The Rheology Handbook

Transcription

1 Thomas G. Mezger The Rheology Handbook For users of rotational and oscillatory rheometers 2nd revised edition

2 10 Contents Contents 1 Introduction Rheology, rheometry and viscoelasticity Deformation and flow behavior 17 2 Flow behavior and viscosity Introduction Definition of terms Shear stress Shear rate Viscosity Shear load dependent flow behavior Idealviscous flow behavior according to Newton 26 3 Rotational tests Introduction Basic principles Test modes CSR and CSS, raw data and rheological parameters Flow curves and viscosity functions Description of the test Shear-thinning flow behavior Structures of polymers showing shear-thinning behavior Structures of dispersions showing shear-thinning behavior Shear-thickening flow behavior Structures of polymers showing shear-thickening behavior Structures of dispersions showing shear-thickening behavior Yield point Determination of the yield point using a flow curve diagram Determination of the yield point using a tangent method Further information on yield points Summary: Flow curves and viscosity functions Fitting functions for flow and viscosity curves Model function for idealviscous flow behavior Model functions for shear-thinning and shear-thickening flow behavior Model functions for flow behavior including zero-shear and infinite-shear viscosity Model functions for flow curves including a yield point Time-dependent flow behavior and viscosity function Description of the test Time-dependent flow behavior of samples showing no hardening Structural decomposition and regeneration (thixotropy and rheopexy) Test methods for investigating thixotropic behavior Time-dependent flow behavior of samples showing hardening Temperature-dependent flow behavior and viscosity function Description of the test Temperature-dependent flow behavior of samples showing no hardening Temperature-dependent flow behavior of samples showing hardening Fitting functions for temperature-dependent viscosity curves Pressure-dependent flow behavior and viscosity function 72

3 Contents 11 4 Elastic behavior and shear modulus Introduction Definition of terms Deformation and strain Shear modulus Shear load-dependent deformation behavior Idealelastic deformation behavior according to Hooke 78 5 Viscoelastic behavior Introduction Basic principles Viscoelastic liquids according to Maxwell The Maxwell model Examples of the behavior of VE liquids in practice Viscoelastic solids according to Kelvin/Voigt The Kelvin/Voigt model Examples of the behavior of VE solids in practice Normal stresses 88 6 Creep tests Introduction Basic principles Description of the test Idealelastic behavior Idealviscous behavior Viscoelastic behavior Analysis Behavior of the molecules The Burgers model Curve discussion Definition of terms Zero-shear viscosity Creep compliance, creep recovery compliance Retardation time Retardation time spectrum Data conversion 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

4 12 Contents Relaxation time spectrum Data conversion Determination of the molar mass distribution Oscillatory tests Introduction Basic principles Idealelastic behavior Idealviscous behavior Viscoelastic behavior Definition of terms The test modes CSR and CSD, raw data and Theological parameters Amplitude sweeps Description of the test The structural character of a sample The limiting value of the LVE range Values of the permissible maximum strain (limit of the LVE range) Important values of the shear stress (limit of the LVE range) Determination of the yield point and the flow point using amplitude sweeps Yield point or yield stress Flow point (orflow stress) Yield zone between yield point and flow point Evaluation of the two terms yield point and flow point Frequency-dependence of amplitude sweeps Behavior outside of the LVE range Frequency sweeps Description of the test Behavior of unlinked polymers Single Maxwell model for polymers showing a narrow molar mass distribution The generalized Maxwell model for polymers showing a wide MMD Behavior of cross-linked polymers Behavior of dispersions and gels Comparison of superstructures using G'-curves of frequency sweeps Multiwave test Data conversion Time-dependent behavior at constant dynamic-mechanical and isothermal conditions Description of the test Time-dependent behavior of samples showing no hardening Structural decomposition and regeneration (thixotropy and rheopexy) Test methods for investigating thixotropic behavior Time-dependent behavior of samples showing hardening Temperature-dependent behavior at constant dynamic mechanical conditions Description of the test Temperature-dependent behavior of samples showing no hardening Structures and temperature curves of polymers Temperature-curves of dispersions and gels Temperature-dependent behavior of samples showing hardening Thermoanalysis (TA) 162

