2{s) )

- 2k.Gl2l2(t - s) (k3d 2 2 (s) + d 3 3(s) ) ]ds

2 2 = Y22 + [ {Gliu(t - s) [k 2d 22{s) + k 7(d,.{s) + d 3 3(s) ) ]- 2k,k,Gl212(t - s) (d1 3 (s) + d 3 3(s) ) }ds

33 = ^ 3 3 + [ x tGnii(t " s) (dn(s) + k id 22{8) + d 3 3(s) )- 2k,G1212(t - s) (d3 1(s) + k 3d 2 2 (s) ) ]ds

(9.7a,b,c,d,e,f)

The parameter k 3 (t) from Equation (9.6c) is related to

differences in Poisson's ratio and compressibility in

different directions. As our materials are incompressible,

we lose little in generality by setting


k3(t) = l445

(9.8)

Applying Equation (9.8) to Equation (9.7) leaves Equations

(9.7d,e,f) where k 3 (t) occurs to:

The four independent relaxation moduli are Gm i(t) , G 1 2 1 2 (t),

ki (t) , and k 2 (t) .

Isotropy requires the 4 relaxation moduli to go to 2

relaxation moduli.

This involves

[G1113(t - s) (d13(s) + k 2d 22{s) + d33(s) + ^G^jjftJdjJs) ]ds

22 + f {G,1,.(t - s) [k2d 22(s) + (d..(s) + d33(s) ) ]“ — J - » *

+ 2k1G.212(t - s)d22(s) j d s

[Gllll(t - s) (d,,(s) + d22(s) + d 23(s) + 2fc.G.212(t - s)d33(s) Jds

(9.9a,b,c)

kx(t) -> 1 , k 2 (t) 1 (9.10a)

or

Gi3 1 3 (t ) —> Gi2 i2 (t) and G 2 2 2 2 (t) —► G i m (t) (9.10b)


446Thus remain only two relaxation moduli Gmi(t) and

Gi2 i2 (t) as remains in Equation (9.6) .

9. 3 Application Of Non-linear Transversely

Isotropic Plastic Viscoelastic Fluid Model

A three-dimensional non-linear transversely isotropic

plastic viscoelastic model was developed by White and Suh

(240). They applied Finger deformation tensor (231. 232)

as a large deformation tensor and relaxation modulus

tensor. They expressed the deviatoric stress tensor in the

form

They put this equation into a formulation using a

deformation tensor. To do this, they introduce the tensor

relaxation function 0 ( t ) defined by

T = Y + H (9.12)

0 ( t ) (9.13a)

®ijkm ( £) (9.13b)


So Equation (9.12) can be rewritten as447

T = Y + - s) • e(s) ds (9.14)

where e is the infinitesimal strain tensor (24JL., 242)

1 du. .- (— - + — -) of linear elasticity and 0 i jkm( t ) may be seen2 ex. d x1

to be

t ) = £ —G ..

ri jkm. s

(9.15)

For large strains and deformation rates one must expect

that e i j will need to be replaced by a suitable large strain

deformation measure. White and Suh (240) suggested using

the Finger deformation tensor Ci j ' 1 (231. 232) where

-i ^ ,Q ^Ch 1 = -------- (9.16)e x e x

will become some mijka (t, deformation) . This leads

to Equation (9.14) as


448T = Y + fm(t - s) • c 1 (s) ds

= Y + L " s)c^ 1{s) d s(9.17)

where the integral is to be deviatoric. This is of course

a non-unique generalization of the earlier linear theory.

It is one of the finite infinity of proper non-linear

formulations. It further has the restriction that trT is

zero.

If we accept the symmetries of Equation (8.36) for

mijton(t) , the formulation leading to

(9.18)

Equation (9.17) gives the stress components

ds

32


449T2. = Y22 + [m,122(t - s) c.: 1 (s) + m2222(t - s)c22‘(s

+ m1122(t - s) c33'"(s) ] ds

33 = Yn + I tm n 33(t “ s ) c l l '1{s) + m1122( t - s ) c 221{s«A- x *

+ mlu,(t - s) c^'^s) ] ds

(9 .19 . a, b, c , d, e , f)

9.4 Considerations from experimental rheological

measurements

9.4.1 Shear Flow Behavior For Simple Shear Flow

For simple shear flow

0 y 0 1 + y i t - s) y{t - s)

d = ! y 0 c =0 0 0

l0

01

(9 . 2 0 :

