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1 Basics of Rheology 1 Rheology and Viscous Behavior Rheology to describe deformation and flow behavior of all kinds of materials rhei or rheo to flow Very Welcome! Markus Nemeth Rheometry measurement of rheological data Foto: Drugstore (Apotheken) Museum in Heidelberg, Germany 1

2 1 Rheology and Viscous Behavior Each material under load shows viscoelastic behavior as a mixture of viscous and elastic behavior. Using a simple illustrative picture ideally viscous liquids such as water, oils Viscosity Law The Rheology Road viscous viscoelastic elastic viscoelastic liquids such as glues, shampoos viscoelastic solids such as pastes, gels, rubbers ideally elastic solids rigid, as a stone, steel Elasticity Law Rotational Tests Oscillatory Tests 1 Rheology and Viscous Behavior What is Viscosity? Internal Friction between the molecules and particles, when gliding along each other in a flowing state, or: Flow Resistance (Newton, in 1687: defectus lubricitatus) Comparison of size molecules of solvents: about 0.5 nm macro-molecules (polymer coils): about 50 nm particles (minerals): about 5 µm = 5000 nm Thus: Size ratio of molecules and particles is about 1:100 to 1:10,000 (e.g. 1:1000) illustrative comparison for 1:1000 a molecule as a 10 cm (0.1m) long fish, a particle as a 100 m long ship. 0.5 nm 0 50 nm 2

3 2 Simple Viscosity Tests 2 Simple Viscosity Tests Flow Cups Trowel Test - highly viscous fluids: thick - low-viscosity fluids: thin e.g. for dispersions Finger Test - tacky: long - less tacky: short e.g. for adhesives, offset-printing inks, dough Measurement of the Flow Time of low-viscosity liquids Determination of the kinematic Viscosity weight-dependent viscosity Examples: oils, solvent-based coatings, gravure printing inks and flexo printing inks 3

4 2 Simple Viscosity Tests Falling - Ball Viscometers Falling Time of the ball to travel downwards over a defined distance for testing transparent liquids according to ISO and DIN thermometer Example: Micro-Falling Ball Viscometer Lovis of Anton Paar for low-viscosity liquids such as biological fluids (e.g. protein dispersions), polymer solutions, beer wort, inks 2 Simple Viscosity Tests measuring tube and ball stand jacket, for temperature control Movie (motor oils) Glass Capillary Viscometers Measurement of the Flow Time of transparent liquids, Determination of the Alternative: Stabinger - Viscometer SVM of Anton Paar for low-viscosity liquids such as mineral oils and acquous solutions kinematic Viscosity Examples: mineral oils, diluted polymer solutions 4

5 2 Simple Viscosity Tests Rotational Viscometers Preset: Rotational Speed Determination : Torque 2 Simple Viscosity Tests Relative values of viscosity are measured when typical Brookfield-spindles are used - cylinders - disks - pins - T - bars All these kinds of stirrers are Relative Measuring Systems - helix (1 & 2) - for building materials - starch stirrer - blade - anchor-shaped - vane rotor - pin rotor - Krebs spindle, paddle (for coatings, KU, Krebs units) - ball MS 5

6 3 Rheometers and Measuring Systems Measuring Geometries for Rotational and Oscillatory Rheometers according to DIN (for all the 3 geometries) and ISO 3219 (only for CC and CP) to measure absolute values of viscosity Concentric Cylinders, CC for low-viscosity liquids, ratio of radii R e /R i Cone - Plate, CP for liquids; for dispersions only with limitted particle size, recommended: α 2 Example: For CP 25-1, with 2R = 25 mm and α = 1, typically a = 50 µm; thus, for a max. particle size of d (a/10) = 5 µm 3 Rheometers and Measuring Systems Bearings for rheometers Each drive requires a bearing. Example: Wheel bearing Problem: Mechanical bearings show a relatively large bearing friction. Ball bearing Example: - inner ring (rotor), - rolling element (e.g. balls, cylinders, cones), - outer ring (stator) Parallel-Plates, PP useful for gels, pastes, soft solids, polymer melts; recommended: 0.50 mm H 1.00 mm 1 Air bearing radial and axial: only pressurized air in the narrow gap between disc (rotor) and porous graphite wall (stator) 2 Measuring drive (electromotor, for torque) 3 Encoder (opto-electronic, for deflection angle) 4 Motor shaft (with coupling for measuring systems) (i 6

7 4 Definitions: Shear Stress, Shear Rate, Viscosity The Two - Plates Model Shear Stress τ = A F unit: Shear Rate Laminar flow showing flowing layers in contrast to turbulent flow showing vortices γ& = dv const. = = const. dh const. 1 N / m 2 = 1 Pa v γ& = (D) = h unit: 1 m / (s m) = 1 / s = 1 s -1 e-learning (laminar, 2-P-M) 4 Definitions: Shear Stress, Shear Rate, Viscosity Typical values of shear rates Movie (peas) Process Shear Rates (s -1 ) sedimentation < to 0.01 surface levelling 0.01 to 0.1 sagging 0.01 to 1 dip coating 1 to 100 extrusion 10 to 1000 pipe flow, pumping, filling into containers 10 to 10,000 mixing, stirring 10 to 10,000 coating, painting, brushing 100 to 10,000 spraying 1000 to 10,000 Movie (turbulence) (high - speed) coating, blade coating 100,000 to 1 mio. 7

