Thomas G. Mezger The Rheology Handbook For users of rotational and oscillatory rheometers 2nd revised edition
10 Contents Contents 1 Introduction 16 1.1 Rheology, rheometry and viscoelasticity 16 1.2 Deformation and flow behavior 17 2 Flow behavior and viscosity 19 2.1 Introduction 19 2.2 Definition of terms 19 2.2.1 Shear stress 19 2.2.2 Shear rate 21 2.2.3 Viscosity 24 2.3 Shear load dependent flow behavior 26 2.3.1 Idealviscous flow behavior according to Newton 26 3 Rotational tests 29 3.1 Introduction 29 3.2 Basic principles 29 3.2.1 Test modes CSR and CSS, raw data and rheological parameters 29 3.3 Flow curves and viscosity functions 30 3.3.1 Description of the test 30 3.3.2 Shear-thinning flow behavior 33 3.3.2.1 Structures of polymers showing shear-thinning behavior 35 3.3.2.2 Structures of dispersions showing shear-thinning behavior 40 3.3.3 Shear-thickening flow behavior 40 3.3.3.1 Structures of polymers showing shear-thickening behavior 43 3.3.3.2 Structures of dispersions showing shear-thickening behavior 43 3.3.4 Yield point 44 3.3.4.1 Determination of the yield point using a flow curve diagram 45 3.3.4.2 Determination of the yield point using a tangent method 46 3.3.4.3 Further information on yield points 47 3.3.5 Summary: Flow curves and viscosity functions 51 3.3.6 Fitting functions for flow and viscosity curves 53 3.3.6.1 Model function for idealviscous flow behavior 53 3.3.6.2 Model functions for shear-thinning and shear-thickening flow behavior 53 3.3.6.3 Model functions for flow behavior including zero-shear and infinite-shear viscosity 54 3.3.6.4 Model functions for flow curves including a yield point 55 3.4 Time-dependent flow behavior and viscosity function 58 3.4.1 Description of the test 58 3.4.2 Time-dependent flow behavior of samples showing no hardening 59 3.4.2.1 Structural decomposition and regeneration (thixotropy and rheopexy) 60 3.4.2.2 Test methods for investigating thixotropic behavior 62 3.4.3 Time-dependent flow behavior of samples showing hardening 67 3.5 Temperature-dependent flow behavior and viscosity function 69 3.5.1 Description of the test 69 3.5.2 Temperature-dependent flow behavior of samples showing no hardening 69 3.5.3 Temperature-dependent flow behavior of samples showing hardening 69 3.5.4 Fitting functions for temperature-dependent viscosity curves 70 3.6 Pressure-dependent flow behavior and viscosity function 72
Contents 11 4 Elastic behavior and shear modulus 74 4.1 Introduction 74 4.2 Definition of terms 74 4.2.1 Deformation and strain 74 4.2.2 Shear modulus 75 4.3 Shear load-dependent deformation behavior 78 4.3.1 Idealelastic deformation behavior according to Hooke 78 5 Viscoelastic behavior 80 5.1 Introduction 80 5.2 Basic principles 80 5.2.1 Viscoelastic liquids according to Maxwell 80 5.2.1.1 The Maxwell model 80 5.2.1.2 Examples of the behavior of VE liquids in practice 82 5.2.2 Viscoelastic solids according to Kelvin/Voigt 84 5.2.2.1 The Kelvin/Voigt model 85 5.2.2.2 Examples of the behavior of VE solids in practice 86 5.3 Normal stresses 88 6 Creep tests 90 6.1 Introduction 90 6.2 Basic principles 90 6.2.1 Description of the test 90 6.2.2 Idealelastic behavior 91 6.2.3 Idealviscous behavior 92 6.2.4 Viscoelastic behavior 92 6.3 Analysis 92 6.3.1 Behavior of the molecules 92 6.3.2 The Burgers model 93 6.3.3 Curve discussion 94 6.3.4 Definition of terms 96 6.3.4.1 Zero-shear viscosity 96 6.3.4.2 Creep compliance, creep recovery compliance 97 6.3.4.3 Retardation time 99 6.3.4.4 Retardation time spectrum 100 6.3.5 Data conversion 102 6.3.6 Determination of the molar mass distribution 102 Relaxation tests 103 Introduction 103 Basic principles 103 Description of the test 103 Idealelastic behavior 104 Idealviscous behavior 105 Viscoelastic behavior 106 Analysis 106 Behavior of the molecules 106 Curve discussion 106 Definition of terms 107 Relaxation modulus 107 Relaxation time 109
