Guideline for Rheological Measurements Typical Measurements, Diagrams and Analyses in Rheology www.anton-paar.com
General Information: = Measurement = Diagram = Analysis Important Rheological Variables: Rotational Tests: η = viscosity [Pas] τ = shear stress [Pa] γ& = shear rate [s -1 ] γ = deformation [%] Oscillatory Tests: γ = deformation [%] ω = angular frequency [s -1 ] G = storage modulus [Pa] G = loss modulus [Pa] Iη*I = complex viscosity [Pas] tan δ = damping factor [1] (= G /G ) CSR: controlled shear rate CSS: controlled shear stress CSD: controlled shear deformation 1. Choosing the Measuring System - low-viscosity materials, drying samples concentric cylinder system - Samples with particles > 5 µm, highly viscous and viscoelastic materials, e.g. polymer melts parallel plate system - all other samples cone and plate system 2
2 Rotational Tests 2.1 Flow and Viscosity Curves, CSR, linear (lin) or logarithmic (lg): γ& = 0.5 to 500 s -1 lin τ/ γ& lin η/ γ& lg τ/lg γ& lg η/lg γ& 1) ideal-viscous, Newtonian 4) without yield stress 2) shear thinning, pseudoplastic 5) with yield stress 3) shear thickening, dilatant Rheological models for flow curves: for curve 1: Newton for curves 2 and 3: Ostwald-de Waele, for curve 5: e.g Bingham, Casson, Herschel/Bulkley 3
2.1a) Without a Yield Stress (curves 1 to 4): Flow and viscosity curve CSR, log: extended shear rate range ball bearing: γ& = 1 to 1000 s -1 ; air bearing: γ& = 0.01 to 1000 s -1 lg η/lg γ& lg η/lg γ& Determination of the zero-shear viscosity η 0 (see also 3.2) and possibly the infinite-shear viscosity η at γ& = 0.01 to 0.1 s -1 or using analysis models e.g. Carreau-Yasuda or Cross 2.1b) With a Yield Stress (curve 5): flow curve CSS, log ball bearing: M = 0.5 to 5 mnm; air bearing: M = 0.5 µnm to 5 mnm lg τ/lg γ& lg γ/lg τ Determination of the yield stress: as a constant τ - value in the low shear range using the tangent method (at γ& < 1 s -1, e.g at γ& = 0.01 s -1 ) (analysis method Yield stress ) 4
2.2 Time-Dependent Tests constant shear rate: e.g. ball bearing: = 1 s -1, air bearing: = 0.1 s -1 ; const temperature γ& γ& 1) no change of viscosity with time (e.g. calibration oil) 2) decreasing viscosity with time (e.g. polymer solution) 3) Increasing viscosity with time (e.g. curing, drying) Note: Time-dependent tests in oscillatory mode give more detailed information (see 3.3) 5
2.3 Step test 3ITT (Structure Breakdown and Recovery, Thixotropy ) Three intervals in rotation: ball bearing = 1 / 100 / 1 s -1 ; air bearing = 0.1 / 100 / 0.1 s -1 γ& Thixotropy: Thixotropic behavior means a decrease of structural strength during shearing and its full recovery at rest. Recovery can be quick or slow. The breakdown is fully reversible, otherwise the material is not called thixotropic. γ& 3 ITT analysis methods: - Thixotropy as the difference of η ( η) at t 3 and t 2 - Total Recovery Time as the interval between t 2 and the point in time for full recovery - Thixotropy time as the interval between t 2 and a pre-defined percentage of recovery (e.g. 75% of the viscosity value in interval 1) - Percentage of recovery between t 2 and a given point in time in interval 3 (e.g. after 60 s) Note: Step tests in oscillatory mode give more detailed information (see 3.4) 6
2.4 Temperature-Dependent Tests constant shear rate: e.g. ball bearing: = 1 s -1, air bearing: = 0.1 s -1 ; temperature ramp γ& γ& Viscosity as a function of temperature shows a decrease during heating and an increase during cooling Viscosity as a function of temperature for a gelling, hardening or curing material Evaluation using the Arrhenius model results in the following parameters: - thermal shift factor according to the Arrhenius equation to estimate viscosity values at temperature values for which no measurement data are available - activation energy E A Note: Temperature tests in oscillatory mode give more detailed information (see 3.5) 7