We now seek to generalize the formulation we have

developed to non-linear plastic viscoelastic fluids. Based

on the shear viscosity behavior described in Section

8.3.1.1 we prescribe an empirical relationship for the

shear viscosity behavior of talc-thermoplastic compounds as


450

y = 0 when cr,2 < Y sX

<7.2 = Ysl + C Y = Ysl + A (°) Y W h e n si < < Ycbreshcld

i.e. threshold = y»! + A(o)/ (low shear rate)

A M y<7-2 = Kl + K Y = r sl + ~ ------- W h en threshold < <*12

b y + i(high shear rate)

(9.21a,b,c)

where lim Aty) = C , Ysl is the yield value in Equationy —>0

A(9.21b) . At the high shear rates lim — (/) = K , Equationy -*x B

(9.21c) becomes the power law with K = A / B . A / B are the

consistency and n the power law index, respectively. To

fit our viscosity-shear stress data Equation (9.21c) can be

rewritten as

rfiy) = ^ + - A[aj n2) - (9.22:Y Y B y + 1

In terms of Equation (9.19) we have


A(cr ,) r r z t = 2j} zm1212(z)dzBy + 1

451(9.23)

Consider the formulation of Equation (8.92)

T =

P2a1 + M 2

1 2 t r H2

a

H + H =

1 +a1 + M 2

1 t r H 22

H + H (9.24)

For the calcite particle filled system a equals zero.

We may write in general for simple shear where M= 1

=J 1 t r H . . 2V 2

(9.25)

In Figures 9.1 through 9.3, we contrast predictions of

Equation (9.21) with the experimental shear flow behavior

of talc, calcite, and talc/calcite filled thermoplastic

compound melts exhibiting yield values. For the 40 v% talc

filled system we took Y sl equal to 1 kPa and Y chreshoid equal

to 5.1 kPa, and A(0) equal to 825 MPa. Then, A for shear

stresses more than 10 kPa is 0.12 MPa, B is 0.04. For the


45220/20 v% talc/calcite mixed particle compounds have Y s i

equal to 0.96 kPa and Y chreshoid equal to 3.2 kPa. A(0) equal

to 317 MPa. A for shear stress greater than 5 k Pa is 0.18

MPa, B is 0.04. We have also fit this to the 40 v% calcite

compound Y sl equal to 0.43 kPa and Y chreShoid equal to 2.4 kPa,

A (0) equal to 133 MPa. A for shear stress greater than 5

kPa is 0.15 MPa, B is 0.06. The fit of Equation (9.21) is

quite good. Table 9.1 summarizes the parameters of

empirical equations for particle filled thermoplastics.

9.4.2 Comparison of Experimental Results with

Constitutive Equation with New Yield Surface

The experimental studies used include simple shear stress

measurements and uniaxial stress measurements. The

transition from transverse isotropy to isotropy with talc

particle content is considered.

Alternate models for the yield surface of a

transversely isotropic plastic viscoelastic fluid has been

developed in Chapter 8 following Spencer (243-245) .


453

Table 9.1 Parameters of empirical equations for

particle filled thermoplastics

Fillers Ysi Yth A (0) B (0) A B n

(vol%)

kPa kPalim A{y

7 -*0

M P a . s

(s1'") lim A{y7 — K

kPa. s

(s1'")

Talc 1.0 5.1 825 . 0 300 1.22 0 . 04 0 .308

(40)

Talc 0 . 1 0.2 44 . 7 33 1.08 0.08 0 .339

(20)

Talc/Calcite 0 . 9 3.2 317 . 0 80 1. 75 0 . 04 0 .311

(20/20)

Calcite 0.4 2.4 132 . 6 55 1. 50 0 . 06 0 .368

(40)


VIS

CO

SITY

(Pa.

S)

454

O PS/TALC (80:20)

□ PS/TALC (60:40)

106

Mil l. i m i l l

10° 101 102 1 03 1 04 1 0s 10® 107 10s

SHEAR STRESS (Pa)

Figure 9.1 Comparison of empirical equations withexperimental data for talc filled PS system at 200 °C


VISC

OSIT

Y (P

a.s)

455

1 0 1 0 g - T T T TTTTTj 1 ' I M lll| I I j IIIIIJ TTTTTTTT| I HT[ im ( I TTTTTTTj i i i i im j TTTTTT^

I i - ____„„..J10» r I o PS / CALCITE (60 : 40 ]

108 r ° (C )i -4

f 1 I107 k- \ i

106

i mm -I m ill H il lllili10° 101 102 103 10“ 105 106 107 10®

SHEAR STRESS (Pa)

Figure 9.2 Comparison of empirical equations withexperimental data for calcite filled system at 200 °C


F109

rF108C OCO 107

CL

t 1 0 6 b-C O 5O Fco 105 r

104F

1 0 3 b-

102

E PS / TALC / CALCITE (60:20:20)

4 ♦ N

■4

mmI ! ■ 1111?ii i i m i n i — .L : i mi-'l

00

" " I : : ' m ill___ i ■ i m ill

10° 101 102 103 104 105 106 107 10®

SHEAR STRESS (Pa)

Figure 9.3 Comparison of empirical equations withexperimental data for talc/calcite filled system at 200 °C


45This formulation contains two parameters (a, p) which can

be determined from creep and uniaxial extension

experimental studies.