8 4 Definitions: Shear Stress, Shear Rate, Viscosity Practical Example: Shear rates and storage stability of salad dressings (dispersions) dispersions in the beginning after 15 min Dispersion Stability, sedimentation, long-term storage stability Behavior in the low-shear range or at rest, respectively 4 Definitions: Shear Stress, Shear Rate, Viscosity Practical Example: Painting with a Brush Movie (sedimentation) coatings Leveling, Sagging, Brush marks, wet - layer Thickness of coatings at very low shear rates between 0.01 and 1 s -1 (or at rest, respectively) 8

9 4 Definitions: Shear Stress, Shear Rate, Viscosity Practical Example: Painting with a Brush coatings brush velocity (v = 0.5 m/s) wet layer thickness (h = 200 µm) Calculation of the Shear Rate: similar to the Two-Plates Model γ& Δv 0.5 m = = Δh 2 10 m s 1 = 2500 s 4 Brushing, Painting at medium and high shear rates between 100 and 10,000 s -1 4 Definitions: Shear Stress, Shear Rate, Viscosity Practical Example: Squeezing out a Tooth Paste flow volume V = 1 cm 3 flow time t = 1 s thus: flow rate V / t = 10-6 m 3 / s tube nozzle (pipe radius, half diameter) d = 2R = 6 mm, thus: R = m pastes Calculation of the Shear Rate: Formula of γ& = (4 V) / (π R 3 t) = ( m 3 /s) / (π m 3 ) = 47.2 s -1 = about 50 s -1 Flow in Pipes, Capillaries at shear rates between 1 and 1000 s -1 Hagen and Poiseuille 9

10 4 Definitions: Shear Stress, Shear Rate, Viscosity Definition of the (shear) viscosity Isaac Newton (1643 to 1727); he writes about the flow resistance of fluids (e.g. of air and water). However, this laterly so-called Viscosity Law of Newton was formulated not before the 19. century (e.g. by G.G. Stokes in 1845). Kinematic Viscosity unit: 1 m 2 / s 1 m 2 / s = 10 6 mm 2 / s = γ τ η & previously used unit: 1 cst = 1 mm 2 /s (centi-stokes) However, this is not an SI unit. (SI, in French: système international d unités) Pa = 1/s [ Pas] unit: 1 Pa / (1/s) = 1 Pas = 1000 mpas pascal - seconds, milli - pascal - seconds Previously used unit: 1 cp = 1 mpas (centi - poises) However, this is not an SI - unit. 4 Definitions: Shear Stress, Shear Rate, Viscosity ν = ρ η unit of Density ρ: 1 g/cm 3 = 1000 kg/m 3 Kinematic viscosity is measured ever then, when gravity is the driving force (or the weight of the sample, resp.), for example, when using Flow Cups, Falling Ball Viscometers, and Capillary Viscometers 10

11 5 Rotational Tests Preset of the Rotational Speed shear rate ramp, usually in the form of a step - like funktion upstairs or downstairs (CSR: controlled shear rate) 6 Flow Behavior Overview: Viscosity Curves Preset of the Torque shear stress ramp, usually in the form of a step - like funktion upstairs or downstairs (CSS: controlled shear stress) 1 ideally viscous (Newtonian) 2 shear-thinning (pseudoplastic) 3 shear-thickening (dilatant) 11

12 6 Flow Behavior Ideally viscous or Newtonian Flow Behavior Flow curves 6 Flow Behavior viscosity constant viscosity Viscosity curves shear stress mineral oils Mineral Oil CC 27 concentric cylinders T = +50 C shear rate 12

13 6 Flow Behavior silicone oils 6 Flow Behavior constant viscosity Silicone Oil CP 50-2 cone - plate Water constant viscosity T = +23 C Diagrams on a logarithmic scale Advantage: Here, also the range of very small values can be presented clearly. DG 42 Double-Gap System T = +20 C Double-gap measuring systems are especially designed for low-viscosity liquids Movie (Taylor vortices, via PIV, particle imaging velocimetry 13

14 6 Flow Behavior 1) Wall Paper Paste polymer solution, aqueous methylcellulose, pressure or velocity-dependent viscosity, respectively 2) Mineral Oil constant viscosity 6 Flow Behavior Double-Tube Experiment in the outlet capillary are decreasing continuously the acting weight force, and therefore, the hydrostatic pressure, and therefore, the shear stress sense of the double-tube experiment, with decreasing shear stress Movie (double tube) 1 Polymer Solution viscosity is Velocity-dependent shear-thinning 2 Mineral Oil constant viscosity ideally viscous 14

15 6 Flow Behavior Flow Curve 6 Flow Behavior Polymers with chain-like macro-molecules at rest shear-thinning pseudoplastic Molecules are coiled, entanglements η 1 η 2 Viscosity Curve η ( γ& 1 ) > η 2 (& 2 ) 1 γ when shearing polymers Deformation in shear direction, disentanglements Consequence: Shear-thinning flow behavior, decreasing viscosity Typical size: molecule coil, hydrodynamic diameter 5nm to 50nm Example: polyethylene PE, molar mass M = 100kg/mol, Molecules with L = 1µm = 1000nm (stretched), d = 0.5nm, ratio L/d = 2000:1, Comparison: spaghetti noodles, 1mm thick and 2m long 15

