工程材料科学与基础-余永宁-答案

1、Chapter 6 - Problem SolutionsFIND: Compare the structure of a glass to that of the liquid. GIVEN: Both are noncrystalline.SOLUTION: The structure of a glass is essentially that of a frozen liquid. There is SRO but no LRO. Since the glass is at a lower temperature than the liquid of the same composit

2、ion and most materials contrast as they are cooled, the density of the glass is usually less than that of the liquid. The density of the glass is usually considerably greater than that of the crystal, however. Density is mass per unit volume, and the units we see most often are g/3n The most common

3、units of reciprocal density are cn3/g. This is volume per unit mass, or specific volume. It is frequently used by chemical physicists, who study noncrystalline materials.FIND: How does Cp of an amorphous material change as the temperature is increased through the glass transition temperature?SOLUTIO

4、N: Heat capacity is an intensive property, one that does depend on the bulk properties of the material. Most thermodynamic intensive properties behave exactly the same as (molar) volume in the vicinity of the glass transition temperature. Hence, heat capacity changes slope through the Tg.FIND: Estim

5、ate the volume thermal expansion coefficient of a glass. GIVEN: Its linear thermal expansion coefficient in the melt is 10 x 10 oC-1. ASSUMPTIONS: The material behaves typically, so that the thermal expansion coefficient of the glass is about 1/3 of that of the melt. SOLUTION: The linear thermal exp

6、ansion coefficient is th and the volumetric thermal expansion coefficient is v.th(glass)th(melt)/3 and v(glass) 3 th(glass)Hence,v(glass) 3 th(melt) = 10 x 10-6 oC-1FIND: Derive the relationship between th and v:th/ v = 1/3SOLUTION: consider a cube of materials, length 1 on a side. With heat, the ma

7、terials expands isotropically to length 1 + 1. We do the problem first1 d 1 d 1由= dT = dT = 1v 1 dV 1 d( )31 3 2 3V dT 3 dT 3using differentials.1 / 13 TOC o 1-5 h z 11th _t _ 1一 1V = 12- 3vy(3 )2 3Now with deltas: V = ( + )3 = 13 + 3 2 + . V 32 . Therefore, 9. FIND: Is Tg a temperature or range of

8、temperatures?SOLUTION: Although we often cite a glass transition temperature, the glass transition occurs over a range of temperatures.T g is rate sensitive and structure sensitive; it depends on the rate of heating or cooling and on the local structure which is statistically variable in a glass or

9、melt.10.FIND: The temperature range for transitions that involve units smaller than a mer.SKETCH:SOLUTION:In a polymer, the repeat unit is a mer. If the repeat unit gainsmobility, then the entire molecule and all of its parts are mobile. It requires less thermal input, kT, to excite smaller units, s

10、uch as rotation of the ring side group in the polystyrene shown in the figure. Hence, such transition are sub- Tg.COMMENTS: Transitions in the crystalline regions can occur above Tand below Tm.FIND: Design a rubber gasket for use in outer space.GIVEN: Outer space can fluctuate between cold and hot,

11、and the atmosphere depends on the location in space.Solar radiation is very strong in space.ASSUMPTIONS: Well design for space being a vacuum. SOLUTION: Fortunately the seal will probably never see solar radiation, so this is not a design problem. That is fortunate, since flexible materials (polymer

12、s) do not stand up to radiation. (Look at what happens to your skin when you expose it to bright sunshine.) Temperature can also be a problem. High temperatures can soften, melt or degrade polymers. Low temperature can change a rubber to a glass, making a material that is flexible at room temperatur

13、e to brittle at high temperature. Rubber seals that have become glassy may break or leak. Metal seals will decrease in volume as the temperature is decreased. If your choice is a rubber gasket, then it needs to remain flexible at use temperature. Liquid oxygen is very cold and embrittles many materi

14、als.2 / 13FIND: Provide examples of materials that behave like silly putty.GIVEN: Silly putty is used at a temperature that it sometimes behaves in a fluid-like manner and sometimes in a solid-like manner.SOLUTION: There are many such examples, but they are sometimes hard to identify. Consider these

15、 materials:Plumbers puttyRubber mounts for car engines and vibrating machinesRubber bumpersWater. (Consider jumping off a 100 foot cliff into a water-filled quarry)Bullet-proof vest (Textile-like in ordinary use and bullet-proof when necessary)COMMENTS: For a number of applications we need materials

