What happens to Tg with increasing pressure?

1. What happens to Tg with increasing pressure?

2. Bar = 1 atm = 100 kPa Why?

3. A Demonstration of Polymer Viscoelasticity Poly(ethylene oxide) in water

4. “Memory” of Previous State Poly(styrene) Tg ~ 100 °C

5. Chapter 5. Viscoelasticity Is “silly putty” a solid or a liquid? Why do some injection molded parts warp? What is the source of the die swell phenomena that is often observed in extrusion processing? Expansion of a jet of an 8 wt% solution of polyisobutylene in decalin Under what circumstances am I justified in ignoring viscoelastic effects?

6. What is Rheology? Rheology is the science of flow and deformation of matter Rheology Concepts, Methods, & Applications, A.Y. Malkin and A.I. Isayev; ChemTec Publishing, 2006

8. Temperature & Strain Rate

10. Time dependent processes: Viscoelasticity The response of polymeric liquids, such as melts and solutions, to an imposed stress may resemble the behavior of a solid or a liquid, depending on the situation.

12. increasing loading rate Stress Strain

13. Network of Entanglements There is a direct analogy between chemical crosslinks in rubbers and “physical” crosslinks that are created by the entanglements. The physical entanglements can support stress (for short periods up to a time tT), creating a “transient” network.

14. Entanglement Molecular Weights, Me, for Various Polymers Me (g/mole) Poly(ethylene) 1,250 Poly(butadiene) 1,700 Poly(vinyl acetate) 6,900 Poly(dimethyl siloxane) 8,100 Poly(styrene) 19,000

15. Pitch drop experiment • Started in 1927 by University of Queensland Professor Thomas Parnell. • A drop of pitch falls every 9 years Pitch drop experiment apparatus Pitch can be shattered by a hammer

16. ? Viscoelasticity and Stress Relaxation Whereas steady-shear measurements probe material responses under a steady-state condition, creep and stress relaxation monitor material responses as a function of time. • Stress relaxation studies the effect of a step-change in strain on stress.

17. g Constant strain applied s Stress relaxes over time as molecules re-arrange time Stress relaxation: Physical Meaning of the Relaxation Time time

18. Introduction to Viscoelasticity All viscous liquids deform continuously under the influence of an applied stress – They exhibit viscous behavior. Solids deform under an applied stress, but soon reach a position of equilibrium, in which further deformation ceases. If the stress is removed they recover their original shape – They exhibit elastic behavior. Viscoelastic fluids can exhibit both viscosity and elasticity, depending on the conditions. Viscous fluid Polymers display VISCOELASTIC properties Viscoelastic fluid Elastic solid

19. Static Testing of Rubber Vulcanizates • Static tensile tests measure retractive stress at a constant elongation (strain) rate. • Both strain rate and temperature influence the result Note that at common static test conditions, vulcanized elastomers store energy efficiently, with little loss of inputted energy.

20. Dynamic Testing of Rubber Vulcanizates: Resilience Resilience tests reflect the ability of an elastomeric compound to store and return energy at a given frequency and temperature. • Change of rebound • resilience (h/ho) with • temperature T for: • 1. cis-poly(isoprene); • 2. poly(isobutylene); • 3. poly(chloroprene); • 4. poly(methyl methacrylate).

21. Hooke and Newton • It is difficult to predict the creep and stress relaxation for polymeric materials. • It is easier to predict the behaviour of polymeric materials with the assumption  it behaves as linear viscoelastic behaviour. • Deformation of polymeric materials can be divided to two components: • Elastic component – Hooke’s law • Viscous component – Newton’s law • Deformation of polymeric materials  combination of Hooke’s law and Newton’s law.

22. Hooke’s law & Newton’s Law • The behaviour of linear elastic were given by Hooke’s law: or • The behaviour of linear viscous were given by Newton’s Law: E= Elastic modulus s= Stress e =strain de/dt = strain rate ds/dt = stress rate = viscosity ** This equation only applicable at low strain

23. Viscoelasticity and Stress Relaxation Stress relaxation can be measured by shearing the polymer melt in a viscometer (for example cone-and-plate or parallel plate). If the rotation is suddenly stopped, ie. g=0, the measured stress will not fall to zero instantaneously, but will decay in an exponential manner. . Relaxation is slower for Polymer B than for Polymer A, as a result of greater elasticity. These differences may arise from polymer microstructure (molecular weight, branching).

24. STRESS RELAXATION CREEP Constant strain is applied  the stress relaxes as function of time Constant stress is applied  the strain relaxes as function of time

25. Time-dependent behavior of Polymers The response of polymeric liquids, such as melts and solutions, to an imposed stress may under certain conditions resemble the behavior of a solid or a liquid, depending on the situation. Reiner used the biblical expression that “mountains flowed in front of God” to define the DEBORAH number

26. metal elastomer Viscous liquid

27. Glassy Leathery Rubbery Viscous Static Modulus of Amorphous PS Polystyrene Stress applied at x and removed at y

28. Stress Relaxation Test Strain Elastic Viscoelastic Stress Stress Stress Viscous fluid Viscous fluid Viscous fluid 0 Time, t

29. Stress relaxation Stress relaxation after a step strain go is the fundamental way in which we define the relaxation modulus: • Go (or GNo) is the “plateau modulus”: where Me is the average mol. weight between entanglements • G(t) is defined for shear flow. We can also define a relaxation modulus for extension:

30. Glassy behavior Transition Zone Plateau Zone Terminal Zone (flow region) slope = -1 perse Stress relaxation of an uncrosslinked melt Mc: critical molecular weight above which entanglements exist 3.24

32. Network of Entanglements There is a direct analogy between chemical crosslinks in rubbers and “physical” crosslinks that are created by the entanglements. The physical entanglements can support stress (for short periods up to a time tT), creating a “transient” network.

33. Relaxation Modulus for Polymer Melts tT Elastic tT= terminal relaxation time Viscous flow

34. Viscosity of Polymer Melts ho Extrapolation to low shear rates gives us a value of the “zero-shear-rate viscosity”, ho. Shear thinning behaviour Poly(butylene terephthalate) at 285 ºC For comparison: h for water is 10-3 Pa s at room temperature.

35. Slope = 3.4 o Entanglement molecular weight Slope = 1 Mn Rheology and Entanglements. The elastic properties of linear thermo-plastic polymers are due to chain entanglements. Entanglements will only occur above a critical molecular weight. When plotting melt viscosity o against molecular weight we see a change of slope from 1 to 3.45 at the critical entanglement molecular weight.

36. Scaling of Viscosity: ho ~ N3.4 Viscosity is shear-strain rate dependent. Usually measure in the limit of a low shear rate: ho 3.4 Data shifted for clarity! h ~ tTGP ho ~ N3.4N0 ~ N3.4 Universal behaviour for linear polymer melts Applies for higher N: N>NC Why? G.Strobl, The Physics of Polymers, p. 221

38. Application of Theory: Electrophoresis From Giant Molecules

40. Mechanical Model • Methods that used to predict the behaviour of visco-elasticity. • They consist of a combination of between elastic behaviour and viscous behaviour. • Two basic elements that been used in this model: • Elastic spring with modulus which follows Hooke’s law • Viscous dashpots with viscosity h which follows Newton’s law. • The models are used to explain the phenomena creep and stress relaxation of polymers involved with different combination of this two basic elements.

41. Dynamic Viscosity (dashpot) Shear stress • Lack of slipperiness • Resistance to flow • Interlayer friction SI Unit: Pascal-second Shear rate 1 centi-Poise = milli Pascal-second

42. stress stress input Strain in dashpot dashpot

43. Maxwell model • In series • Viscous strain remains after load removal. stress input Model Strain Response Maxwell model

44. Kelvin or Voigt model • In parallel • Nonlinear increase in strain with time • Strain decreases with time after load removal because of the action of the spring (and dashpot). stress input Model Strain Response Voigt model

45. Asphalt Binder --------------- Polymer Melt ----------------- Molasses ---------------------- Liquid Honey ----------------- Glycerol ----------------------- Olive Oil ----------------------- Water -------------------------- Acetic Acid -------------------- 100,000 1,000 100 10 1 0.01 0.001 0.00001 Typical Viscosities (Pa.s) Courtesy: TA Instruments

46. Casson Plastic Bingham Plastic Pseudoplastic (or Shear thinning) Newtonian Dilatant (or Shear thickening) Shear stress Non Newtonian Fluids Shear rate

47. The Theory of Viscoelasticity The liquid behavior can be simply represented by the Newtonian model. We can represent the Newtonian behavior by using a “dashpot” mechanical analog: The simplest elastic solid model is the Hookean model, which we can represent by the “spring” mechanical analog. stress strain viscosity Gmodulus

48. Maxwell Model Let’s create a VISCOELASTIC material: At least two components are needed, one to characterize elastic and the other viscous behavior. One such model is the Maxwell model: stress strain viscosity Gmodulus

49. Maxwell Model Let’s try to deform the Maxwell element stress strain viscosity Gmodulus

50. Maxwell: solid line Experiment: circles Maxwell model too primitive