16 6 Flow Behavior Suspensions with particles showing the shape of needles or platelets at rest Particles are suspended randomly (when without interaction forces) when shearing Particles are orientated in flow direction. Consequence: Shear-thinning flow behavior, decreasing viscosity Typical size: 1) Metallic-effect pigments, aluminum flakes, diameter d = 7µm to 30µm, thickness h = 0.2µm to 1µm, ratio d/h = 30:1 2) Ceramics, such as Bentonite: length/ width/ thickness, L x b x h = 800 x 800 x 1 (in nm) 6 Flow Behavior Suspensions with agglomerated particles at rest Agglomerates are including and immobilizing also a part of the dispersion liquid. when shearing Agglomerates are disintegrated. dispersions dispersions Consequence: shear-thinning flow behavior, decreasing viscosity Typical size: Primary particles 1nm to 10nm, aggregates up to 100nm, agglomerates up to 100µm = 0.1mm 16

17 6 Flow Behavior dispersions Emulsions with dispersed droplets Consequence: at rest Droplets show the shape of spheres. Droplets are deformed and show the shape of ellipsoides. shear-thinning flow behavior, decreasing viscosity Typical size: droplets in milk, fat particles: 0.1 to 10 µm 6 Flow Behavior when shearing Rheo - Microscopy: Emulsion Water in Silicone Oil Movie (emulsion 1) lg γ& Size and shape of the droplets are dependent on sample preparation and shear rate. Perhaps viscosity increase due to droplet size division, hence an increase in the volume specific surface Movie (emulsion 2) 17

18 6 Flow Behavior polymers, adhesives 6 Flow Behavior Wall Paper Paste aqueous methylcellulose solution T = +23 C Typical behavior of polymer solutions continued shear-thinning O/W Emulsion E1 undiluted E2 with 10% additional water Typical behavior of dispersions initially strongly, and then less shear-thinning dispersions 18

19 6 Flow Behavior measuring range of the flow cup 6 Flow behaviour These 3 samples with the same pigment concentration showed the same flow time when testing with a flow cup Gravure Printing Inks diluted S1 Binder the useful one S3 Binder spattering S2 Binder 50/50 mix of 1 & 2 Summary: Flow cup tests take place only in a limited shear rate range printing inks Ceramic Feedstock passing during application several times a twin screw Influence on viscosity is significant 19

20 6 Flow Behavior 6 Flow Behavior Wall Paper Paste aqueous solution of methylcellulose, uncrosslinked polymer T = +23 C γ& for < 0.1 s -1 Plateau of the zero - shear viscosity Presentation on a logarithmic scale to evaluate the behavior in the low-shear range Uncrosslinked polymers in the low-shear range, and the zero-shear viscosity Superposition of two processes 1) Orientation of the macro-molecules under shear load disentanglements here, the viscosity is decreasing 2) Re - coiling due to visco - elastic behavior re - entanglements here, the viscosity is increasing Result: In the low-shear range there is no change in the total viscosity value, which is referred to as the η 0 - value. This low-shear range mostly occurs for < 1 s -1 polymers, adhesives polymers γ& 20

21 6 Flow Behavior Cosmetics cosmetics, surfactants Pas lg η 6 Flow Behavior lg γ& s -1 S1 Hair Gel with a solid structure-at-rest S2 Shampoo with a liquid structure-at-rest, showing the plateau of zero-shear viscosity (maybe caused by worm-like surfactants ) Flow Curve Viscosity Curve shear-thickening dilatant Movie (starch dispersion) 21

22 6 Flow Behavior dispersions Suspensions 6 Flow Behavior 1 φ... volume fraction solid (proportion of the entire volume of the suspension) shear-thickening shear-thickening may occur with a high proportion of solid matter high shear conditions Ceramic Suspension Firstly orientation of the platelet-shaped particles until reaching the viscosity minimum, followed by increasing inhomogeneities of the flow. dispersions 22

23 6 Flow Behavior Influence of the Particle Shape dispersions Comparison of aqueous chalkstone suspensions (left) cube-shaped particles Both suspensions containing the same proportion of solid particles, suspension (1) showed shear-thickening already at a lower shear rate compared to suspension (2). The reason is the difference in the required amount of volume, since source: REM images, University of Karlsruhe (right) spherical particles in flowing dispersions, particles are permanently in a rotational motion. 6 Flow Behavior polymer particles surrounded by softener Plastisol paste containing a too low softener amount Problem: blocking of the spray nozzle dispersions shear-thickening Example: Softener, molar mass M = 500g/mol, molecules of L= 5nm and d = 0.5nm, ratio L/d = 10:1 Comparison: like very short spaghetti noodles, 1mm thick and 10mm long Movie (walk on water) 23

24 6 Flow Behavior Overview: Diagrams on a linear scale Flow Curves Viscosity Curves 1 ideally viscous (Newtonian) 2 shear-thinning (pseudoplastic) 3 shear-thickening (dilatant) 7 Yield Point (via Flow Curves) Yield point as the Limiting Value of Shear Stress Flow curves on a linear scale Break of the structure-at-rest. There is a super - structure due to a chemical-physical network of interactive forces. 1 without a yield point 2 with a yield point τ y interception on the τ - axis 24

25 7 Yield Point (via Flow Curves) τ B τ C τ HB 1) Bingham model τ = τ B + η B with Bingham yield point and Bingham viscosity 2) Casson model τ = τ C + η C with Casson yield point and Casson viscosity 3) Herschel / Bulkley model τ = τ HB + η HB p with HB yield point, HB viscosity and exponent p 7 Yield Point (via Flow Curves) Yield Point Analysis in the low - shear range using Flow Curves on a Logarithmic Scale γ& Yield Point determination by Mathematical Curve Fitting for flow curves on a linear scale (approximation, "regression") Regression Models γ& γ& Method 1: read on the τ - axis Yield Points are not material constants since they depend as well on the measuring method as well as on the analysis method used. Method 2: read at a certain previously fixed very low shear rate, e.g. at = 0.01 s -1 γ& 25

