ExperimentalObservations 2014 CM4650

Transcription

1 Done with Material Functions. What now? 1. Intro 2. Vectors/tensors 3. Newtonian 4. Standard Flows 5. Material Functions 6. Experimental Behavior 7. Inelastic effects 8. Memory effects 9. Advanced 1. Rheometry 1 Investigating Stress/Deformation Relationships (Rheology) (7) What are material functions and why do we need them? For non- Newtonian fluids: (4) (2) We do not know the stress/deformation relationship We approach stress/deformation investigations from two directions (modeling, measuring) to reveal the physics; Material functions organize comparisons Hypothetical Constitutive equation + Standard Velocity and pressure fields (5) (1) Material Functions (stress responses) = predictions of: (6) (3) material + measurements of = + Ability to measure stresses Standard Velocity and pressure fields 1. Choose a material function 2. Predict what Newtonian fluids would do 3. See what non-newtonian fluids do 4. Hypothesize a 5. Predict the material function 6. Compare with what non-newtonian fluids do 7. Reflect, learn, revise model, repeat. Let s focus more on material observations 3 1

2 Chapter 6: Experimental Data Small-Amplitude Oscillatory Shear - Storage and Loss Moduli CM465 Polymer Rheology Michigan Tech 1 1 modulus, Pa Terminal zone Rubbery zone Glassy zone G' G'' o G N E E-1 1 1E Figure 6.3, p. 192 Plazek and O Rourke; PS frequency, rad/s 3 Steady Shear Flow Material Functions Imposed Kinematics:, constant Material Stress Response:, Material Functions: Viscosity First normal-stress coefficient Second normalstress coefficient Ψ Ψ 4 2

3 Experimental Data (Chapter 6) First recipe card: Steady shear flow What do we observe for Linear Polymers Limits on measurability Material effects - MW, MWD, branching, mixtures, copolymers Temperature and pressure later... (the rest of the recipe cards) Unsteady shear flow (SAOS, step strain, start up, cessation) Steady elongation Unsteady elongation 5 Steady shear viscosity and first normal stress coefficient 1.E+5 o 1, Poise 1.E+4 o 1, (dyn/cm 2 )s 2 1.E+3 1 Ψ 1.E Figure 6.1, p. 17 Menzes and Graessley conc. PB solution, 1 s 6 3

4 Steady shear viscosity and first normal stress coefficient 1.E+6 1.E+5 1.E+9 1.E+8 1.E+4 1.E kg/mol 517 kg/mol 35 kg/mol 2 kg/mol, Poise 1.E+3 1.E+2 1.E+6 1.E+5 1, dynes/cm 2 1.E+1 1.E E+ 1.E+3 Figure 6.2, p. 171 Menzes and Graessley conc. PB solution; c=.676 g/cm 3 1.E-1 1.E , s 1 7 Steady shear viscosity and first normal stress coefficient 1 stress, Pa, Pa s 1 1 1, Pa s Figure 6.5, p. 173 Binnington, s, and Boger; PIB soln 8 4

5 Steady shear viscosity and first and second normal stress coefficient 1 PS/TCP squares PS/DOP circles steady shear material functions (Pa) 1 (Pa s 2 ) 2 (Pa s 2 ) Figure 6.6, p. 174 Magda et al.; PS solns ,, s 9 Limits on Measurements: Flow instabilities in rheology cone and plate flow capillary flow Figures 6.7 and 6.8, p. 175 Hutton; PDMS Figure 6.9, p. 176 Pomar et al. LLDPE 1 5

6 Spurt instability 1, 4Q R 3 (s -1 ) 1, LPE-1 LPE-2 LPE-3 LPE-4 Piston F Instron capillary rheometer A Barrel 2R b 1 Polymer melt reservoir B Figure 6.1, p. 177 Blyler and Hart; PE 1 1.E+5 1.E+6 1.E+7 PR, 2L dynes / cm 2 Q 11 Steady shear viscosity and first normal stress coefficient - Molecular weight effects 1.E+6 1.E+5 1.E+9 1.E+8 1.E+4 1.E kg/mol 517 kg/mol 35 kg/mol 2 kg/mol, Poise 1.E+3 1.E+2 1.E+6 1.E+5 1, dynes/cm 2 1.E+1 1.E E+ 1.E+3 Figure 6.2, p. 171 Menzes and Graessley conc. PB solution; various MW 1.E-1 1.E ,, s

