Chapter 8

1. Chapter 8 Flow and mechanical properties of polymers chapter 8

2. Concepts, coefficients, definitions • Fluid shear: the shear stress on a fluid element is related to the viscosity gradient by • Volume change on deformation: some fluids (constant density under shear) and solids (cross-linked elastomers) deform isochorically. Poisson’s ratio, 0 < n < 0.5. • Modulus of elasticity (Young’s modulus). The strain in a solid is related to the load by the modulus of elasticity. chapter 8

3. Concepts, coefficients, definitions, cont’d. • Shear modulus: the shear stress of a solid is related to the strain by • The elastic and shear moduli are related using the bulk modulus (measures how the solid volume changes with pressure) and Poisson’s ratio. When Poisson’s ratio = 0.5 (perfect elasticity), the tensile modulus is three times the shear modulus. • Compliance: the inverse of the elastic modulus. chapter 8

4. Concepts, coefficients, definitions, cont’d. • Dynamic measurements of solids and fluids yield two coefficients (Young’s modulus used as the example) • The dynamic modulus contains a storage (or elastic) component and a loss (or damping) component chapter 8

5. Rheology chapter 8

6. Fluid element under simple shear Newtonian fluid: the coefficient linking shear stress to shear rate is constant over the entire range of the variable. Molecular relaxations are much faster than the time scale of the shear force or shear rate. Steady flows – velocity profile is constant; oscillating flows – fluid responds instantly to forcing function. chapter 8

7. Defining relationship chapter 8

8. Non-Newtonian fluid Viscosity changes with shear rate. Apparent viscosity is always defined by the relationship between shear stress and shear rate. Many polymeric fluids are shear-thinning, i.e., their viscosities decrease with shear rate or shear stress. chapter 8

9. Generalized Oswald fluid Pseudoplastic: shear thinning. Shear thickening: viscosity increases with shear stress. Dilatant: shear thickening fluids that contain suspended solids. Solids can become close packed under shear. Time-dependent: in many polymeric fluids, the response time of the material may be longer than response time of the measurement system, so the viscosity will change with time. Thixotropic: shear thinning with time; antithixotropic: shear thickening with time. Rheopectic: thixotropic materials that can recover original viscosity under low shear. chapter 8

10. Generalized Oswald fluid • Shear rate vs. shear stress with high and low stress limits on viscosity • Viscosity vs. shear rate. Zero shear rate, m0, and infinite shear rate, m∞, viscosities. • Pseudoplastic: shear thinning. • Shear thickening: viscosity increases with shear stress. • Dilatant: shear thickening fluids that contain suspended solids chapter 8

11. Pseudoplastics Flow of pseudoplastics is consistent with the random coil model of polymer solutions and melts. At low stress, flow occurs by random coils moving past each other w/o coil deformation. At moderate stress, the coils are deformed and slip past each other more easily. At high stress, the coils are distorted as much as possible and offer low resistance to flow. Entanglements between chains and the reptation model also are consistent with the observed viscosity changes. chapter 8

12. Viscometers In order to get meaningful (universal) values for the viscosity, we need to use geometries that give the viscosity as a scalar invariant of the shear stress or shear rate. Generalized Newtonian models are good for these steady flows: tubular, axial annular, tangential annular, helical annular, parallel plates, rotating disks and cone-and-plate flows. Capillary, Couette and cone-and-plate viscometers are common. chapter 8

13. Power law parameters chapter 8

14. chapter 8

15. Ballpoint pen ink László Bíró, a Hungarian newspaper editor, was frustrated by the amount of time that he wasted in filling up fountain pens and cleaning up smudged pages, and the sharp tip of his fountain pen often tore the paper. Bíró had noticed that inks used in newspaper printing dried quickly, leaving the paper dry and smudge free. He decided to create a pen using the same type of ink. Since, when tried, this viscous ink would not flow into a regular fountain pen nib, Bíró, with the help of his brother George, a chemist, began to work on designing new types of pens. Bíró fitted this pen with a tiny ball in its tip that was free to turn in a socket. As the pen moved along the paper, the ball rotated, picking up ink from the ink cartridge and leaving it on the paper. Bíró filed a British patent on 15 June 1938.[5] Earlier pens leaked or clogged because of incorrect viscosity of the ink, and depended on gravity to deliver the ink to the ball. Depending on gravity caused difficulties with the flow and required that the pen be held nearly vertically. The original Biro pen used capillary action and a piston that pressurised the ink column, solving the ink delivery flow problems. Later Biro pens had a spring that kept pressure on the piston, and still later the Biro pens used just gravity and capillary action.[6] chapter 8