26 7 Yield Point (via Flow Curves) Comparison of lin / log diagrams food Ketchup flow curve on a linear scale as the axis intercept on the τ axis: Yield Point can hardly be read 8 Further Flow and Viscosity Curves flow curve on a logarithmic scale Yield Point can be read clearly: τ y = 48Pa, here at the shear rate of 1s -1 Sealants 1 without a zero-shear viscosity stability at rest 2 with a zero-shear viscosity η 0 self-levelling flow Both sealants show the same flow behavior, but different behavior at rest polymers, dispersions 26

27 8 Further Flow and Viscosity Curves 9 Time-dependent Behavior (Rotation) Sometimes cats are very curious Transient Viscosity Peak in the low-shear range, i.e., for γ& < 1 s -1 when presetting a too short measuring point duration Reason: In the beginning, in the entire shear gap there is no homogeneous flow behavior or shear rate, respectively. Example: Offset Printing Ink 1... t MP = 10 s (for all measuring points) 2... t MP = 50 to 2 s 3... t MP = 100 to 2 s (now without peak) Rule of Thumb: t MP = 1 / Sometimes cats are very stupid γ& Requirements for coatings: structure recovery in the right time 1) not too fast, and thus, good levelling 2) not too slow, and thus, not too much sagging, desired wet-layer thickness 27

28 9 Time-dependent Behavior (Rotation) Structure Recovery 9 Time-dependent Behavior (Rotation) Step Test (3ITT), 3 intervals thixotropy test Here as a rotational test, to determine thixotropic behavior Preset 1 low-shear conditions 2 high-shear conditions 3 low-shear conditions Measuring result 1 state at rest 2 structural decomposition 3 structural regeneration Coatings step tests coatings 1 with gellant fast structural recovery less sagging high wet-layer thickness maybe poor levelling 2 with viscosifier slow structural recovery good levelling maybe too much sagging structure recovery 28

29 9 Time-dependent Behavior (Rotation) γ& 9 Time-dependent Behavior (Rotation) Thixotropy Test (old - fashioned) Analysis methods of step tests for thixotropic behavior comparison to the viscosity reference value of the 1 st interval M1 Structural Recovery in Percent at the end of the 3 rd interval (or after t = 60s, example: up to 80%) M2 Time Points of 25% and 50% Recovery M3 Curve Slope during Recovery e.g. in t = 60s; as ( η / t) in Pas/s Preset of 3 test intervals as a shear rate profile: upward ramp, hold time, downward ramp, Analysis: Hysteresis Area between the flow curves upwards and downwards Disadvantages: 1) testing in an instationary state 2) no measurement of structural regeneration t The Hysteresis Area is not more than a measure of structural decomposition. Summary: In order to evaluate thixotropic behavior, this test method is out-dated now. 29

30 9 Time-dependent Behavior (Rotation) Gelation Preset: Measuring example: Powder Coating or Curing Process constant shear conditions (shear rate or shear stress) resins, powder coatings Result: viscosity / time curve t S point in time at the start of gelation or reaction, t V time when reaching a previously selected viscosity value isothermic curing at a constant shear rate of = 1s -1 Problem: In principle, a complete curing process cannot be evaluated via rotational tests because here, the viscosity values are finally increasing towards infinity. Therefore, For testing curing materials we recommend to perform Oscillatory Tests. 10 Temperature-dependent Behavior (Rotation) Softening or Melting when heating γ& or Solidification, Crystallization or Cold-Gelation when cooling Preset: 1) constant shear conditions, e.g. at a constant shear rate 2) temperature ramp upwards (or downwards) Result: Viscosity / Temperature Function with steadily decreasing or increasing viscosity values, respectively e-learning (honey) 30

31 10 Temperature-dependent Behavior (Rotation) silicone oils Silicone Oil 10 Temperature-dependent Behavior (Rotation) Crude Oil and other kind of oils softening when heating Presented in a log η / lin T diagram, these kind of Viscosity Functions often show a linear shape. visosity / temperature curve Onset of crystallization of waxes and paraffines when cooling mineral oils Possible analysis methods: top: Pourpoint (PP) as bending point (fitting function according to Arrhenius) bottom: Cloudpoint (CP) as bending point (1), Pourpoint (PP) as inflection point (2), or PP as bending point (3) 31

32 10 Temperature-dependent Behavior (Rotation) 10 food η Pas Crystallization Temperature of Cocoa Butter crystallization C 40 temperature 10 Temperature-dependent Behavior (Rotation) T Gel Formation or when heating Chocolate Melt Crystallization when cooling Curing e-learning (choc cake) Movie (choc-fountain) Result: Viscosity / Temperature Function with a Minimum Viscosity Starch Dispersion (6 % in water) Gelation 1 - starch gelation when heating (from 15 C to 98 C, beginning at 72 C) 2 behavior when cooking (at T = 98 C = const) 3 cold gelation when cooling (down to 15 C) measuring geometry: starch stirrer pressure p = 0.5 MPa (= 5 bar) 32

