Viscoelasticity, Creep and Oscillation Experiment Basic Seminar Applied Rheology
Overview Repetition of some basic terms Viscoelastic behavior Experimental approach to viscoelasticity Creep- and recovery Oscillation Repetition of some basic terms Amplitude sweep Frequency sweep Temperature sweep Time sweep Expansion of the measuremnent range for Oscillation Time Temperature Superposition (TTS) principle Cox-Merz Rule 2
Repetition of some basic terms Calculation of the dynamic viscosity Viscosity (dynamic) [Pa s] Shear stress [Pa] Deformation [-] Shear rate. [1/s] = 3
Repetition of some basic terms Calculation of the dynamic viscosity y A F y x v = Force Area = F A N m 2 = Pa = Displacement Distance = x y m m = dv dy = d dt m 1 = s m s 4
Viscoelasticity Repetition of some basic terms Viscoelastic behavior Experimental approach to viscoelasticity Creep and recovery Oscillation Viscoelastic behavior Amplitude sweep Frequency sweep Time sweep Temperature sweep Expansion of the measurement range for oscillation Time Temperature Superposition (TTS) principle Cox-Merz Rule 5
Viscoelastic behavior Reasons for viscoelasticity Entenglements Network formation Polymer solutions Polymer melts Emulsions Suspensions 6
Viscoelastic behavior Appying Hookke s law to rheology Purely elastic behavior Viscoelastic behavior Spring l y x A F l F k = Spring constant = F l = x y = F A Result Complex modulus G* G* = Pa 7
Viscoelastic behavior Models for viscoelasticity Viscous Viscoelastic =. = G* Elastic F = k l Dash pot Maxwell Model Burgers Model Voigt/Kelvin Model Spring 8
Viscoelasticity Repetition of some basic terms Viscoelastic behavior Experimental approach to viscoelasticity Creep and recovery Oscillation Experimental approach to viscoelasticity Amplitude sweep Creep Frequency and sweep recovery Time sweep Temperature sweep Expansion of the measurement range for oscillation Time Temperature Superposition (TTS) principle Cox-Merz Rule 9
Experimental approach to viscoelasticity Creep and recovery The viscoelastic behavior is observed by applying instantaneous shear stress changes. Non-destructive method (within the LVB) Destinguishes between elastic and viscous properties Determination of the time-dependent reaction to such changes 10
Shear stress Deformation Experimental approach to viscoelasticity Creep and recovery Viscous Sample = Rheometer input Irreversible deformation Applied energy dissipates completely Time 11
Shear stress Deformation Experimental approach to viscoelasticity Creep and recovery Elastic sample F = k l Rheometer input Reversible deformation Applied energy is stored Time 12
Elastic part Shear stress Deformation Experimental approach to viscoelasticity Creep and recovery Viscoelastic sample Rheometer input 1 3 2 2 1 3 1 2 Viscous part Time 13
Elastic part Shear stress Deformation Experimental approach to viscoelasticity Creep and recovery Results Rheometer input 0 Zero shear viscosity e0 Equillibrium deformation r Recoverable deformation 0 Retardation time G 0 Elastic modulus Applications Leveling Sagging Shear stability Yield stress Viscous part Time 14
Shear stress Deformation Experimental approach to viscoelasticity Creep and recovery Results Rheometer input 0 Zero shear viscosity e0 Equillibrium deformation r Recoverable deformation 0 Retardation time G 0 Elastic modulus Applications t. t = =. Leveling Sagging Shear stability Yield stress Time 15
Shear stress Deformation Experimental approach to viscoelasticity Creep and recovery Results 0 Zero shear viscosity e0 Equillibrium deformation r Recoverable deformation 0 Retardation time G 0 Elastic modulus Applications Rheometer input e0 Leveling Sagging Shear stability Yield stress Time 16
Shear stress Deformation Experimental approach to viscoelasticity Creep and recovery Results Rheometer input 0 Zero shear viscosity e0 Equillibrium deformation r Recoverable deformation 0 Retardation time G 0 Elastic modulus r Applications Leveling Sagging Shear stability Yield stress Time 17
Shear stress Deformation Experimental approach to viscoelasticity Creep and recovery Results Rheometer input 0 Zero shear viscosity e0 Equillibrium deformation r Recoverable deformation 0 Retardation time G 0 Elastic modulus 0 Applications Leveling Sagging Shear stability Yield stress Time 18