16. Disposable pens are chiefly made of plastic throughout and discarded when the ink is consumed; refillable pens are metal and some plastic and tend to be much higher in price. The refill replaces the entire internal ink reservoir and ball point unit rather than actually refilling it with ink, as it takes special high-speed centrifugation to properly fill a ball point reservoir with the viscous ink. The simplest types of ball point pens have a cap to cover the tip when the pen is not in use, while others have a mechanism for retracting the tip. This mechanism is usually controlled by a button at the top and powered by a spring within the pen body, but other possibilities include a pair of buttons, a screw, or a slide. Rollerball pens combine the ballpoint design with the use of liquid ink and flow systems from fountain pens; Space Pens, developed by Fisher in the United States, combine a more than normally viscous ballpoint pen ink with a gas-pressured piston which forces the ink toward the point. This design allows the pen to write even upside down or in zero gravity environments.[8] A graphite pencil can also be used in this way but produces graphite dust, requires sharpening, and is erasable, making it undesirable or unsuitable for use in some situations. chapter 8

17. The earliest fabric softeners were developed during early 20th century to counteract the harsh feel which the drying methods imparted to cotton. The cotton softeners were typically based on water emulsion of soap and olive oil, corn oil, or tallow oil. Contemporary fabric softeners tend to be based on quaternary ammonium salts with one or two long alkyl chains, a typical compound being dipalmitoylethyl hydroxyethylmonium methosulfate.[3] Other cationic compounds can be derived from imidazolium, substituted amine salts, or quaternary alkoxy ammonium salts. One of the most common compounds of the early formulations was dihydrogenated tallow dimethyl ammonium chloride (DHTDMAC). Anionic softeners and antistatic agents can be, for example, salts of monoesters and diesters of phosphoric acid and the fatty alcohols. These are often used together with the conventional cationic softeners. Cationic softeners are incompatible with anionic surfactants used in the bulk of surfactants used in detergents, with which they form a solid precipitate. Therefore, they have to be added during the rinse cycle instead. Anionic softeners can be combined with anionic surfactants directly. Other anionic softeners can be based on smectite clays. Some compounds, such as ethoxylated phosphate esters, have softening, anti-static, and surfactant properties.[4] chapter 8

18. The softening compounds differ in affinity to different materials. Some are better for cellulose-based fibers, others have higher affinity to hydrophobic materials like nylon, polyethylene terephthalate, polyacrylonitrile, etc. Silicone-based compounds such as polydimethylsiloxane comprise the new softeners which work by lubricating the fibers. Derivatives with amine- or amide-containing functional groups are used as well. These groups help the softeners bind better to fabrics. As the softeners themselves are often of hydrophobic nature, they are commonly occurring in the form of an emulsion. In the early formulations, soaps were used as emulsifiers. The emulsions are usually opaque, milky fluids. However there are also microemulsions where the droplets of the hydrophobic phase are substantially smaller[not specific enough to verify]. The advantage of microemulsions is in the increased ability of the smaller particles to penetrate into the fibers. A mixture of cationic and non-ionic surfactants is often used as an emulsifier. Another approach is using a polymeric network, an emulsion polymer. Other compounds are included to provide additional functions; acids or bases for maintaining the optimal pH for adsorption to the fabric, electrolytes, carriers (usually water, sometimes water-alcohol mixture), and others, eg. silicone-based anti-foaming agents, emulsion stabilizers, fragrances, and colors.[5] A relatively recent form on the market are the ultra-concentrates, where the amount of carriers and some other chemicals is substantially lower and much smaller volumes are used. In recent years, the importance of delivering perfume onto the clothes has possibly exceeded that of softening.[citation needed] The perfume levels in fabric softeners has gradually increased, requiring high-shear mixing technology to be used to incorporate greater amounts of perfumes within the emulsions. Long term release of perfume on the fabric is a key technology now being utilized. Each country tends to have different perfume requirements and brands may have different softener/perfume ratio depending on the country. chapter 8

19. Molten chocolate Follows Bingham plastic behavior chapter 8

20. Non-Newtonian fluids chapter 8

21. applications • Dilatant: all wheel drive systems with viscous coupling unit for power transmission • Pseudoplastic: paint flows readily off the brush but should not drip excessively • Bingham plastic: finite yield stress before flow; drilling mud, toothpaste, mayonnaise, chocolate, mustard; at rest, these fluid surfaces can hold peaks • Rheopectic: chapter 8