5 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 Measuring systems Introduction Concentric cylinder measuring systems (CC MS) Cylinder systems in general Geometry of cylinder systems showing a large gap Operating methods Calculations Narrow-gap concentric standard cylinder measuring systems Geometry Calculations Conversion between raw data and Theological parameters Flow instabilities and secondary flow effects in a cylinder MS Advantages and disadvantages of cylinder MS Double-gap measuring systems (DG MS) High-shear cylinder measuring systems (HS MS) Cone-and-plate measuring systems (CP MS) Geometry Calculations Conversion between raw data and Theological parameters Flow instabilities and secondary flow effects in a CP MS Cone truncation Maximum particle size and gap setting Filling of the CP system Advantages and disadvantages of CP MS Parallel-plate measuring systems (PP MS) Geometry Calculations Conversion between raw data and Theological parameters Flow instabilities and secondary flow effects in a PP MS Recommendations for gap setting Automatic gap settings (AGS) and automatic gap control (AGC) using the normal force control (NFC) option Determination of the temperature gradient in the sample Advantages and disadvantages of PP MS Mooney/Ewart measuring systems (ME MS) Relative measuring systems Measuring systems with sandblasted, profiled or serrated surfaces Spindles in the form of disks, pins and balls Krebs spindles Paste spindles showing pins and vanes Ball measuring systems Measuring systems for torsion bars Bars showing a rectangular cross section Bars showing a circular cross section 197

6 14 Contents 10 Instruments Introduction Short overview: methods for testing viscosity and elasticity Very simple determinations Flow on a horizontal plane Spreading or slump on a horizontal plane after lifting a container Flow on an inclined plane Flow on a vertical plane or over a tool Flow in a channel, trough, bowl Flow cups and other pressureless capillary viscometers Devices showing rising, sinking, falling, rolling elements Penetrometers, consistometers, texture analyzers Pressurized capillary devices Simple rotational viscometer tests Devices with vibrating or oscillating elements Rotational and oscillatory curemeters (for rubber testing) Tension testers Compression testers Linear shear testers Flexure or bending testers Torsion testers Flow cups The ISO cup Capillary length Calculations Flow instabilities, secondary flow effects, turbulent flow conditions in flow cups Other types of flow cups Capillary viscometers Glass capillary viscometers Calculations Determination of the molar mass of polymers from diluted polymer solutions Determination of the Viscosity Index VI of petrochemicals Pressurized capillary viscometers MFR and MVR testers driven by a weight ("low-pressure capillary viscometers") High-pressure capillary viscometers (HP CV), driven by an electric drive, for testing highly viscous and paste-like materials High-pressure capillary viscometers (HP CV), driven by gas pressure, for testing liquids Falling-ball viscometers Rotational and oscillatory rheometers Rheometer set-ups Control loops Devices to measure torques Devices to measure deflection angles and rotational speeds Bearings Temperature control systems Guideline for Theological tests Selection for the measuring system, 245

7 Contents Rotational tests Flow and viscosity curves Time-dependent flow behavior (rotation) Step tests (rotation): structure breakdown and recovery ("thixotropy") Temperature-dependent flow behavior (rotation) Oscillatory tests Amplitude sweeps 247 lt.3.2 Frequency sweeps Time-dependent viscoelastic behavior (oscillation) Step tests (oscillation): structure breakdown and recovery ("thixotropy") Temperature-dependent viscoelastic behavior (oscillation) Selection of the test type Behavior of the rest Flow behavior Structural recovery ("thixotropic behavior", e.g. of coatings) Rheologists and the historical development of rheology Developments until the 19 th Century Developments between 1800 and Developments between 1900 and Developments between 1950 and Developments between 1980 and Appendix Symbols, signs and abbreviations used Greek alphabet Conversion table for units References Publications and books ISO standards (International Standards Organisation) ASTM International standards (American Society for Testing and Materials) DIN standards (Deutsche Industrie Norm, German Industry Standards) Index 290