9. 4. 2.1 Yield Surface from Constitutive Relationships

The mixed particle-filled system developed in Chapter

8 can be represented as Equation (9.31) .

It involves two parameters material a and P and M is

the ratio of the two invariants which is determined by the

flow. For an isotropic material a is zero ana obtain the

von Mises criteria. The parameter a measures the level of

a isotropy.

In terms of the mixed particle system, we should have

for the yield surface of Equation (9.31),

a = 0 ;isotropic particle filled

t z T(9.31)

system


4580 < a < maximum ;isotropic/anisotropic particle

filled system

a = maximum ,-anisotropic particle filled

system

(9.32)

9.4.2.2 Yield Surface of Anisotropy Parameter a as a

9.4.2.2.1 Simple shear flow parallel to disc surfaces and

1-direction Uniaxial Flow (Yen/Ysl)

The shear flow intended is shown in Figure 8.la or

Figure 8.1b and uniaxial flow in Figure 8.3. It is this

type of shear flow with discs sliding parallel to each

other that occurs in rheometers (£2., ££, 240. 276) and

uniaxial flow stretch to 1-direction. The relationship

between Yen and Ysi follows from Equation (8.56)

Function of Various Yield Stress Ratios

63 +(9.36)


4599.4.3 Experimental Results for PS/Talc, PS/Calcite,

PS/Talc/Calcite System

Table 9.2 summarizes the elongational (Yexi) and shear

(Ysl) yield values for PS/talc, PS/calcite, and

PS/talc/calcite system at 40 volume% loadings of fillers.

Figure 9.4 represents yield surface of Yen/Ysl as a

function of the anisotropy parameter a for talc, calcite,

and talc/calcite filled thermoplastics. When the

anisotropy parameter a is positive, the yield stress ratio

Yeii/Y.i ranges from %/i” to 3 . PS/talc 40 v% filled system

showed yield stress ratio Y en / Y sl = 2.95-37.2,

PS/talc/calcite 40 v% filled system showed Yeii/Ysi = 2.8-

23.0, and PS/calcite 40 v% filled system showed Yen/Ysi =

1.8-12.4. The minimum values are as follows

calcite talc/calciteY Y1 fj cl 1 ^ ci.1Y Yxsl Asl

The mean values are as follows

calcite talc/calcite

3 . 2 - ^ < — (9.5)Y.i Ysl

talc< L n

V..

talc< _ 1 0 . 2

YS1


460

Y /Y1 eir 1 s1

3talc

talc/calcite

AV calcite

1 -

a20 40 60 80 100 120

Figure 9.4 Yield surface of anisotropy parameter a as afunction of minimum yield stress ratio Yeii/Ysi for talc(40v%), calcite (40v%) , and talc/calcite(40v%) filled polystyrene


461

Table 9.2 Yield values of shear and elongational flowexperiments for PS/talc, PS/calcite, and PS/talc/calcite filled system

Fillers Shear Elongation Yield Stress

Yield Stress Yield Stress Ratio

(Pa) (Pa)

Ysi Yell Yeli/Ysl

Talc 292-1009 2977-10864 2.95-37 .2

4 0v%

Talc/CaC03 282-958 2682-6486 2.80-23 . 0

4 0v%

CaC03 239-428 770-2961 1.80-12 .4

40v%


9.4.4 Discussion462

In this chapter, we have sought to formulate

constitutive equations suitable for thermoplastics

containing concentrated suspensions of talc particles and

talc/calcite particles, which orient parallel to the metal

surfaces. This constitutive equation in plastic

viscoelastic in character.

Our linear model includes a yield surface with two

parameters and five independent relaxation functions, which

reduce to four with the introduction of incompressibility.

When we consider that flow occurs only in the 1-3 plane

direction such as well oriented talc flow, the relaxation

modulus remains as only one yield value parameter.

We represented a new rheclogical model for mixed

particle filled thermoplastic.