7 Variation of viscosity with molecular weight M c log constant 1 slope= Figure 6.12, p. 178 Berry and Fox, 1968; various polymers log M + constant Faith A. 13Morrison, Michigan Tech U. Entanglements strongly affect polymer relaxation M<M c M>M c Unentangled relaxation is rapid Entangled relaxation is retarded 14 7

8 Effect of Distribution of Molecular Weight A - M w /M n =1.9 B - M w /M n =2. C - branched 2 Figure 6.14, p. 179 Berry and Fox; PVA solns in DEP 15 Types of polymer architecture short-chain branching long-chain branching hyperbranching star dendrimer 16 8

9 Motion of Branched Polymers Entangled linear polymer chains move principally along their contour Entangled branched polymer branch points retard motion once disentangled (high shear rate), branched polymers flow more freely 17 Effect of Branching on low 22 s 1 linear 3-arm star 4-arm star linear 3-arm star 4-arm star Figures 6.17, 6.18, pp. 181,3 Kraus & Gruver; PB 18 9

10 Steady shear rheology of PAMAM dendrimers viscosity, poise 1.E+9 1.E+8 1.E+7 1.E+6 1.E+5 Gen Gen 1 Gen 2 Gen 3 Gen 4 Gen 5 Gen 6 1.E+4 1.E+3 1.E+2 1.E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+ 1.E+1 1.E+2, a T * shear rate, 1/s Figure 6.2 p. 183; from Uppuluri 19 Steady Shear Summary: 1. General traits 2. Effect of MW on linear polymers 3. Effect of architecture 4. Measurement issues 2 1

11 Mixtures of Polymers with other materials - Filler Effect (specific chemical interactions) (no specific interactions) Figure 6.22, p. 184 Chapman and Lee; PP and filled PP For more on filled systems, see Larson, The Structure and Rheology of Complex Fluids, Oxford, Mixtures of Polymers with other materials - Filler Effect (specific chemical interactions) Figure 6.21, p. 184 Chapman and Lee; filled PP For more on filled systems, see Larson, The Structure and Rheology of Complex Fluids, Oxford,

12 Steady shear viscosity - shear thickening For discussion of causes of shear thickening, see Wagner and Brady, Phys. Today, October 29 1 ( Pa s) vol % TiO Figure 6.27, p. 188 Metzner,, s and Whitlock; TiO 2 /water suspensions 23 Steady shear viscosity - shear thickening Wagner and Brady, Phys. Today, Oct 29 Latex spheres in Newtonian fluid Filler effect Shear thickening 24 12

13 Steady shear viscosity - shear thickening Wagner and Brady, Phys. Today, Oct 29 Particles bump into each other Layers of particles slide past each other Clusters of particles bump into each other Hydrodynamic interaction causes shear thickening: The pressure distribution in the Newtonian suspending fluid exerts forces on the particles and causes them to form structures in flow. 25 Steady shear viscosity - temperature dependence 1 Poise 1 viscosity (Poise) 3 K viscosity (Poise) 339 K viscosity (Poise) 38 K viscosity (Poise) 425 K Figure 6.28, p. 189 Gruver and,, s Kraus; PB melt 26 13

14 Steady shear viscosity - pressure dependence 1, apparent viscosity, Pa s 1, 1, 1 PS, T=196C PE, T=149C Figure 6.29, p. 189 Maxwell and Jung; PS and PE hydrostatic pressure, MPa 27 Steady Shear Summary: 1. General traits 2. Effect of MW (linear polymers) 3. Effect of architecture 4. Measurement issues 5. Effect of chemical composition 6. Effect of temperature 7. Effect of pressure 28 14

15 Experimental Data (continues) Next: Unsteady shear flows (small and large strain) Steady elongation Unsteady elongation 29 Small-Amplitude Oscillatory Shear - Storage and Loss Moduli 1 1 modulus, Pa G' G'' o G N Rubbery plateau 1 4 slope=1 Figure 6.3, p. 192 Plazek and O Rourke; PS slope=2 1 1E E-1 1 1E , / frequency, rad/s 3 15

