Brno, 28-29th march 2012 – School of Rheology Part I: Rotational Rheometry How to measure Shear Viscosity correctly? ω M Rotation Outline • Basic terms in shear rheometry • Principle of Operation: Rotational Rheometer • Applications: A) Steady State Flow Curves using a Rotational Rheometer: Impact of particle size, volume fraction and polydispersity on dispersion flow properties, Polymer Melt Rheology B) Time-dependent Flow Behaviour Yield Stress of Dispersions and it`s relation to Zeta Potential, Thixotropy, Structure Recovery - with Live Tests on Kinexus Rheometer Basic Terms in Shear Rheometry displacement u Tangential-force F s area = a · b Gap = s b a u γ = s . dγ γ = dt Ftan τ = A strain [] Shear rate [1/s] Shear stress [Pa=N/m2] Typical Shear Rate Ranges Sagging, Levelling Extrusion, Injection Moulding Roll Coating, Spraying Mixing, Blade Coating, Brushing 10-3 10-1 100 101 102 103 104 106 s -1 Rotational-Rheometer Sample: Water up to solids Results: Shear-Viscosity, Yield Stesses, Visco-Elasticity, Relaxation... High Pressure Capillary-Rheometer Sample: Water up to high viscous Results: Shear-Viscosity, Elongational-Viscosity, Wall Slip... Shear Viscosity Resistance of a sample against the flow η = η − τ − . γ − τ . γ Shear Viscosity Shear Stress Shear Rate Typical Shear Viscosities Material Shear-Viscosity (Pas) 10-6 10-4 10-3 10-1 100 103 108 1012 1040 Air Aceton Water Olive Oil Glycerol Molten Polymers Bitumen Glass at 500°C Glass at ambient Units: Pascal second Poise Pas (SI) P (CGS) Remember 1 Pas = 10 P 1 mPas = 1 cP Shear-Viscosity depends on… . η (Τ, p, t, γ) = τ . γ • Physical-chemical structure of the sample • Temperature (up to 20% / K) • Pressure • Time • Shear Rate Steady-State Flow Behaviour Shear Thinning Shear Rate Shear Rate Shear Rate Shear Rate Cornflower . Shear Rate Viscosity Inks, Paints Viscosity Viscosity Silicon Oil, Suspension Shear Thickening Stress Stress Stress Newtonian Shear Rate Principle of Operation: Rotational Rheometer Stress- and Strain Control possible. Motor • Air bearing • Position sensor • Upper Measuring Plate The drive is situated above the sample, not below. The driven spindle is air bearing supported so torque can be measured. The separate torque transducer is eliminated! Advantages: Sample Temperature Controller • • • • Wide Torque Range 10e-9 to 10e-1 Nm Short Response times Small inertia design Direct Stress and Direct Strain Choice of Geometry: From Fluids to Solids Apply Torque / Measure Torque M ω Measure Displ. Apply Displacement δ R • the higher the viscosity, the smaller the geometry Rule of Thumb for dispersions: Gap Size > 10 * D90 Parallel Plates • the higher the shear rate, the smaller the gap. Cup&Bob Solids Fixture Cone-Plate / Plate-Plate • Cone Adv: Const Shear Rate along the complete gap, easy cleaning, low sample volume, wide viscosity range • Cone DisAdv: only for homogeneous samples, for disperse samples D90 < 10 x gap, solvent evaporation • Plate Adv: flexible gap, auto-tension possible, low sample volume, often used for temperature dependent tests, good for disperse systems • Plate DisAdv: shear rate dependency, solvent evaporation 0s-1 10s-1 10s-1 10s-1 10s-1 Cup & Bob / Double Gap • Cup&Bob Adv: large gap, works well for disperse systems, also for samples showing sedimentation, large surface area, nearly no evaporation effects, good for low viscous samples, less impact of loading errors • Cup&Bob DisAdv: high moment of inertia limits oscillation and transient steps, high cleaning effort, large sample volumes (ca 2ml – 15ml) • Double Gap Adv: highest sensitivity for low viscous samples, lower inertia compared to cup&bob, nearly no impact on loading errors • Double Gap DisAdv: large sample volume (ca. 15ml – 30ml), difficult cleaning Cup&Bob acc DIN53019 Double Gap Basic Viscometry: How to run a flow curve CS-Mode: Steady state and non-steady state measurements Steady state: τ . γ Table of stresses t t non-steady state: τ . γ Linear ramp t t 1. Steady State Flow Properties η = Newton: Flow Curve: . τ = τ (γ) equivalent CR-Mode Shear Viscosity Curve: . η = η (γ) τ . γ . . γ = γ (τ) CS-Mode equivalent η = η (τ) Steady State Condition Kinexus Rheometer γ J= τ ⇒ dLnJ/dLnt = 1 for pure viscous flow! ⇒ Deviations show measurement errors! Steady State Calculation ⎛ γ (t ) ⎞ d ln⎜ ⎟ d ln J τ ⎠ d (ln γ (t ) − ln τ ) d ln γ (t ) d ln τ ⎝ = = − = d ln t d ln t d ln t d ln t d ln t τ η 0 t Newtons Law : γ = ∫ ⋅ dt = τ ⋅t η η (t ) = const , τ (t ) = const ⇒ ⎛τ ⎞ ⎛τ ⎞ d ln⎜⎜ ⋅ t ⎟⎟ d ln⎜⎜ ⎟⎟ d ln γ (t ) d ln τ ⎝ η ⎠ + d ln t − d ln τ = ⎝ η ⎠ − d ln τ = = − = d ln t d ln t d ln t d ln t d ln t d ln t d ln t = d (ln τ − ln η ) d ln t d ln τ + − d ln t d ln t d ln t = d ln τ d ln η d ln t d ln τ − + − d ln t d ln t d ln t d ln t ⇒ d ln J =1 d ln t for steady state. Comparison Stress- and Rate Controlled Test Shower Gel: Comparison CS □ und CR ∆ Shear Viscosity Curve Live Measurement on Kinexus: Shower Gel Flow Curve Normal Stress Difference N1 Shower Gel Ft Fn Edge failure ⇒ Always watch the Normal Stress during a Shear Viscosity Measurement! Steady State Flow Curves: Impact of Particle Size η (Pa.s) 102 101 175 µm 100 Increase the size of latex particles in a pressure sensitive adhesive from D50=175µm to D50=750mm Polydispersity and Volume Fraction similar 10-1 750 µm 10-2 10-1 100 101 102 103 . γ (s-1) 104 105 106 Smaller size means an increase in number of particles which causes an increase in particle-particle interactions. Hence an increase in low shear viscosity. Reason for Shear Rate Dependency Log η Entanglement Network / Particle-Particle-Interaction . Log γ Equilibrium Destruction > Recovery No Entanglements Molecules / Particles Entanglements / Particle Interaction Steady State Flow Curves: Impact of Particle Loading Changing the Volume Fraction of Particles… Newtonian φm < 0.1 0.1 < φ φm < 0.5 Log Zero Shear Viscosity φ Shear Thinning Shear Thickening φ φm > 0.5 Krieger-Dougherty: η η medium Volume Fraction ⎛ φ = ⎜⎜1 − ⎝ φm ⎞ ⎟⎟ ⎠ − [η ]φ m Shear Thickening of concentrated dispersions Kinexus Rheometer ⇒ those shear thickening effects can have negative impact on processability – see section capillary rheometry Steady State Flow Curves: Impact of Polydispersity We keep the volume fraction (φ) constant But changing polydispersity… Particle Size Distribution Volume (%) 20 15 10 5 0 0.1 1 10 Particle Size (µm) What happens to the viscosity? 100 1000 3000 Impact of Polydispersity on Flow Behaviour Zero Shear Viscosity Fine talc of different D50, mixed into an epoxy resin 100% 175 µm 100% 750 µm Krieger-Dougherty 0% Increasing amount of 175 µm particles 100% η 100% Increasing amount of 750µm particles 0% η medium ⎛ φ = ⎜⎜1 − ⎝ φm If you want to increase the solid content of the sample but keep the viscosity the same, increase the particle size distribution (polydispersity) as well. Conversely, narrow the particle size distribution to increase the viscosity. ⎞ ⎟⎟ ⎠ − [η ]φ m Steady State Flow Curves: Impact of Matrix Additives Xanthan Solution - measured with Cone Plate and Double Gap 1000 η sp Mw= 2.400.000 g/mol 1% c 100 M = Shear viscosity[Pas]. 0.5% = [η ] + k h [η ] c 2 10 π ⋅N 3 A ⋅ R h3 [η ] 10 1% 0.3% 0.5% 1 0.3% 0.1% CP 0.1% 0,1 0.1% DG 0,01 0,001 1,0E-04 1,0E-03 1,0E-02 1,0E-01 1,0E+00 1,0E+01 1,0E+02 1,0E+03 Shear Rate [1/s] ==> the higher the concentration of Xanthan, the higher the zero shear viscosity. Further Factors Influencing Dispersion Rheology Spray Particle Analyzer Laser Diffraction volume fraction, φ Particle size Particle size distribution Digital Microscopy Vs Light Scattering Size and Zeta Electrostatic interactions Steric Hindrance Particle shape Dry + + + + + + + + ------ Wet Polymer Melt Rheology: Determination of Mw from Flow Curves . γ Polymer Melt Rheology: Effect of Molecular Weight Distribution Log Viscosity (Pa.s) ÂA Polymer with a broad MWD exhibits nonNewtonian flow at a lower rate of shear than a polymer with the same η0 but has a narrow MWD Narrow MWD Broad MWD Log Shear Rate (1/s) 2. Time Dependent Flow Properties Viscosity is not only dependent on shear rate it is also time dependent. Think of paint. Thick in the can when left in the shed for months, but thins when stirred. However, it is thixotropic as it does not rebuild straight away on stopping the stirring. Shear rate Thixotropic Example Two samples… one very thixotropic, one not so thixotropic. Viscosity Time Bad paint – leaves brush marks. Rebuilds too thick too quickly. Good paint – leaves smooth finish. Rebuilds quite slowly. Enough time to allow ridges to smooth out. Time Thixotropy 3- Step-Shear profile Thixotropy: Decrease of viscosity vs. time at constant shear + complete recovery under rest 1 2 3 1 = Initial Viscosity at low shear 2 = high shear phase (time-and rate dependent) 3 = Recovery Another Time Dependent Property: Yield Stress Some samples require a certain stress until they flow – a yield stress. A transition to go from solid to liquid. Or… Why toothpaste needs to be squeezed to get out of the tube. However, does not flow into bristles on tooth brush. Why Heinz tomato sauce needs a whack. But still looks thick on the plate. Or why pumps take time to get going. Relation to Flow Curves “YIELD STRESS” An ever increasing viscosity as the shear rate approaches zero, i.e. a does not flow / solid like when stationary. ZERO SHEAR VISCOSITY Log Viscosity The viscosity plateau’s as the shear rate approaches zero, i.e. flows / liquid like when stationary. THIXOTROPIC Both materials can be, and tend to be “thixotropic” – viscosity depends on time. Rheometer measurement range Viscometer Measurement range 10-6 Studying weaker interactions Log Shear Rate 106 Studying stronger interactions Yield Stress Determination by Stress Ramp and Creep Tests Viskoses Fleßen Schubspannung 3Pa Schubspannungen 1Pa, 1.5Pa, 2Pa, 2.5Pa Fließgrenze = 3Pa Linear or logarithmic Stress Ramp Energy absorbed - strong association - no flow Mutliple Creep Tests at different Stresses Usually Stress Ramp is used as a pre-test, whereas Multiple Creep gives precise Yield Stress Example: Stable Metal Oxide Dispersions In this case study we have a sample of silica (silicon oxide) which has an average particle size greater than 1 micrometer. Conventional colloidal theory of increasing the zeta potential to ±30mV is insufficient to counter the effect of gravity on these large particles… Particle Size Sample characterised on a Mastersizer 2000, showing a particle size greater the 1 micrometer. Laser Diffraction Zeta Potential Titrating a silica sample with HCl on a Zetasizer Nano with MPT-2 autotitrator. The isoelectric point (where the zeta potential is zero) is in the very acidic (pH 1) region. Steady-Shear Viscosity vs Zeta-Potential Log Viscosity Suspension with micron particles and zeta potential -> 0mV Associated structure strong enough to induce a yield stress. Suspension with sub-micron particles and high zeta potential Log Shear Stress At isoelectric point the zero shear viscosity gets infinite Stronger associated structures which resist even high shear stresses. Resultant Rheology for the Silica Supsension As the particles associate more, with pH’s closer to the iso-electric point, the viscosity increases. pH2.42 pH3.97 pH3.52 Materials with higher low shear viscosities are regards as more resistance to separation. Resulting Yield Stress for the Silica Suspension Yields stress measurements (the stress at the peak of instantaneous viscosity) is a measurement of the internal strength of material. pH2.42 – yield stress = 15.8 Pa pH3.52 – yield stress = 2.5 Pa pH3.97 – no yield stress Thank you for your attention! Please join our sessions on: Capillary Rheometry and Oscillatory Rheometry. Any Questions? [email protected]