White and Suh (240) represented Hill's five relaxation

moduli as expansion parameter X ( t ) and shear modulus

parameter G(t). We presented Spencer's five relaxation

moduli as expansion parameter Gim(t) and shear modulus

parameter Gi2i2 (t). Both models applied incompressibility.

The final form is similar to a three-dimension non-linear


463transversely isotropic plastic viscoelastic model,

developed by White and Suh (240).

9.5 Conclusions

We measured anisotropy parameter a, and parameter p, A,

B, and Ysi. Ysl was measured from experiments, a from yield

ratio of Yeii/Ys, p from Equation (8.42b) and Equation

(8.54), and A and B from Equation (9.25) . The values are

summarized in Table 9.1 through Table 9.3.

Experimentally, we measured Yen/Ysi from simple shear

(Ysi) and elongation (Yeii) experiments. As shown on Figure

9.4, the anisotropy parameter a exhibits increasing

function as yield stress ratio Yen/Ysi increases. The yield

stress ratio Yen/Ysi of the talc/calcite mixed particle filled system appeared between the talc and calcite

particle filled system at the same concentration. The

yield stress ratio Yeii/Ysl of the talc/calcite mixed

particle filled system depends on calcite particles

concentration. When the calcite particle concentration is

high in the mixed particle filled system the Yen / Y si value

exhibited close to calcite filled system which is the same

as the von Mises yield surface. The anisotropy parameter a


464for 40 v% talc particle filled system would be 115 if

Ye11/Ysi is equal to 2.95 where the real yield value measured from experiments Y eii is 2977 Pa and Y si is 1009 Pa. This

ratio is minimum yield stress to fit into the yield surface

curve. When we compare Y eii at 2977 Pa and Ysl at 292 Pa the

ratio is 10.2. For the 40 v% talc particle filled system,

anisotropy parameter a showed a very high number, which

represents the state of highest anisotropy. Anisotropy

parameter a for the 40 v% talc/calcite particle filled

system exhibited 25 at Y e i i / Y si and is set equal to 2.80

where Y e n is 2682 Pa and Y sl is 958 Pa. When we compare Yenat 2682 Pa and Y gl at 282 Pa the ratio is 9.5. At the 40 v%

talc/calcite particle filled system the anisotropy

parameter a is located between zero and infinity, which

represents between the isotropy and anisotropy states.

Anisotropy parameter a for 40 v% calcite particle filled

system exhibited 0.25 at Yen/Ysi and is set equal to 1.80

where Y en is 770 Pa and Y si is 428 Pa. When we compare Y en

at 770 Pa and Y sl at 23 9 Pa the ratio is 3.2. Anisotropy

parameter a showed almost zero at the 40 v% calcite

particle filled system, which represents highest isotropy.

Table 9.3 summarizes the anisotropy parameter a for various

particle-filled systems as a function of Yen/Ysl.


465

Table 9.3 The anisotropy parameter a for variousparticle filled systems as a function of Y ei i / Y sl

Fillers Anisotropy

Parameter

(a)

Parameter

(P>

Talc 115 9.955x10°

40v%

Talc/CaC03 25 2.147x10s

40v%

CaC03 0 .25 0.125x10s

40v%


466The Spencer's yield model is valid only if yield

stress ratio Yeii/Ysl is less than three. For the PS/talc

(40 v%) , PS/talc/calcite (20/20 v%) , PS/'calcite (40 v%)

system as shown in Section 9.4.3, the minimum yield stress

ratio Yeii/Ysi ranges from 1.8 to 2.95. This yield stress

ratio can be represented on Spencer's yield surface.

However, the mean value exhibited ranges from 3 to 10 and

is higher than Spencer's yield criteria. This implies that

Spencer's model is valid only for minimum yield stress

ratios in our system. If the yield stress ratio Yen/Ysi exhibits higher than three, Spencer's yield surface is not

valid.

There are two ways to consider this behavior.

First, elongational measurement. The elongational

yield values were measured in the nitrogen gas chamber as

an alternative to the silicone oil bath method. This

nitrogen gas chamber method should be developed further to

obtain accurate elongational viscosity/yield measurements.

Second, Hill's yield criteria. Hill's yield criteria

may be valid to present the yield stress ratio Yeii/YsX

higher than three. However, Hill's yield surface has three

constants that were not possible to be determined by

practical experiments.