12 Contents 7.3.3.3 Relaxation time spectrum 109 7.3.4 Data conversion 112 7.3.5 Determination of the molar mass distribution 113 8 Oscillatory tests 114 8.1 Introduction 114 8.2 Basic principles 114 8.2.1 Idealelastic behavior 115 8.2.2 Idealviscous behavior 116 8.2.3 Viscoelastic behavior 117 8.2.4 Definition of terms 118 8.2.5 The test modes CSR and CSD, raw data and Theological parameters 122 8.3 Amplitude sweeps 124 8.3.1 Description of the test 124 8.3.2 The structural character of a sample 125 8.3.3 The limiting value of the LVE range 125 8.3.3.1 Values of the permissible maximum strain (limit of the LVE range) 126 8.3.3.2 Important values of the shear stress (limit of the LVE range) 128 8.3.4 Determination of the yield point and the flow point using amplitude sweeps... 128 8.3.4.1 Yield point or yield stress 128 8.3.4.2 Flow point (orflow stress) 129 8.3.4.3 Yield zone between yield point and flow point 129 8.3.4.4 Evaluation of the two terms yield point and flow point 129 8.3.5 Frequency-dependence of amplitude sweeps 129 8.3.6 Behavior outside of the LVE range 130 8.4 Frequency sweeps 131 8.4.1 Description of the test 132 8.4.2 Behavior of unlinked polymers 132 8.4.2.1 Single Maxwell model for polymers showing a narrow molar mass distribution 133 8.4.2.2 The generalized Maxwell model for polymers showing a wide MMD 135 8.4.3 Behavior of cross-linked polymers 138 8.4.4 Behavior of dispersions and gels 139 8.4.5 Comparison of superstructures using G'-curves of frequency sweeps 141 8.4.6 Multiwave test 142 8.4.7 Data conversion 143 8.5 Time-dependent behavior at constant dynamic-mechanical and isothermal conditions 143 8.5.1 Description of the test 143 8.5.2 Time-dependent behavior of samples showing no hardening 144 8.5.2.1 Structural decomposition and regeneration (thixotropy and rheopexy) 145 8.5.2.2 Test methods for investigating thixotropic behavior 146 8.5.3 Time-dependent behavior of samples showing hardening 150 8.6 Temperature-dependent behavior at constant dynamic mechanical conditions 153 8.6.1 Description of the test 153 8.6.2 Temperature-dependent behavior of samples showing no hardening 154 8.6.2.1 Structures and temperature curves of polymers 154 8.6.2.2 Temperature-curves of dispersions and gels 159 8.6.3 Temperature-dependent behavior of samples showing hardening 160 8.6.4 Thermoanalysis (TA) 162
Contents 13 Time/temperature shift 163 Temperature shift factor according to the WLF method 163 The Cox/Merz relation 168 Combined rotational and oscillatory tests 169 Presetting rotation and oscillation in series 169 Superposition of rotation and oscillation 169 9 Measuring systems 171 9.1 Introduction 171 9.2 Concentric cylinder measuring systems (CC MS) 171 9.2.1 Cylinder systems in general 171 9.2.1.1 Geometry of cylinder systems showing a large gap 171 9.2.1.2 Operating methods 171 9.2.1.3 Calculations 172 9.2.2 Narrow-gap concentric standard cylinder measuring systems 173 9.2.2.1 Geometry 173 9.2.2.2 Calculations 174 9.2.2.3 Conversion between raw data and Theological parameters 176 9.2.2.4 Flow instabilities and secondary flow effects in a cylinder MS 176 9.2.2.5 Advantages and disadvantages of cylinder MS 177 9.2.3 Double-gap measuring systems (DG MS) 178 9.2.4 High-shear cylinder measuring systems (HS MS) 178 9.3 Cone-and-plate measuring systems (CP MS) 179 9.3.1 Geometry 179 9.3.2 Calculations 179 9.3.3 Conversion between raw data and Theological parameters 181 9.3.4 Flow instabilities and secondary flow effects in a CP MS 181 9.3.5 Cone truncation 181 9.3.6 Maximum particle size and gap setting 182 9.3.7 Filling of the CP system 182 9.3.8 Advantages and disadvantages of CP MS 183 9.4 Parallel-plate measuring systems (PP MS) 184 9.4.1 Geometry 184 9.4.2 Calculations 185 9.4.3 Conversion between raw data and Theological parameters 186 9.4.4 Flow instabilities and secondary flow effects in a PP MS 186 9.4.5 Recommendations for gap setting 186 9.4.6 Automatic gap settings (AGS) and automatic gap control (AGC) using the normal force control (NFC) option 187 9.4.7 Determination of the temperature gradient in the sample 187 9.4.8 Advantages and disadvantages of PP MS 188 9.5 Mooney/Ewart measuring systems (ME MS) 189 9.6 Relative measuring systems 190 9.6.1 Measuring systems with sandblasted, profiled or serrated surfaces 190 9.6.2 Spindles in the form of disks, pins and balls 191 9.6.3 Krebs spindles 193 9.6.4 Paste spindles showing pins and vanes 194 9.6.5 Ball measuring systems 195 9.7 Measuring systems for torsion bars 195 9.7.1 Bars showing a rectangular cross section 196 9.7.2 Bars showing a circular cross section 197