33 Appendix: Pressure-dependent Behavior (Rotation) mineral oils η 600 mpa s increasing pressure p lg s Viscoelastic Behavior ideally viscous liquids such as water, oils Viscosity Law γ& Using a simple illustrative picture viscoelastic liquids such as glues, shampoos The Rheology Road Used Motor Oil viscosity increase with increasing pressure p p = 95 bar ( = 9.5 MPa) p = 60 bar ( = 6 MPa) p = 30 bar ( = 3 MPa) p = 1 bar ( = 0.1 MPa) at T = +23 C viscous viscoelastic elastic viscoelastic solids such as pastes, gels, rubbers ideally elastic solids rigid, as a stone, steel Elasticity Law Rotational Tests Oscillatory Tests Lit.: Durou, J.-F.: Cérémonie du Thé, Mauritanie, Nouvelles Images, Lombreuil. e-learning (Eiffel Tower) 33

34 11 Viscoelastic Behavior Result: Tack and stringiness, e.g. of adhesives, printing inks, or food (mouth sensation) Stirring Process: Weissenberg effect, Rod Climbing, poor mixing result (Karl Weissenberg, 1893 to 1976, rheologist) Extrusion: Extrudate Swelling e.g. dimension stability In many cases, viscosity values only are not sufficient since elastic effects are occurring, resulting in viscoelastic behavior. 11 Viscoelastic Behavior Polymer Solutions (here: poly-iso-butylene, PIB) polymers Die Swell or Extrude Swell when flowing out of a capillary, a pipe or a bottle Weissenberg Effect when stirring Movie (PVA surfactant solution) 34

35 11 Viscoelastic Behavior polymers Polymer Melts Extrusion (e.g. polystyrene, PS): extrudate swelling and melt fracture Blow Moulding (e.g. polyethylene, PE): orange peel or shark skin 12 Definitions: Strain, Deformation, Shear Modulus The Two-Plates Model F Shear Stress τ = A unit: 1 N / m 2 = 1 Pa (Pascal) Shear Deformation or unit: 1 m / m = 1 = 100 % Shear Strain γ = h s 35

36 12 Definitions: Strain, Deformation, Shear Modulus Robert Hooke (1635 to 1703); in 1676 he describes for solids proportionality of force and deformation. However, the laterly so-called Elasticity Law of Hooke was formulated not before the 19. century (e.g. by T. Young in 1807, or A.L. Cauchy in 1827). G = τ γ Law of Springs: spring force deflection path spring constant Definition Shear Modulus F / s = C unit: (1 Pa / 1 = ) 1 Pa Further units: 1 GPa = 1000 MPa = 10 6 kpa = 10 9 Pa Giga-pascals, Mega-pascals, kilo-pascals 12 Definitions: Strain, Deformation, Shear Modulus Material Stiffness and Shear Moduli Example: Different Types of Cheeses cheese type example shear modulus (around) 1 cream Philadelphia 1 kpa 2 soft French Camembert 10 kpa F s C (stiffness) Movie (bouncing balls) 3 semi-hard Holland Gouda (young) 4 hard Swiss Emmentaler 5 extra hard Italian Parmigiano 0.1 MPa 0.5 MPa 1 MPa 3 food 2 e-learning (cheese mice) 36

37 13 Yield Point (via γ / τ - Diagrams) Testing with controlled shear stress Method 1: Yield Point τ y via the best straight fitting line ( tangent ) in the linear-elastic deformation range 13 Yield Point (via γ / τ - Diagrams) Yield point as the limiting value of the shear stress The sample starts to flow not before the external forces are exceeding the network-of-forces of the internal structure. Below the yield point there is purely elastic deformation. Method 2: Yield Point τ y via the tangent crossover method Ketchups food 1 without binder yield point 13.5 Pa 2 with binder yield point 114 Pa 37

38 13 Yield Point (via γ / τ - Diagrams) Coatings C1 Primer C2 Top Coat Flow curves left side: on a linear scale, 13 Yield Point (via γ / τ - Diagrams) right side: on a logarithmic scale coatings Yield points, e.g. read at 0.01 s -1 : C2 with 15 Pa, and C1 with 0.2 Pa Coatings coatings 1 Primer without a yield point (initially large deformation, no inflection point) 2 Top Coat yield point τ y = 7.02 Pa 38

39 14 Oscillatory Tests Two-Plates - Model, equipped with two two sensors, on top: preset of deflection path (strain or deformation) bottom: measurement of resulting force (shear stress) Sinusoidal Preset For ideally elastic behavior of a totally stiff sample (e.g. a stone, or steel): There is no time shift between the sine curves of preset strain and resulting shear stress: the curves of γ and τ are in phase 14 Oscillatory Tests Preset: Result: constant frequency and constant amplitude Movie (2-plates-model, ideal elastic behavior) Most samples show viscoelastic behavior with the phase shift δ between the sine curves of the test preset (here: strain) and the measuring result (then: stress), as the retardation of the measuring response compared to the preset. Movie (2-plates-model, viscoelastic behavior) 39

40 14 Oscillatory Tests phase shift angle 90 δ 0 ideally viscous behvior ideally elastic behavior fluid, liquid: 90 δ > 45 and solid, gel-like: 45 > δ 0 illustrative idea: δ as the street number in the Rheology Road ideally viscous: δ = 90 (like sine and cosine curve), ideally elastic: δ = 0 14 Oscillatory Tests Vector Diagram to determine the parameters G' and G'' Application example: Dairy Pudding, with controlled shear strain - preset of deflection angle or γ A, respectively - measurement of torque or τ A, respectively, and of phase shift angle δ - calculation: complex shear modulus G* Elasticity Law for oscillatory shear tests index A for amplitude τ γ A A G * = 40

