The Rheology-Handbook

behavior and viscosity function3.5.1 Description of the test3.5.2 Temperature-dependent flow behavior of samples showing no hardening3.5.3 Temperature-dependent flow behavior of samples showing hardening3.5.4 Fitting functions for curves of the temperature-dependent viscosity...3.6 Pressure-dependent flow behavior and viscosity function4 Elastic behavior and shear modulus4.1 Introduction4.2 Definition of terms4.2.1 Deformation and strain4.2.2 Shear modulus4.3 Shear load-dependent deformation behavior4.3.1 Ideally elastic deformation behavior according to Hooke5 Viscoelastic behavior5.1 Introduction5.2 Basic principles5.2.1 Viscoelastic liquids according to Maxwell5.2.1.1 Maxwell model5.2.1.2 Examples of the behavior of VE liquids in practice5.2.2 Viscoelastic solids according to Kelvin/Voigt5.2.2.1 Kelvin/Voigt model5.2.2.2 Examples of the behavior of VE solids in practice5.3 Normal stresses6 Creep tests6.1 Introduction6.2 Basic principles6.2.1 Description of the test6.2.2 Ideally elastic behavior6.2.3 Ideally viscous behavior6.2.4 Viscoelastic behavior6.3 Analysis6.3.1 Behavior of the molecules6.3.2 Burgers model6.3.3 Curve discussion6.3.4 Definition of terms6.3.4.1 Zero-shear viscosity6.3.4.2 Creep compliance, and creep recovery compliance6.3.4.3 Retardation time6.3.4.4 Retardation time spectrum6.3.5 Data conversion6.3.6 Determination of the molar mass distribution7 Relaxation tests7.1 Introduction7.2 Basic principles7.2.1 Description of the test7.2.2 Ideally elastic behavior7.2.3 Ideally viscous behavior7.2.4 Viscoelastic behavior7.3 Analysis7.3.1 Behavior of the molecules7.3.2 Curve discussion7.3.3 Definition of terms7.3.3.1 Relaxation modulus7.3.3.2 Relaxation time7.3.3.3 Relaxation time spectrum7.3.4 Data conversion7.3.5 Determination of the molar mass distribution8 Oscillatory tests8.1 Introduction8.2 Basic principles8.2.1 Ideally elastic behavior8.2.2 Ideally viscous behavior8.2.3 Viscoelastic behavior8.2.4 Definition of terms8.2.5 The test modes controlled shear strain and controlled shear stress, raw data and rheological parameters 8.3 Amplitude sweeps8.3.1 Description of the test8.3.2 Structural character of a sample8.3.3 Limiting value of the LVE range8.3.3.1 Limiting value of the LVE range in terms of the shear strain 8.3.3.2 Limiting value of the LVE range in terms of the shear stress8.3.4 Determination of the yield point and the flow point by amplitude sweeps8.3.4.1 Yield point or yield stress 8.3.4.2 Flow point or flow stress 8.3.4.3 Yield zone between yield point and flow point8.3.4.4 Evaluation of the two terms yield point and flow point8.3.4.5 Measuring programs in combination with amplitude sweeps 8.3.5 Frequency-dependence of amplitude sweeps8.3.6 SAOS and LAOS tests, and Lissajous diagrams8.4 Frequency sweeps8.4.1 Description of the test8.4.2 Behavior of unlinked polymers (solutions and melts)8.4.2.1 Single Maxwell model for unlinked polymers showing a narrow MMD....8.4.2.2 Generalized Maxwell model for unlinked polymers showing a wide MMD8.4.3 Behavior of cross-linked polymers8.4.4 Behavior of dispersions and gels8.4.5 Comparison of superstructures using frequency sweeps8.4.6 Multiwave test8.4.7 Data conversion8.5 Time-dependent behavior at constant dynamic-mechanical and isothermal conditions8.5.1 Description of the test8.5.2 Time-dependent behavior of samples showing no hardening8.5.2.1 Structural decomposition and regeneration (thixotropy and rheopexy)8.5.2.2 Test methods for investigating thixotropic behavior8.5.3 Time-dependent behavior of samples showing hardening8.6 Temperature-dependent behavior at constant dynamic mechanical conditions8.6.1 