14 Contents 10 Instruments 199 10.1 Introduction 199 10.2 Short overview: methods for testing viscosity and elasticity 199 10.2.1 Very simple determinations 199 10.2.2 Flow on a horizontal plane 200 10.2.3 Spreading or slump on a horizontal plane after lifting a container 203 10.2.4 Flow on an inclined plane 201 10.2.5 Flow on a vertical plane or over a tool 201 10.2.6 Flow in a channel, trough, bowl 202 10.2.7 Flow cups and other pressureless capillary viscometers 202 10.2.8 Devices showing rising, sinking, falling, rolling elements 203 10.2.9 Penetrometers, consistometers, texture analyzers 204 10.2.10 Pressurized capillary devices 206 10.2.11 Simple rotational viscometer tests 206 10.2.12 Devices with vibrating or oscillating elements 208 10.2.13 Rotational and oscillatory curemeters (for rubber testing) 208 10.2.14 Tension testers 209 10.2.15 Compression testers 210 10.2.16 Linear shear testers 210 10.2.17 Flexure or bending testers 210 10.2.18 Torsion testers 211 10.3 Flow cups 211 10.3.1 The ISO cup 212 10.3.1.1 Capillary length 213 10.3.1.2 Calculations 213 10.3.1.3 Flow instabilities, secondary flow effects, turbulent flow conditions in flow cups 215 10.3.2 Other types of flow cups 216 10.4 Capillary viscometers 216 10.4.1 Glass capillary viscometers 216 10.4.1.1 Calculations 218 10.4.1.2 Determination of the molar mass of polymers from diluted polymer solutions 219 10.4.1.3 Determination of the Viscosity Index VI of petrochemicals 224 10.4.2 Pressurized capillary viscometers 225 10.4.2.1 MFR and MVR testers driven by a weight ("low-pressure capillary viscometers") 225 10.4.2.2 High-pressure capillary viscometers (HP CV), driven by an electric drive, for testing highly viscous and paste-like materials 229 10.4.2.3 High-pressure capillary viscometers (HP CV), driven by gas pressure, for testing liquids 231 10.5 Falling-ball viscometers 233 10.6 Rotational and oscillatory rheometers 234 10.6.1 Rheometer set-ups 235 10.6.2 Control loops 236 10.6.3 Devices to measure torques 239 10.6.4 Devices to measure deflection angles and rotational speeds 239 10.6.5 Bearings 240 10.6.6 Temperature control systems 242 11 Guideline for Theological tests 245 11.1 Selection for the measuring system, 245
Contents 15 11.2 Rotational tests 245 11.2.1 Flow and viscosity curves 245 11.2.2 Time-dependent flow behavior (rotation) 246 11.2.3 Step tests (rotation): structure breakdown and recovery ("thixotropy") 246 11.2.4 Temperature-dependent flow behavior (rotation) 246 11.3 Oscillatory tests 247 11.3.1 Amplitude sweeps 247 lt.3.2 Frequency sweeps 247 11.3.3 Time-dependent viscoelastic behavior (oscillation) 248 11.3.4 Step tests (oscillation): structure breakdown and recovery ("thixotropy") 248 11.3.5 Temperature-dependent viscoelastic behavior (oscillation) 249 11.4 Selection of the test type 249 11.4.1 Behavior of the rest 249 11.4.2 Flow behavior 251 11.4.3 Structural recovery ("thixotropic behavior", e.g. of coatings) 251 12 Rheologists and the historical development of rheology 252 12.1 Developments until the 19 th Century 252 12.2 Developments between 1800 and 1900 254 12.3 Developments between 1900 and 1949 258 12.4 Developments between 1950 and 1979 263 12.5 Developments between 1980 and 2004 265 13 Appendix 267 13.1 Symbols, signs and abbreviations used 267 13.2 Greek alphabet 273 13.3 Conversion table for units 274 14 References 277 14.1 Publications and books 277 14.2 ISO standards (International Standards Organisation) 283 14.3 ASTM International standards (American Society for Testing and Materials) 284 14.4 DIN standards (Deutsche Industrie Norm, German Industry Standards) 288 15 Index 290