3 Oscillatory Tests 3.1 Amplitude Sweep, CSD, log: γ = 0.01 to 100 %, ω = 10 s -1 G > G : Gel-like properties (viscoelastic solid) G > G : fluid character (viscoelastic fluid) τ y τ f lg τ G > G in the LVE range no yield stress as G > G in the LVE range - limit of the linear-viscoelastic range (LVE) at γ L (reversible deformation) - viscoelastic characteristics in the LVE range: Question: Is G > G (gel) or G > G (fluid)? - value of G as gel strength - start of the yield zone at τ y as the limit value of the LVE range (partially reversible deformation as long as G > G ) - yield stress at τ f ; the material starts to flow at G =G (irreversible deformation) 8
3.2 Frequency Sweep, γ within the LVE range (from an amplitude sweep), ω = 100 to 0.1 s -1 With: molar mass M 1 > M 2, ω CO : crossover frequency G P : plateau value - viscoelastic behavior at low (long-term behavior) and high (short-term behavior) frequencies, i.e. is G > G or G > G? - Polymers: a) the crossover frequency (G = G ) is mainly dependent on the average molar mass M (and to a small degree on the molar mass distribution MMD) b) at low frequencies: Maxwell behavior if the slope is 2:1 for G and 1:1 for G Questions: Is the material cross-linked (G > G ) or not (G > G )? Relative degree of cross-linking (the higher G, the higher the degree)? c) Time-Temperature Superposition, Mastercurve acc. to Williams, Landel and Ferry (WLF) d) Molar mass distribution (MMD) 9
Polymers (viscosity curve): - determination of the zero-shear viscosity η 0 at low frequencies, e.g. ω = 0.01 to 0.1 s -1 - average molar mass is proportional to the zero-shear viscosity (η 0 ~ M) - Cox-Merz relation: the values for γ& η( ) from rotational tests and for Iη*I(ω) from oscillatory tests are identical in the low shear range. This behavior is shown by many polymer melts and solutions. This conversion can be used for Maxwell fluids only. η 0 =const. Cox-Merz relation 10
lg Iη*I lg G lg Iη*I lg G lg G lg G lg G Dispersions and Gels: Measurement at low ω - values: e.g. ω = 0.01 to 0.1 s -1 Questions: - gel-like behavior and therefore long-term stability (if G' > G'')? - structural strength at rest (G value)? - instability (if G > G )? - hardening or syneresis (if G» G, i. e. tanδ too low)? 11
3.3 Time-Dependent Tests constant deformation and frequency: e.g. γ = 1% ; ω = 10 s -1, constant temperature 1) time independent 2) increase of structural strength 3) decrease of structural strength Curing material with t CR as the time for the onset of the reaction Curing material with sol-gel transition at t SG ( gelation time ) - Minimum of lg G (t) curve (using the analysis method Curve Paramters ) - Sol-gel transition at t SG, i.e. the development of a gel-like structure at G = G during the curing reaction (gelation time, gel point) - final values of G and G 12
3.4 Step Test (Structure breakdown and recovery, Thixotropy ) a) three intervals: oscillation / rotation / oscillation: γ in the LVE range and e.g. γ& = 100 s -1 b) three oscillation intervals: γ within / above / within LVE range 3 ITT evaluation methods: - Thixotropy as the difference of G ( G ) at t 3 and t 2 - Total Recovery Time as the interval between t 2 and the point of time for full recovery - Thixotropy time as the interval between t 2 and a pre-defined percentage of recovery (e.g. 75% of the G value in interval 1) - Thixotropy time until G = G - Percentage of recovery for G between t 2 and given point in time in interval 3 (e.g. after 60 s) 13
3.5 Temperature-Dependent Tests constant deformation and frequency: γ = 1 % (from LVE) ; ω = 10 s -1, temperature ramp Polymers (internal structure) 1) amorphous 2) partially crystalline 3) a) densely cross-linked (thermoset) b) sparsely cross-linked (elastomer) 1) 2) 3b) - glass transition temperature T g as the temperature at the maximum of G or of tanδ - melting temperature T m (above T m : G > G ) 14
4) Behavior of a crystalline material during heating or cooling 5) Curing material with T CR as the temperature at the onset of the reaction to 4): crossover of G and G represents the crystallization temperature T k to 5): curing material: - melt temperature T m, at the transition from G >G to G >G - temperature T CR at the onset of the chemical reaction e.g. at the minimum of G ( reaction temperature ) - sol-gel transition at T SG, at the transition from G >G to G >G ( gel temperature or gel point ) 15