16 Small-Amplitude Oscillatory Shear - Storage and Loss Moduli 1 1 modulus, Pa Terminal zone Rubbery zone Glassy zone G' G'' o G N 1 4 Figure 6.3, p. 192 Plazek and O Rourke; PS 1 1E E-1 1 1E , / frequency, rad/s 31 Step Shear Strain - Relaxation Modulus 1.E Glassy zone Rubbery zone Terminal zone G(t) Pa 1.E Rubbery plateau 1.E E E time, s Figure 6.31, p. 192 Plazek and O Rourke; PS 32 16

17 Ferry s Summary of Viscoelastic properties of several classes of polymers Storage modulus Figure2-3 from Ferry, Viscoelastic Properties of Polymers, Wiley, 198, / 33 Key to Ferry s plots I. Dilute polymer solutions: atactic polystyrene,.15 g/ml in Aroclor 1248, a chlorinated diphenyl with viscosity 2.47 poise at 25 o C. M w =86,, M w /M n near 1. II. Amorphous polymer of low molecular weight: poly(vinyl acetate), M=1,5, fractionated. III. Amorphous polymer of high molecular weight: atactic polystyrene, narrow MW distribution, M w =6,. IV. Amorphous polymer of high molecular weight with long side groups: fractionated poly(n-octyl methacrylate), M w =3.62 X 1 6. V. Amorphous polymer of high molecular weight below its glass transition temperature: poly(methyl methacrylate). VI. Lightly cross-linked amorphous polymer: lightly vulcanized Hevea rubber. VII. Very lightly cross-linked amorphous polymer: styrene butadiene random copolymer, 23.5% styrene by weight. VII. Highly crystalline polymer: linear polyethylene

18 Ferry s Summary of Viscoelastic properties of several classes of polymers Loss modulus Figure2-4 from Ferry, Viscoelastic Properties of Polymers, Wiley, Ferry s Summary of Viscoelastic properties of several classes of polymers Relaxation modulus Figure2-2 from Ferry, Viscoelastic Properties of Polymers, Wiley,

19 Ferry s Summary of Viscoelastic properties of several classes of polymers Loss tangent Figure2-8 from Ferry, Viscoelastic Properties of Polymers, Wiley, Cox-Merz Rule An empirical way to infer steady shear data from SAOS data. * ( ) ( ) Figure 6.32, p. 193 Venkataraman et al.; LDPE 38 19

20 Small-Amplitude Oscillatory Shear - G molecular weight dependence Level of plateau G N related to M e Breadth of plateau depends on MW All materials show terminal behavior When MW is below M c, there is no plateau. Figure 6.34, p. 195 Onogi et al; narrow MWD PS log, / 39 Entanglements form a temporary network M>M c M e crosslinked elastic network constant modulus G at all Entangled polymers over a range of w when unable to disentangle, exhibit a constant modulus 4 2

21 Small-Amplitude Oscillatory Shear - G molecular weight dependence Level of plateau is related to (molecular theory for temporary networks) M c 2M e G M G 4 k 5 T density of effective cross links N B cross links/volume e N mass crosslinks volume mole crosslinks 4 5 volume N AkBT M e N A Larger the MW between entanglements, the softer the network See Larson, The Structure and Rheology of Complex Fluids, Oxford, Small-Amplitude Oscillatory Shear - G molecular weight dependence Breadth of minimum depends on MW; structure is more complex All materials show terminal behavior When MW is below M c, there is no minimum. Figure 6.36, p. 196 Onogi et al; narrow MWD PS log, / 42 21

22 Small-Strain Unsteady Shear Summary: 1. General traits 2. Effect of MW (linear polymers) 3. Effect of architecture 4. Relationship to steady flow material functions 5. Measurement issues 6. Effect of chemical composition 43 Small-Amplitude Oscillatory Shear - G as a function of temperature for copolymers Block copolymers Random copolymers Figure 6.39, p. 198 Cooper and Tobolsky; SIS block and SBS random 44 22

23 Small-Amplitude Oscillatory Shear - temperature dependence J' (cm 2 /dyne) 1.E-5 1.E-6 1.E-7 1.E-8 T ( o C) E-9 1.E , 1, (hz) Figure 6.43, p. 22 Dannhauser et al.; P-OctylMethacrylate 45 Time-Temperature Superposition Material functions depend on g i, l i relaxation times G G(,, g G G(,, g i i i ) i ) relaxation moduli g i, l i are in turn functions of temperature and material properties Theoretical result: in the linear-viscoelastic regime, material functions are a function of wl i rather than of w and l i individually