Shear stress Deformation Experimental approach to viscoelasticity Creep and recovery Results 0 Zero shear viscosity e0 Equillibrium deformation r Recoverable deformation 0 Retardation time G 0 Elastic modulus Applications Rheometer input 0 Leveling Sagging Shear stability Yield stress = G Time 19
Viscoelasticity Experimental approach to viscoelasticity Oscillation 20
Oscillation Principle of measurement Two-Plates-Model x 2 x 2 x 1 x 1 y A usually sinosoidal oscilllation is being applied by the rheometer Controllable parameters are the maximum amplitude ( x i ) of the shear stress ( ) or deformation ( ) as well as the (angular) frequency (f, ) and the temperature (T) 21
Deformation Y Axis Title Shear stress Oscillation Principle of measurement Rheometer input B e.g. Plate Rotor Rotor Rotor 0 Sample 0 2 4 6 X Axis Title Time Stationäre Stationary plate Platte 22
Y Axis Title Shear stress Deformation Oscillation Principle of measurement Purely elastic sample B B Input Shear stress (CS) Deformation (CD) resp. Response Deformation 0 = 0 Shear stress resp. 23 Phase angle 0 2 4 6 0 2 X Axis Title 4 6 X Axis Title Time
Y Axis Title Shear stress Deformation Oscillation Principle of measurement Purely viscous sample B Input Shear stress (CS) Deformation (CD) resp. Response 0 Deformation Shear stress Phase angle resp. = 90 0 2 4 6 X Axis Title Time 24
Y Axis Title Y Axis Title Y Axis Title Shear stress Deformation Oscillation Principle of measurement Viscoelastic sample B B B Input Shear stress (CS) Deformation (CD) resp. 0 Response Deformation 0 0 25 Shear stress resp. Phase angle 0 2 4 6 0 0 2 2 4 4 6 6 X Axis Title 0 < < 90 X Axis Title X Axis Title Time
Y Axis Title Shear stress Deformation Oscillation Principle of measurement B CS-Input Shear stress (t) = sin( t) 0 Response Deformation 0 2 4 6 X Axis Title Time (t) = sin( t - ) 26
Imaginary part Oscillation Results I Complex modulus G* = G + i G (i 2 = -1) Storage modulus G (elastic part) Pure Viscoelastic viscouse sample G = G* G = > 0 G = > 90 0 Loss modulus G (viscous part, damping) G* G Real part 27
Imaginary part Oscillation Results I Complex modulus G* = G + i G (i 2 = -1) Storage modulus G (elastic part) Pure elastic sample Purely viscous sample G = G* G = 0 = 90 Loss modulus G (viscous part, damping) G = G* Real part 28
Imaginary part Oscillation Results I Complex modulus G* = G + i G (i 2 = -1) Storage modulus G (elastic part) Purely elastic sample G = 0 = 0 Loss modulus G (viscous part, damping) G = G* Real part 29
Oscillation Results II Phase angle (0 90 ) Loss factor tan = G / G Complex viscosity Angular frequency *= G* / i = 2 f (f = frequency) 30
Viskoelastizität Oscillation Amplitude sweep 31
Oscillation Amplitude sweep Increasing amplitude in shear stress (CS) or deformation (CD) with constant frequency Determination of the linear-viscoelastic range (LVR), where material functions (G,G, ) are independent of the stress or the deformation applied Information about product stability e.g. gel strength 32
Deformation Shear stress Oscillation Amplitude sweep Increasing amplitude inshear stress (CS) or deformation (CD) with const. frequency Time 33
Storage modulus G Oscillation Amplitude sweep Plotted over 10 Hz 1 Hz Width of the linearviscoelastic regime (LVB) depends on the frequency 0.1 Hz Plotted over End of LVR Width of LVB is less frequency depending Shear stress 34
Viskoelastizität Oscillation Frequency sweep 35
Oscillation Frequency sweep Variation of frequency with constant shear stress or deformation respectively Determination of material s structure Determination of material s properties, which cannot be measured in shear 36
Deformation Shear stress Oscillation Frequency sweep Variation of Frequency with const. shear stress or deformation Time 37
log Storage modulus G log Loss modulus G Oscillation Frequency sweep Viscous Flow The samples behaves mainly viscous over the entire measuring range G < G log Angular frequency For ideal viscous samples: Slope G ( ) = 2 Slope G ( ) = 1 38
log Storage modulus G log Loss modulus G Oscillation Frequency sweep Elastic Plateau Sample behavior is dominated by the elastic properties G > G log Angular frequency Examples: Cross linked Polymers Physical Networks 39
log Storage modulus G log Loss modulus G Oscillation Frequency sweep Viscoelastic behavior In the region of low frequencies the sample behaves viscous At high frequencies the elastic behavior predominates Cross-Over-Point G = G log Angular frequency 40