41 14 Oscillatory Tests Vector Diagram For scientists: G' (G - prime) for the stored, G* Complex Shear Modulus, viscoelastic behavior in total. G' Storage Modulus, elastic portion G'' Loss Modulus, viscous portion of the viscoelastic behavior, unit: Pa, for all G-values. G'' (G - double prime) for the lost (dissipated) Deformation Energy due to internal friction when flowing 14 Oscillatory Tests left-hand side: freely movable, unlinked molecules, right-hand side: crosslinked molecules tan δ = G''/ G' Loss Factor or Damping Factor tangent delta unit: dimensionless (or 1) The Viscoelastic Ratio of viscous and elastic portions Practical example: Point of Phase Transition when G' = G'' or tan δ = 1 41

42 14 Oscillatory Tests tanδ = G'' / G' viscous viscoelastic elastic G'' >> G' G'' > G' G'' = G' G' > G'' G' >> G'' tanδ >> 1 liquid, fluid state sol / gel transition gel-like, solid state tanδ > 1 tanδ = 1 tanδ < 1 tanδ << 1 0 In practice: ideally viscous: tanδ > 100:1 = 100; ideally elastic: tanδ < 1:100 = 0.01 For scientists: tanδ > 1000 or tanδ < 0.001, respectively 15 Amplitude Sweeps Preset: constant Frequency (e.g. angular frequency ω = 10rad/s) and variable Strain (Deformation) Strain Sweep or alternatively, with variable stress, as Stress Sweep Frequency Conversion: ω = 2π f with Angular Frequency ω in rad /s (or in s -1 ) and Frequency f in Hz Please note: Hz is not an SI unit. Movie (amplitude sweep) 42

43 15 Amplitude Sweeps Limiting value of the LVE range Result: storage modulus G' (elastic behavior), loss modulus G'' (viscous behavior) Limiting Value of the Linear Viscoelastic (LVE- ) Range when reaching γ L (linearity limit of strain) at the given test conditions, i.e., at the preset (angular) frequency left hand side: G' > G'' (gel-like, solid structure) in the LVE - range right hand side: G'' > G' (liquid, fluid structure) in the LVE - range 15 Amplitude Sweeps Polymer Melt liquid state because G'' > G' viscoelastic fluid polymers limit of the LVE range at γ L = 10% = 0.1 ω = 10rad/s T = +180 C 43

44 15 Amplitude Sweeps 15 Amplitude Sweeps Yield Point and Flow Point Diagram showing the shear stress τ on the x-axis Yield Point: τ - value at the limit of the LVE - range Flow Point: τ - value at the crossover point G' = G'' Brittle fracture, if τ y = τ f For both values counts: At the given test conditions, i.e. at the preset (angular) frequency 44

45 15 Amplitude Sweeps pastes Flowpoints of ceramic pastes differ between different Batches and the base product (grey) 15 Amplitude Sweeps Dispersions, water - based dispersions, coatings Additive 1, Gellant e.g. clay Yield Stress τ y = 6.9Pa Flow Stress τ f = 42Pa Additive 2, Viscosifier e.g. associative thickener Yield Stress τ y = 1.5Pa but no Flow Stress Summary, in the LVE range: with Gellant G' > G'' (gel-like state, solid), with Viscosifier G'' > G' (liquid), hence no physical stability) 45

46 16 Frequency Sweeps Preset: constant Amplitude as shear strain within the LVE - range (or alternatively, as shear stress) and variable Frequency Precondition: Firstly, the LVE - range has to be checked by an Amplitude Sweep. 16 Frequency Sweeps Movie (frequency sweep) uncrosslinked polymers PDMS poly - di - methyl - siloxane typical behavior of uncrosslinked polymers with crossover point G' = G'' γ = 10% T = +23 C 46

47 16 Frequency Sweeps polymers 16 Frequency Sweeps Polyethylene with functional groups uncrosslinked crosslinked at a low frequency: a higher G'- value indicates a higher degree of crosslinking γ = 1% T = +170 C Dispersions water-based dispersions, coatings Long-term Behavior, Sedimentation Stability at Low Frequencies Additive 1, Gellant e.g. clay G' > G'' hence gel-like solid stable Additive 2, Viscosifier e.g. an associative thickener G'' > G' hence liquid, unstable 47

48 16 Frequency Sweeps dispersions Syneresis (phase separation) may occur for gels showing too low values of tanδ = G'' / G' 17 Time-dependent Behavior (Oscillation) Dispersions physical dispersion stability evaluation at a low frequency L1, stable with G' > G'' L2, unstable with G'' > G γ = 0.3% T = +20 C Structure Recovery, Step Test (3ITT), 3 intervals thixotropy test Here as an oscillatory test to determine the thixotropic behavior Preset 1 low-shear conditions 2 high-shear conditions 3 low-shear conditions Test Result 1 state of rest 2 structure decomposition 3 structure regeneration - in the 2 nd interval: G'' > G' thus liquid - in the 1 st & 3 rd interval: when G' > G'' solid structure (at rest) 48

49 17 Time-dependent Behavior (Oscillation) adhesives structure recovery 17 Time-dependent Behavior (Oscillation) source: Teschner, H., Offsetdrucktechnik, Fachschriftenverlag, Fellbach SMD Adhesive for surface - mounted devices, e-technics Step Test: 3x Oscillation γ 1 = γ 3 = 0.2% γ 2 = 100% ω = 10rad/s T = +23 C Printing Inks Structure Recovery Requirements: Problem: dripping because G'' > G' Fixing on the substrate Halftone Printing dot sharpness Area Printing sufficient leveling printing inks 49