Description of the test8.6.2 Temperature-dependent behavior of samples showing no hardening8.6.2.1 Temperature curves and structures of polymers8.6.2.2 Temperature-curves of dispersions and gels8.6.3 Temperature-dependent behavior of samples showing hardening8.6.4 Thermoanalysis (TA)8.7 Time/temperature shift8.7.1 Temperature shift factor according to the WLF method8.8 The Cox/Merz relation8.9 Combined rotational and oscillatory tests8.9.1 Presetting rotation and oscillation in series8.9.2 Superposition of oscillation and rotation 9 Complex behavior, surfactant systems9.1 Surfactant systems9.1.1 Surfactant structures and micelles9.1.2 Emulsions9.1.3 Mixtures of surfactants and polymers, surfactant-like polymers9.1.4 Applications of surfactant systems9.2 Rheological behavior of surfactant systems9.2.1 Typical shear behavior9.2.2 Shear-induced effects, shear-banding and "rheo chaos"10 Measuring systems10.1 Introduction10.2 Concentric cylinder measuring systems (CC MS)10.2.1 Cylinder measuring systems in general10.2.1.1 Geometry of cylinder measuring systems showing a large gap10.2.1.2 Operating methods10.2.1.3 Calculations10.2.2 Narrow-gap concentric cylinder measuring systems according to ISO 321910.2.2.1 Geometry of ISO cylinder systems10.2.2.2 Calculations10.2.2.3 Conversion between raw data and rheological parameters10.2.2.4 Flow instabilities and secondary flow effects in cylinder measuring systems10.2.2.5 Advantages and disadvantages of cylinder measuring systems10.2.3 Double-gap measuring systems (DG MS)10.2.4 High-shear cylinder measuring systems (HS MS)10.3 Cone-and-plate measuring systems (CP MS)10.3.1 Geometry of cone-and-plate systems10.3.2 Calculations10.3.3 Conversion between raw data and rheological parameters 10.3.4 Flow instabilities and secondary flow effects in CP systems10.3.5 Cone truncation and gap setting10.3.6 Maximum particle size10.3.7 Filling of the cone-and-plate measuring system10.3.8 Advantages and disadvantages of cone-and-plate measuring systems10.4 Parallel-plate measuring systems (PP MS)10.4.1 Geometry of parallel-plate systems10.4.2 Calculations10.4.3 Conversion between raw data and rheological parameters10.4.4 Flow instabilities and secondary flow effects in a PP system10.4.5 Recommendations for gap setting 10.4.6 Automatic gap setting and automatic gap control using the normal force control option10.4.7 Determination of the temperature gradient in the sample10.4.8 Advantages and disadvantages of parallel-plate measuring systems10.5 Mooney/Ewart measuring systems (ME MS)10.6 Relative measuring systems10.6.1 Measuring systems with sandblasted, profiled or serrated surfaces10.6.2 Spindles in the form of disks, pins, and spheres10.6.3 Krebs spindles or paddles10.6.4 Paste spindles and rotors showing pins and vanes10.6.5 Ball measuring systems, performing rotation on a circular line10.6.6 Further relative measuring systems10.7 Measuring systems for solid torsion bars10.7.1 Bars showing a rectangular cross section 10.7.2 Bars showing a circular cross section10.7.3 Composite materials10.8 Special measuring devices10.8.1 Special measuring conditions which influence rheology10.8.1.1 Magnetic fields for magneto-rheological fluids10.8.1.2 Electrical fields for electro-rheological fluids10.8.1.3 Immobilization of suspensions by extraction of fluid10.8.1.4 UV light for UV-curing materials10.8.2 Rheo-optical measuring devices10.8.2.1 Terms from optics10.8.2.2 Microscopy10.8.2.3 Devices for measuring anisotropy in terms of optical rotation and birefringence10.8.2.4 SALS for diffracted light quanta10.8.2.5 SAXS for diffracted X-rays10.8.2.6 SANS for scattered neutrons10.8.2.7 Velocity