Phase angle Oscillation Frequency sweep Flow Cross-Over-Point log Loss modulus G log Storage modulus G 45 The Cross-Over-Point G = G separates viscous flow at low frequencies and elastic behavior at higher frequencies Elastic behavior log Angular frequency 41
log Loss modulus G log Storage modulus G Oscillation Frequency sweep Narrow distribution High M w Low M w Polymer Fluids The location of the cross over point depends on: Broad distribution The average molecular weight (M w ) The molecular weight distribution (MWD) log Angular frequency 42
Oscillation Frequency sweep log Loss modulus G log Storage modulus G c Polymere Fluide T T The location of the cross over point depends on: The temperature T c The polymer concentration c (for polymer solutions) log Angular frequency 43
Viskoelastizität Oscillation Temperature sweep 44
Oscillation Temperature sweep Variation of the temperature with constant shear stress or deformation and (angluar) frequency,f Determination of the temperature depending sample charteristics Determination of the glas transition, softening and melting temperature Investigation of chrystallization processes and sol-gel transitions 45
Deformation Shear stress Temperature Oscillation Temperature sweep Variation of the temperatur with const. shear stress or deformation and (agular) frequency,f Time 46
log loss modulus G log storage modulus G tan Oscillation Temperature sweep Amorphous polymers Not cross linked No positional order Random orientation Examples: Glass transition T g Temperature T Polystyrene Polyvinylchloride Polycarbonate 47
log loss modulus G log storage modulus G tan Oscillation Temperature sweep Semi crystalline Polymers Melting temperature T m Not cross linked Partially ordered structure Partially oriented Glass transition T g Temperature T Examples: Low Density Polyethylen High Density Polyethylen Polypropylen 48
log loss modulus G log storage modulus G tan Oscillation Temperature sweep Cross-linked Polymers Glass transition T g Temperature T Via covalent or ionic bonds cross-linked macro molecules Examples: Depending on the cross-link density Elastomers (wide-meshed) Thermosets (close-meshed) 49
Viscoelasticity Repetition of some basic terms Viscoelastic behavior Experimental approach to viscoelasticity Creep and recovery Oscillation Expansion of the measurement range for oscillation Amplitude sweep Time Temperature Superposition (TTS) principle Frequency sweep Time sweep Temperature sweep Expansion of the measurement range for oscillation Time Temperature Superposition (TTS) principle Cox-Merz Rule 50
log Storage modulus G log Loss modulus G Oscillation Frequency sweep Viscous Flow Elastic Plateau Glassphase Inertia effects of rheometer limit the measurement range towards high frequencies Long Measurement times limit the measurement range towards small frequencies Measuring range log Angular frequency 51
Oscillation Frequency sweep Freq. [Hz] Time [s] Time [min] Time [h] Time [d] 100 0.01 10 0.1 1 1 0.1 10 0.17 0.01 100 1.67 0.001 1000 16.7 0.28 0.0001 10000 167 2.78 0.12 0.00001 100000 1670 27.8 1.2 0.000001 1000000 16700 278 12 52
log Loss modulus G Expansion of the measurement range Time Temperature Superposition (TTS) Performance Several frequency sweeps are being performed at different temperatures log Storage modulus G ( ) = T 1 = T 2 = T 3 T 1 < T 2 < T 3 Standard frequency range 53
log Storage modulus G log Loss modulus G Expansion of the measurement range Time Temperature Superposition (TTS) Expanded frequency range 54
log Loss modulus G log Storage modulus G log Complex viscosity Expansion of the measurement range Time Temperature Superposition (TTS) * = G* / i Expanded frequency range 55
log Loss modulus G log Storage modulus G log Complex viscosity Expansion of the measurement range Time Temperature Superposition (TTS) Determination of the zero shear viscosity 0 Expanded frequency range Determination of the viscosity at high frequencies / velocities and short relaxation times 56
log Dynamic viscosity log Complex viscosity Expansion of the measurement range Cox-Merz Rule Empiric Rule Valid for numerous unfilled polymer melts and polymer solutions Validity in the Non- Newtonian may vary * [rad/s] = [s -1 ] Not valid for dispersions, suspensions and gels. log Shear rate [s -1 ] / log Angular frequency [rad/s] 57
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