50 17 Time-dependent Behavior (Oscillation) 17 Time-dependent Behavior (Oscillation) Structure Recovery, Step Test (3ITT), 3 intervals thixotropy test, here as an ORO - Test Oscillation / Rotation / Oscillation to determine thixotropic behavior Preset 1 low-shear conditions (strain in the LVE-range, oscillation) 2 high-shear conditions (rotation) 3 low-shear conditions (strain in the LVE-range, oscillation) Test Result 1 state of rest 2 structure decomposition 3 structure regeneration - in the 2 nd interval: liquid - in the 1 st & 3 rd interval: when G' > G'' solid structure (at rest) Dispersion step test as an ORO - test γ 1 = γ 3 = 1% ω = 10rad/s γ& = 100s -1 T = +23 C dispersions structure recovery 50

51 17 Time-dependent Behavior (Oscillation) 17 Time-dependent Behavior (Oscillation) Analysis methods for step tests to evaluate thixotropic behavior (2) The best method is M4 Time point at the Crossover Point of in the 3 rd interval Analysis methods for step tests to evaluate thixotropic behavior (1) comparison to the reference value G' of the 1 st interval M1 Structural Recovery in Percent at the end of the 3 rd interval (or after t = 60s, example: up to 80%) M2 Time Points of 25% and 50% Recovery M3 Curve Slope during Recovery e.g. in t = 60s; as ( G'/ t) in Pa/s G' and G'' coatings 51

52 17 Time-dependent Behavior (Oscillation) coatings source: Daimler- Museum, Stuttgart 17 Time-dependent Behavior (Oscillation) Practical Example: Automotive Coatings high-rotational atomizer ( bell ), electrostatically supported spray process Problem with Spray Coatings: Sagging source: Degussa Automotive Spray Coatings ORO - Tests AC1: AC2: AC3: coatings (a) as long as G'' > G' liquid state, flowing, leveling, sagging (b) when finally G' > G'' solid state, sagging is stopped Time Point of Crossover G' = G'' can be controlled using rheology additives: Sag Control 52

53 17 Time-dependent Behavior (Oscillation) Gelation or Curing Process isothermal curing at constant dynamic-mechanical shear conditions resins, powder coatings lg G' lg G'' Preset: - constant measuring temperature - constant amplitude (strain or stress) in the LVE region - constant (angular) frequency (usually with ω = 10rad/s) 17 Time-dependent Behavior (Oscillation) 10 4 Pa 10 3 curing Result: time-dependent G' and G'' curves t CR t SG point in time at the start of gelation or chemical reaction time when reaching crossover point G' = G'' as sol / gel transition Two - Component Adhesive curing reaction isothermal T = +23 C crossover G' = G'' after t = 35s with G' = 1360Pa adhesives, resins s time t MS - PP 25 disposable measuring system γ = 0.1% ω = 10rad/s 53

54 17 Time-dependent Behavior (Oscillation) curing 17 Time-dependent Behavior (Oscillation) resins, powder coatings Powder Coating with an epoxy resin isothermal curing time point t SG of sol / gel transition at cross-over point G' = G'' T = 120 C: t SG = 1370s T = 140 C: t SG = 360s T = 160 C: t SG = 140s γ = 0.1% ω = 10rad/s T = const disposable plates UV- curing Resin resins γ = 0.1% ω = 10rad/s T = +23 C (isothermal) soft touch, because finally G' = 0.1MPa temperature peak: end of the exothermic crosslinking reaction G'' > G' gel point at G' = G'' curing G' > G'' bottom plate made of quartz glass 54

55 17 Time-dependent Behavior (Oscillation) resins 18 Temperature-dependent Behavior (Oscillation) heating, melting UV- curing Resin fast curing reaction isothermal finally very rigid, because G' > 1GPa (already after 10 s) MS - PP 08 γ = 0.02% ω = 63rad/s (or f = 10Hz) tanδ = G'' / G' ABS Resin blend of 3 polymers polymers melting temperature T m = +215 C at crossover point G' = G'' γ = 1% ω = 10rad/s 55

56 18 Temperature-dependent Behavior (Oscillation) Polymers configuration of the macro-molecules, super-structure amorphous partially crystalline chemically cross-linked uncrosslinked, uncrosslinked, covalent primary bonds without any order partially crystalline order T g glass transition temperature 18 Temperature-dependent Behavior (Oscillation) melting T m... melting temperature Polymer - modified Bitumen (PMB) with 5 w-% polymer behavior of an amorphous polymer Preset in 2 intervals, because the G'-values spread over 7 decades 1) γ 1 = 0.1% (for T < 35 C) 2) γ 2 = 1% (for T > 35 C) polymers, bitumen ω = 10 rad/s 56

57 18 Temperature-dependent Behavior (Oscillation) melting 18 Temperature-dependent Behavior (Oscillation) heating, softening Hotmelt Adhesive uncrosslinked, partially crystalline polymer with a pronounced rubber-elastic region T g = -18 C (G'' max) T g = 0 C (tanδ max) finally as a melt, because G'' > G' for T > T m = +78 C tanδ = G'' / G' polymers, adhesives Rubber cross-linked polymer T g = -22 C (G'' max), T g = -16 C (tanδ max) no melting, because G' > G'' also at high temperatures γ = 0.25% ω = 10rad/s tanδ = G'' / G' 57