16、 with similar but different properties - a material that flows under low stress but does not flow under its own weight (Bingham plastic). Plumbers putty is an example, but it also shows the characteristics of silly putty.FIND: Is it unique that motor oils do not thin with increasing temperature? SOL

17、UTION: Recall equation 6.3-5b:=o exp (Q/RT).This equation tells you that as temperature increases, viscosity decreases exponentially. If motor oil does not behave this way, then it behaves in an unusual manner.COMMENTS: Motor oil, in fact, does behave in an unusual manner. Its viscosity is essential

18、ly constant with temperature! Let me try to explain how this is accomplished. Oil contains polymer molecules in a solvent. The molecules do not like the solvent all that much, so they tend to ball up or coil somewhat tightly on themselves. As the temperature is increased, the interaction between sol

19、vent and polymer changes. The polymer begins to like the solvent, so it uncoils. The polymer molecules then become entangled in one another, raising the viscosity, which counteracts the normal decrease with increasing temperature.FIND: Whether it is more difficult to obtain a GIVEN: shear strain rat

20、e with a high viscosity fluid or a low viscosity fluid.ASSUMPTIONS: The oils behave in a similar fashion in a stress field. SKETCH:SOLUTION: Newton s Law of Viscosity states that shear stress is proportional to velocity gradient. The constant of proportionality is viscosity:= (dv/dx). Since the velo

21、city gradient is invariant in this problem, the3 / 13shear stress varies with viscosity. The higher viscosity oil will require a larger stress to maintain the plate velocity. Skotch? tape is a polymer film with a thin coating of an oil-like material. It is simply the thinness of the oil film and its

22、 viscosity that prevents slippage between substrate and film. COMMENTS: When a large stress is required to shear a fluid, then much work is lost so that heat is generated in the fluid.FIND: Explain how viscosity changes as a material is crystallized or solidifies as a glass.SOLUTION: Let us first co

23、nsider what occurs when a material like molasses or honey is cooled. As cooling proceeds, the material gets thicker and thicker. Technically, we mean that the viscosity decreases with temperature.Eventually the material is so hard that we say it is frozen. What we mean really is that we are below th

24、e glass transition temperature. Thus, viscosity decreases many orders of magnitude as molasses, or any materials that does not crystallize, is cooled from the fluid-like state to the rock-hard state. Now consider a material that crystallizes, say, water, since we are all familiar with it. As water i

25、s cooled, it changes viscosity very little. At 0 C both water and ice coexist. Below 0 C only ice exists. Thus, the viscosity of H2O changes orders of magnitude at 0C.Unlike materials that do not crystallize, viscosity changes orders of magnitude over a very narrow temperature range - less than a de

26、gree.FIND: Show the atactic and isotactic configurations of PP. Which is more likely to be semicrystalline?GIVEN: The structure of PP is shown in Table 6.4-1. The structure ofatactic and isotactic polymer is shown in Fig. 6.4-5.SKETCH: i-PP has the methyl groups all on the same side. (The H side gro

27、ups are not shown, but each carbon is bonded to 4 atomsYou should mentally visualize all the H atoms.)ccccccccccCH3 rCH3，CH3，CH3，CH3a-PP has the methyl groups appearing randomly on one side or the other.C C C C CC C 二 C 二CH 3 CH 3 CH3 CH? CH3SOLUTION: Since the methyl groups, which are large and bul

28、ky, are all on the same side in i-PP, the molecules can be efficiently packed together (when the molecules are stretched out). Hence, i-PP is semicrystalline. It mechanical properties are generally good up to about the melting temperature, 160. a-PP is noncrystalline, since the molecules cannot be p

29、acked together into a unit cell. Its properties are limited by its glass transition temperature, which is about C.COMMENTS: A-PP is a useless gummy substance. All the PP in use today is i-PP. It is used in huge quantities.4 / 1317. FIND: Show the stereo isomers of PAN.GIVEN: PAN is poly(vinyl cyanid

30、e).5 / 13SKETCH: (H are not shown) isotactic syndiotactic atacticCOMMENTS:Commercially available PAN is atactic.FIND: Which polymer is more likely to be semicrystalline, PVdF (which has 2 Fs) or PVF (a vinyl polymer, which has 1 F)?SOLUTION: Note that the PVdF poly(vinylidene fluoride) is symmetric.