CHAPTER X

CONCLUSIONS AND RECOMMENDATION

10.1 Introduction

It was our purpose in this dissertation to develop a

broad based perspective of the materials science and

engineering behavior of polymer melts filled with high

loadings of talc, calcite, and talc/calcite particles. The

orientation characteristics of particles in simple

rheometers are basic for rheological modeling of

anisotropic compounds and studies of particle orientation

development during the processing of talc-filled

thermoplastics. The rheological behavior of talc, and

calcite-thermoplastic compounds should be important to the

processing of particle filled thermoplastic melts. The

behavior of talc/calcite thermoplastic compounds should be

representative of mixed particle compounds.

467


468The 3-dimensional rheological model, which was

developed, provides deeper perspectives in interpreting the

experimentally obtained flow behavior of filled compounds.

We now summarize the major conclusions of this

dissertation.

10.2 Conclusions

10.2.1 Orientation Studies from Wide Angle X-ray

Diffraction

We investigated talc, calcite, and talc/calcite

compounds from low loadings to high loadings in various

flow geometries.

The degree of orientation of the talc particles from

capillary extrudates was found to increase and then

decrease as talc volume loading increases. Scanning

electron microscopy studies showed that in the outer radii,

the talc particles are parallel to the die surface but

complex particle orientation occurs in the extrudate core.

There was a general tendency in mixed particle systems

for the talc particles to decrease in orientation with

increasing calcite content.


46910.2.2 Quantitative Analysis of Filler Composite

using X-ray Intensity Method

We made a new quantitative investigation of x-ray

absorption using the wide angle x-ray diffraction (WAXD)

intensity method for binary mixture (PS/Talc, PS/Calcite)

system and ternary mixtures (PS/talc/calcite) system. The

Alexander and Klug equation (182) was used to interpret the

data. This was the first application to systems of

crystalline mineral particles and amorphous thermoplastic.

We investigated the talc-calcite-polystyrene systems

assuming the pseudo-binary mixture system.

10.2.3 Rheological Considerations-Experimental

We have presented a broad range of experimental

studies of shear, elongational, and oscillatory flow

behavior of talc, calcite, and talc/calcite filled

thermoplastic melts. The viscosity increases with

increasing particle loading and with decreasing particle

size. The talc, calcite, and talc/calcite filled

thermoplastic melts with smaller particles at higher

loadings exhibit yield values, i.e. stresses below which


470there is no flow. We found a viscosity-shear stress

plateau and named the shear stress at the upper end of the

plateau the 'Threshold Yield Stress'. The true yield

values are much lower than the threshold yield value, which

were usually measured by extrapolation by casual

investigation.

The complex viscosity exhibited much higher than the

steady state shear viscosity at higher loadings of

particles. This represents that the Cox-Merz (263) rule

fails in the filled system.

We found that calcite and talc particle absorb

silicone oil in the elongational viscosity measurement

experiments. In alternative experiments, we measured

elongational creep in the nitrogen gas filled chamber.

This method allowed us to determine elongational yield

values.

10.2.4 Rheological Modeling

A 3-dimensional anisotropic rheological model has been

developed to interpret the anisotropic and plastic

characteristics of talc and talc/calcite particle

compounds.


The formulation is first developed in a linear 3-

dimensional form and finally in a non-linear 3-dimensional

form. The anisotropic plastic viscoelastic fluid model is

specialized to a transversely isotropic form to represent

the suspension behavior of oriented disc particles,

starting from Spencer's (243-245) invariant theory. This

model was developed from constitutive equations and tested

experimentally and compared with the White and Suh (240)

model.

10.3 Recommendations

We suggest the following as future studies on the

rheology and processing of talc or disc filled

thermoplastics.

(i) A study of disc-like particles, such as mica,

suspensions in thermoplastics during flow and

processing with a broader range of particle loadings

is recommended.

(ii) We observed phase orientation redistribution

phenomena from circular and rectangular cross-

section dies at high loadings of talc particles.


472T h i s p h e n o m e n o n s h o u l d b e v e r i f i e d w i t h

a d d i t i o n a l e x p e r i m e n t s a n d a f u r t h e r d e v e l o p e d

t h e o r y .

( i i i ) A d d i t i v e s s u c h a s s t e a r i c a c i d s h o u l d b e s t u d i e d f o r

d i f f e r e n t p a r t i c l e - f i l l e d s y s t e m s .

( i v ) E l o n g a t i o n a l v i s c o s i t y m e a s u r e m e n t s u s i n g s i l i c o n e

o i l s h o u l d b e r e p l a c e d b y a d i f f e r e n t t y p e o f o i l o r

m e d i u m t h a t i s n ' t a b s o r b e d b y t h e f i l l e r .

R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.

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