24 Example: plot a simple function 1 f (, ) sin( ) sin()+ 1.1 sin( ) vs or 1 1 = In general, G G( 1( T), 2( T), 3( T), ) Suppose that the temperature-dependence of l i could be factored out. Let a Ti (T) be the temperature-dependence of l i. ( T) a i Ti ~ ( T) Then we could group the temperature-dependence function with the frequency. i not a function of temperature G G ~, ~, a ~, ( at1 1 at 2 2 T3 3 ) 48 24

25 (for the relaxation mode) Time-Temperature Superposition Relaxation times decrease strongly as temperature increases Moduli associated with relaxations are proportional to absolute temperature; depend on density Empirical observation: for many materials, all the relaxation times and moduli have the same functional dependence on temperature ~ ( T ) a ( T ) i i g ( T ) g~ T( T ) i i T temperature dependence of all relaxation times temperature dependence of all moduli 49 Second theoretical result: the enter into the functions for, such that can be factored out of the function G ~ ~ f ( at, i ) T G ~ ~ h ( at, i ) T Therefore if we plot reduced variables, we can suppress all of the temperature dependence of the moduli. G( T ) Tref ref G r T G ( T ) Tref ref G r T ~ f ( a, ) T T ~ h( a, ) T T i i ref ref ref ref G( T G( T ref ref ) ) Plots of, versus will therefore be independent of temperature. (will still depend on the material through the ) 5 25

26 Small-Amplitude Oscillatory Shear - temperature dependence 1.E-5 1.E-6 J' (cm 2 /dyne) 1.E-7 1.E-8 1.E-9 1.E-1 1.E-7 1.E-5 1.E-3 1.E-1 1.E+1 1.E+3 1.E+5 Figure 6.44, p. 22 Dannhauser et al.; P-OctylMethacrylate a T (hz) 51 Small-Amplitude Oscillatory Shear - temperature dependence experimental WLF a T T ( o C) Figure 6.45, p. 23 Dannhauser et al.; P-OctylMethacrylate 52 26

27 Shift Factors Arrhenius equation a T H exp R 1 T 1 T ref found to be valid for 1 Williams-Landel-Ferry (WLF) equation log a T c c T T 2 1 T T ref ref found to be valid w/in 1 of 53 Shifting other Material Functions Other linear viscoelastic material functions: G( T ) G( T ) G tan G 1/ G J 2 1 tan 1/ G J 1 2 tan 1 G( T ) Tref ref ~ G r f ( at, i ) Tref ref G( Tref ) T G( T ) Tref ref ~ G r h( at, i ) Tref ref G( Tref ) T Independent of temperature 54 27

28 Shifting other Material Functions linear viscoelastic G( T ) Tref r a T G( T ) Tref r a T ref ref T T J( T ) T J r T ref J( T ) T J r T ref ref ref Tref ref a T T Tref ref a T T steady shear ( T) Tref r( at ) a T tan G G T ref = independent of temperature when plotted versus reduced frequency) 55 Steady shear viscosity - Temperature dependence 1 r, Poise 1 1 Poise 1 viscosity (Poise) 3 K viscosity (Poise) 339 K viscosity (Poise) 38 K viscosity (Poise) 425 K.1 a T ,, s Figure 6.46, p. 24 Gruver and Kraus; PB melt /T (K) , a T, s 56 28

29 Another consequence of is the similarity between log and log. 1 1 modulus, Pa G' G'' o G N E E-1 1 1E , rad/s frequency, rad/s T, o C T, o C Figure 6.3, p. 192 Plazek and O Rourke; PS Figure 6.39, p. 198 Cooper and Tobolsky; SIS block and SBS random 57 Take data for G, G at a fixed w for a variety of T. G( T ) Tref G r T G( T ) Tref G r T ref ref ~ f ( a, ) T ~ h( a, ) But since log a T is approximately a linear function of T, T a T i i but, what is a T (T)? We do not know. experimental WLF T ( o C) curves of log G versus T (not log T ) at constant w resemble slightly skewed plots of log G versus log a T w. (mirror image) 58 29

30 Application of SAOS Using G (T) in research on pressure-sensitive adhesives wt% 3 wt% 5 wt% 7 wt% tackifier Figure 6.48, p. 27 Kim et al.; SIS block copolymer with tackifier 59 Entanglements form a temporary network M>M c M e crosslinked elastic network constant modulus G at all w Entangled polymers over a range of w when unable to disentangle, exhibit a constant modulus G N 6 3