profile of flow fields10.8.3 Other special measuring devices10.8.3.1 Interfacial rheology on two-dimensional liquid films10.8.3.2 Dielectric analysis, and DE conductivity of materials showing electric dipoles10.8.3.3 NMR, and resonance of magnetically active atomic nuclei10.8.4 Other kinds of testings besides shear tests 10.8.4.1 Tensile tests, extensional viscosity, and extensional rheology10.8.4.2 Tack test, stickiness and tackiness 10.8.4.3 Tribology11 Instruments11.1 Introduction11.2 Short overview: methods for testing viscosity and elasticity11.2.1 Very simple determinations11.2.2 Flow on a horizontal plane11.2.3 Spreading or slump on a horizontal plane after lifting a container11.2.4 Flow on an inclined plane11.2.5 Flow on a vertical plane or over a special tool11.2.6 Flow in a channel, trough or bowl11.2.7 Flow cups and other pressureless capillary viscometers11.2.8 Devices showing rising, sinking, falling and rolling elements 11.2.9 Penetrometers, consistometers and texture analyzers11.2.10 Pressurized cylinder and capillary devices11.2.11 Simple rotational viscometer tests11.2.12 Devices with vibrating or oscillating elements11.2.13 Rotational and oscillatory curemeters (for rubber testing)11.2.14 Tension testers 11.2.15 Compression testers 11.2.16 Linear shear testers 11.2.17 Bending or flexure testers 11.2.18 Torsion testers 11.3 Flow cups11.3.1 ISO cup11.3.1.1 Capillary length11.3.1.2 Calculations11.3.1.3 Flow instabilities, secondary flow effects, turbulent flow conditions in flow cups11.3.2 Other types of flow cups11.4 Capillary viscometers11.4.1 Glass capillary viscometers11.4.1.1 Calculations11.4.1.2 Determination of the molar mass of polymers using diluted polymer solutions11.4.1.3 Determination of the viscosity index VI of petrochemicals11.4.2 Pressurized capillary viscometers 11.4.2.1 MFR and MVR testers driven by a weight ("low-pressure capillary viscometers")11.4.2.2 High-pressure capillary viscometers driven by an electric drive, for testing highly viscous and paste-like materials 11.4.2.3 High-pressure capillary viscometers driven by gas pressure, for testing liquids11.5 Falling-ball viscometers11.6 Rotational and oscillatory rheometers11.6.1 Rheometer set-ups11.6.2 Control loops11.6.3 Devices to measure torques11.6.4 Devices to measure deflection angles and rotational speeds11.6.5 Bearings11.6.6 Temperature control systems12 Guideline for rheological tests12.1 Selection of the measuring system12.2 Rotational tests12.2.1 Flow and viscosity curves12.2.2 Time-dependent flow behavior (rotation)12.2.3 Step tests (rotation): structural decomposition and regeneration ("thixotropy")12.2.4 Temperature-dependent flow behavior (rotation)12.3 Oscillatory tests12.3.1 Amplitude sweeps12.3.2 Frequency sweeps12.3.3 Time-dependent viscoelastic behavior (oscillation)12.3.4 Step tests (oscillation): structural decomposition and regeneration ("thixotropy")12.3.5 Temperature-dependent viscoelastic behavior (oscillation)12.4 Selection of the test type12.4.1 Behavior at rest12.4.2 Flow behavior12.4.3 Structural decomposition and regeneration ("thixotropic behavior", e.g. of coatings)13 Rheologists and the historical development of rheology13.1. Development until the 19th century13.2 Development between 1800 and 190013.3 Development between 1900 and 194913.4 Development between 1950 and 197913.5 Development since 198014 Appendix14.1 Symbols, signs and abbreviations used14.2 The Greek alphabet14.3 Conversion table for units15 References15.1 Publications and books15.2 ISO standards15.3 ASTM standards 15.4 DIN, DIN EN, DIN EN ISO and EN standards15.5 Important standards for users of rotational rheometers