58 18 Temperature-dependent Behavior (Oscillation) dispersions tanδ = G'' / G' T k... Crystallization Temperature Melting or Crystallization of crystal-forming lotions and dispersions when heating or cooling, resp. Preset constant shear conditions for amplitude and frequency, with an amplitude in the LVE range, and usually with ω = 10rad/s Result 18 Temperature-dependent Behavior (Oscillation) cooling steeply decreasing or increasing curves, in a relatively narrow temperature range Lotion Emulsion Crystallization Temperature dispersions T k = -1 C γ = 0.1% ω = 10rad/s Movie (crystallization) 58

59 18 Temperature-dependent Behavior (Oscillation) 10 7 Pa 10 6 lg G' lg G'' Gel formation when heating Preset: or Curing constant shear conditions (amplitude and frequency) Result: temperature - dependent functions of G' and G'' T m... melting temperature (when G' = G'') T CR... onset of gel formation or curing (chemical reaction) T SG... sol /gel transition (when again G' = G'') 18 Temperature-dependent Behavior (Oscillation) melting curing 300 C T resins, powder coatings Epoxy Powder Coating Melting Temperature (when G' = G'') T m = 206 C t = 638s Onset of Curing T CR = 260 C t = 1291s viscosity minimum η min = 2470Pas min time t Sol / Gel Transition (when again G' = G'') T SG = 291 C t = 1662s γ = 0.1% ω = 10rad/s 59

60 18 Temperature-dependent Behavior (Oscillation) dispersions softening swelling thickening fusion gelation PVC Plastisol 19 Torsional Tests on Solid Specimens fusion and gelation process from plastisol paste to elastomer onset of gelation: T = +65 C end of fusion: T = +96 C γ = 0.2% ω = 10rad/s Torsion Bars typical dimensions of solid specimens 40 x 10 x 1 (in mm) with 40mm of free length outside of the clamps Movies (plastisol fusion 1 & 2) measuring system SRF (solid rectangular fixture), for solid specimens, with a rectangular cross-section 60

61 19 Torsional Tests on Solid Specimens polymers 10,000 kpa 1000 lg G' lg G'' C Temperature T 19 Torsional Tests on Solid Specimens 10 lg tanδ Polycarbonate PC (in literature often as T g = 150 C) DMTA, dynamic mechanical thermo-analysis Discussion T g = 143 C (G' onset) T g = 146 C (G'' peak) T g = 149 C (G' midpoint) 0.01 T g = 152 C (tanδ max.) T g = 154 C (G' endpoint) ω = 10rad/s γ = 0.01% tanδ = G'' / G' torsion bar (SRF) 38.3 x 10 x 1.95 (in mm) Laminates DMTA dynamic mechanical thermo-analysis reinforced laminate unmodified laminate shifting T g from +132 C to +152 C ω = 10rad/s γ = 0.01% torsion bar (SRF) 50 x 10 x 1 (in mm) polymers softening 61

62 20 Tensile Tests Measuring systems SER - Sentmanat Extensional Rheology (rotation), and UXF - Universal Extensional Fixture (rotation and oscillation) for films, foils and fibers (e.g. 50µm thickness) Typical examples: Rotation: Preset: extensional rate ε& (in s -1 ) Result: extensional viscosity η E (in Pas) Oscillation (DMA, DMTA): Preset: extension (strain, deformation), ε (in %), & angular frequency (in s -1 ) Result: storage modulus E' and loss modulus E'' (in Pa) 20 Tensile Tests Tensile Tests elasticity law E - modulus, or Young's modulus (in Pa) σ (sigma), tensile stress (in Pa) ε (epsilon), elongation (in 1 = 100%) E = 2 G (1 + µ) with Poisson's ratio µ For all kinds of materials counts: E = (2 to 3) G factor 2 (or µ = 0) for stiff and brittle materials, and factor 3 (or µ = 0.5) for fluid materials σ E = ε Movies (sample preparation & loading, tensile & relaxation tests of adhesives, rubbers, polymer melts & films; in normal & polarized light) d l0 µ= d l 0 l... length, l = l l 0 d = d 0 d d... thickness of the specimen, change in length, change in thickness 62

63 20 Tensile Tests Comparison of three Coating Films 20 Tensile Tests Measuring System UXF 12 Films: 19 x 10 x (mm) Test program: 1) 30s pre-stress, T = +20 C M = 0 to 1mNm 2) 30s pre-strain, T = +20 C ϕ = 0 to 1 3) Measurement a) Rotation (ramp): σ = 1000 kpa to 10 kpa b) Oscillation (superposed): σ = 400 kpa to 4 kpa and ω = 10 s -1 c) Heating: T = +20 to 120 C with 5K/min T g values via E'' maxima Film 1 (blue): T g = 57 C Film 2 (green): T g = 69 C Film 3 (red): T g = 76 C Co- extrudate Foil 35µm thickness, multilayer foil, compound material PMMA / Poly-Carbonate Analysis of T g via the two E'' maxima PMMA T g = 120 C PC T g = 150 C 63

64 Portfolio Rheometers of Anton Paar MCR MCR MCR RheolabQC TD TwinDrive TwinDrive ready Normal force Isolign Higher stand nnm 230 mnm TruGap CTD One Instrument - Many Combinations Automatic stand ROT & OSC PP / CP / CC / DG / ST LTD / PTD / ETD PC + RheoCompass This wide range of application specific accessories is easily integrated into your MCR rheometer full modularity Manual stand ROT CC / DG / ST LTD / PTD Stand alone / RheoCompass 64

65 End of the Rheo - Seminar Never give up! Have a nice evening 65