31 Small-Amplitude Oscillatory Shear - G molecular weight dependence Level of plateau G N is related to M e (molecular theory for temporary networks) G N 4 5 N AkBT M e Larger the MW between entanglements, the softer the network 61 Using G (T) in research on pressure-sensitive adhesives Shear holding decreasing tack increasing Height of plateau modulus and temperature of glass transition are key performance factors for PSAs. G N Tack if not tacky, will not produce bond Shear holding if too fluid, will slide under shear Figure 6.48, p. 27 Kim et al.; SIS block copolymer with tackifier T g 62 31

32 Small-Strain Unsteady Shear Summary: 1. General traits 2. Effect of MW (linear polymers) 3. Effect of architecture 4. Relationship to steady flow material functions 5. Measurement issues 6. Effect of chemical composition 7. Effect of temperature 63 Experimental Data (continued) Unsteady shear flow Small strain - SAOS, step strain linear polymers, material effects, temperature effects Large strain - start-up, cessation, creep, large-amplitude step strain lastly... Steady elongation Unsteady elongation 64 32

33 Startup of Steady Shearing Ψ Figures 6.49, 6.5, p. 28 Menezes and Graessley, PB soln 65 Cessation of Steady Shearing Ψ Figures 6.51, 6.52, p. 29 Menezes and Graessley, PB soln 66 33

34 Shear Creep J p J ( T ) T T ref ref 21(, t) J ( t, ) Data have been corrected for vertical shift. Figure 6.53, p. 21 Plazek; PS melt 67 Shear Creep - Recoverable Compliance J ( t) R( t) recoverable strain t ( t) t t r ( ) total strain nonrecoverable strain Figures 6.54, 6.55, p. 211 Plazek; PS melt 68 34

35 Step shear strain - strain dependence 1, G(t), Pa 1, 1 1 < Figure 6.57, p. 212 Einaga et al.; PS soln time, s 69 Shear Damping Function Observation: step-strain moduli curves have similar shapes and appear to be shifted down with strain. G( t, ) G( t) h( ) logg( t, ) logg( t) log h( ) The damping function gives the straindependence of the step-strain relaxation modulus. Damping function When G( t, ) ( ) ( ) the G t h This behavior is predicted by behavior is called time-strain some advanced constitutive separable. equations. 7 35

36 Step shear strain - Damping Function 1 damping function, h strain shifted G(t), Pa 1 1 < Figure 6.58, p Einaga et al.; PS soln time, t 71 Large-Strain Unsteady Shear Summary: 1. General traits 2. Measurement issues 72 36

37 Experimental Data (continued) Unsteady shear flow Small strain - SAOS, step strain linear polymers, material effects, temperature effects Large strain - start-up, cessation, creep, large-amplitude step strain lastly... Steady elongation Unsteady elongation 73 Steady State Elongation Viscosity Both tension thinning and thickening are observed. Figure 6.6, p. 215 Munstedt.; PS melt Trouton ratio: Tr 74 37

38 Start-up of Steady Elongation Figure 6.64, p. 218 Kurzbeck et al.; PP Strain-hardening Fit to an advanced constitutive equation (12 mode pom-pom model) Figure 6.63, p. 217 Inkson et al.; LDPE 75 Elongation Step-Strain x3 x1 h(to) R(t) h(t) thin, lubricating layer on each plate R(to) Figures 6.68, 6.69, pp Soskey and Winter; LDPE Relaxation function for step biaxial elongation Damping function for step biaxial elongation 76 38

39 Elongational Flow Summary: 1. General traits 2. Measurement issues 77 More on Material Behavior Polymer Behavior Larson, Ron, The Structure and Rheology of Complex Fluids (Oxford, 1999) Ferry, John, Viscoelastic Properties of Polymers (Wiley, 198) Suspension Behavior Mewis, Jan and Norm Wagner, Colloidal Suspension (Cambridge, 212) Journals Journal of Rheology Rheologica Acta Macromolecules 78 39

40 Done with Experimental Data. Let s move on to Generalized Newtonian Fluids 79 Chapter 7: Generalized Newtonian fluids Carreau- Yassuda Yassuda GNF GNF CM465 Polymer Rheology Michigan Tech log position of break on scale is determined by o curvature here is determined by a slope is determined by n log 8 4