22. Home video assignments Oobleck • An inexpensive, non-toxic example of a non-Newtonian fluid is a suspension of starch (e.g. cornstarch) in water, sometimes called "oobleck" or "ooze" (1 part of water to 1.5–2 parts of corn starch).[7][8] Uncooked imitation custard, being a suspension of primarily cornflour, has the same properties. The name "oobleck" is derived from the children's book Bartholomew and the Oobleck. Flubber • Flubber is a non-Newtonian fluid, easily made from polyvinyl alcohol based glues and borax, that flows under low stresses, but breaks under higher stresses and pressures. This combination of fluid-like and solid-like properties makes it a Maxwell solid. Its behaviour can also be described as being viscoplastic or gelatinous.[9] chapter 8

23. Chilled caramel topping • Another example of this is chilled caramel ice cream topping. The sudden application of force—for example by stabbing the surface with a finger, or rapidly inverting the container holding it—leads to the fluid behaving like a solid rather than a liquid. This is the "shear thickening" property of this non-Newtonian fluid. More gentle treatment, such as slowly inserting a spoon, will leave it in its liquid state. Trying to jerk the spoon back out again, however, will trigger the return of the temporary solid state. A person moving quickly and applying sufficient force with their feet can literally walk across such a liquid. chapter 8

24. Silly Putty • Silly Putty is a silicone polymer based suspension which will flow, bounce, or break depending on strain rate. Ketchup • Ketchup is a shear thinning fluid.[3] Shear thinning means that the fluid viscosity decreases with increasing shear stress. In other words, fluid motion is initially difficult at slow rates of deformation, but will flow more freely at high rates. chapter 8

25. chapter 8

26. assignments chapter 8

27. chapter 8

28. Generalized Newtonian models Power law model Ellis model chapter 8

29. Example 8.2 chapter 8

30. Dependence of viscosity on molecular weight Branched polymers have different rheology. Melt viscosities of LMW materials are lower than those of linear polymers because the volume occupied by a branch unit is smaller than that of a chain element. Melt viscosities of high molecular weight materials have the reverse trend. Branched polymers have a higher zero shear viscosity. Usually, linear polymers are preferred for processing. chapter 8

31. Effects of variables on polymer viscosity The Arrhenius equation can be used to scale the viscosity. This can be applied to constant shear rate or constant shear stress values over moderate ranges of temperature. Plasticizers tend to reduce melt viscosities while fillers tend to increase melt viscosity. chapter 8

32. Molecular weight effects For M < Mc; m = k * M For M > Mc; m = k * M3.4 The critical molecular weight is the point at which molecular entanglements restrict the movement of polymer molecules relative to each other. chapter 8

33. Free volume model chapter 8

34. Shift factors chapter 8

35. Modulus vs. t chapter 8

36. Failure pressure scaled with t, T chapter 8

37. Extensional flow geometry chapter 8

38. Normal stress chapter 8

39. Elongational, extensional, shear-free flows chapter 8

40. Sheet die chapter 8

41. Elastic State chapter 8

42. Unique conditions of polymer elasticity • Elastomers are used above Tg; the temperature range for elastic performance increases with molecular weight • At low stress, there is no visible elongation of the elastomer • Crystallization can occur in the stretched state, and increases the tensile strength • Deformation of elastomers (noncrystalline segments) stores energy in changed conformations (entropic), meaning that the modulus increases with temperature chapter 8

43. Volume vs. P and T • Total derivative of volume • Fractional volume change • Term for temperature derivative is the volume expansivity, b, and that for the pressure derivative is the isothermal compressibility, k. These coefficients are relatively independent of temperature and pressure for moderate ranges. chapter 8

44. elongation vs. T & F • Total derivative of length • Fractional length change • Term for temperature derivative is linear expansivity, a, and that for the force derivative is the Young’s modulus, E. • The fractional change in length is: • This is a mechanical equation of state for elastomers chapter 8

45. In-class exercise • A butyl rubber part is being used to suspend a motor. As the motor is used, the temperature of the part increases by 25 C. Estimate the change in force exerted by the butyl rubber mount when this occurs. chapter 8

46. In-class exercise: solution • A butyl rubber part is being used to suspend a motor. As the motor is used, the temperature of the part increases by 25 C. Estimate the change in force exerted by the butyl rubber mount when this occurs. Suppose that the elongation does not change so e ~ 0. chapter 8

47. Mechanical performance chapter 8

48. Tensile test • A0 – initial cross-sectional area • L0 – initial length • F – force, L – length, A – cross-sectional area • Elastic deformation, a constant volume process for small deformations • seng = engineering stress = load/initial area • eeng = engineering strain = length change/initial length chapter 8

49. Definition of yield Test equipment has some “slack” in it. chapter 8

50. Additional definitions • True stress and strain • At high strains, many polymers crystallize so that DV is not zero and this analysis is not correct • True stress and true strain are always larger than the engineering values • When the volume is constant on strain: chapter 8