31、 Symmetric molecules are easier to pack than nonsymmetric ones.PVdF is semicrystalline. PVF, like PVC, is noncrystalline.FIND: Estimate the glass transition temperature of PET.GIVEN: Its melting temperature is about 255C = 528K.SOLUTION: The melting temperature of nonsymmetric polymers is about 2/3

32、Tm, when the melting temperature is in absolute degrees.Hence, Tg 2/3 x 528K = 353K = 79 C.COMMENTS: The Tg of PET is up to 40 C higher than 80 C, depending on the specific polymer characteristics.FIND: Calculate the number of mers or degree of polymerization is a sample of PP with a molecular weigh

33、t of 150,000 g/mole.DATA: PP is a vinyl polymer with a methyl side group.SOLUTION: There are 3 C and 6 H per repeat unit MW = 3 x 12 + 6 x 1 =42 g/mer. Hence, number of mers = 150,000 g/mole / 42 g/mole of mers = 3571 mers.COMMENTS: We always ignore chain end groups in these sorts of calculations be

34、cause the effect is negligible.FIND: Calculate the MW of a cellulose mer. If a molecule of cotton has a MW of 9,000 g/mole, how many mers are joined?GIVEN: The structure of cellulose is shown in Fig. 6.4-3a.DATA: According to Appendix A, the atomic weight of C is 12.01, H 1.01, and O 16.00 g/mole.SO

35、LUTION: Count the number of atoms of each type per mer: 10 O, 12 C, and 8 H. Thus, the MW of a mer is 10 x 16 + 12 x 12.01 + 8 x 1.01 = 312.206 / 13 g/mole. A molecule of cotton with a MW of 9,000 g/mole has 9,000 g/mole / 312.2 g/mole 29 mers joined.COMMENTS: This is a typical MW of cotton, 9,000 g

36、/mole. It is formed by joining only about 29 mers.FIND: How will the addition of pentaerythritol affect the crystallinity and glass transition temperature of PET?GIVEN: Pentaerythritol is tetra functional.SOLUTION: Any branching agent will disrupt the ability of the molecules to pack efficiently. He

37、nce, crystallinity or the potential for crystallinity will be reduced. Crosslinking makes molecular motion more difficult, so it raises the glass transition temperature.FIND: How does radiation that cleaves covalent bonds effect crystallinity? SOLUTION: Order must be perfect or near perfect in order

38、 to have a crystal.Cleaving bonds in crystals destroys the balance of order. Some bonds are broken, creating a difference in the bond arrangement than exists in the virgin crystal.COMMENTS:Organic molecules form crystals readily under appropriateconditions, but the structure of the crystal and the u

39、nit cell parameters do not resemble those of similar polymers.FIND: Does the fact that PP, crystallized under quiescent conditions, is characterized by Maltese cross patterned spherulites that fill the entire sample imply 100% crystallinity?SOLUTION: Spherulites are aggregates of crystalline and non

40、crystalline material. Thus, a completely spherulitic sample is semicrystalline.FIND: Explain why amorphous PET that is hot stretched becomes opaque and slowly cold drawn amorphous PET may remain transparent. DATA: The glass transition temperature of PET is about 10C.SOLUTION: Stretching a limited ex

41、tent at room temperature does not induce crystallization in PET, whereas stretching above gTand orienting the more mobile molecules into a position similar to those occupied by the molecules in a crystal likely induces crystallization.COMMENTS:In making a very strong PET fiber it is necessary to ori

42、entthe molecules at first without inducing crystallization. Subsequent drawing steps are typically carried out at progressively higher temperatures.FIND: How many O are in a mer of cellulose?GIVEN: The structure of cellulose is shown in Fig. 6.4-3a.SOLUTION: Count the O: There are 2 in the ether pos

43、itions, connecting the rings; there are 3 as OH groups on each of the 2 rings; and there is one as part of each of the 2 rings. Add them up: 2 + 2 x 3 + 1 x 2 = 10 O per mer. COMMENTS: They are extremely important in providing cellulose its properties!7 / 13FIND: Why are CaO and N边O added to Si% in

44、most applications for silicate glasses?SOLUTION: According to Table 6.5-1, neither CaO nor N空O are glass forming systems. Rather, they are network modifiers, as stated in Table 6.5-2. They loosen the silicate network, lowering the glass transition temperature significantly.Thus, they are added to si

45、lica to reduce the cost of raw materials and, more importantly, the cost of processing.COMMENTS: The Tg of silica in on the order of 1000 C and that of sodalime -silicate can be on the order of 500C.FIND: Is lead oxide a good glass former?29.SOLUTION: Zachariasen s rules state that the metal should

46、have a coordination number of 3 or 4. The valence of lead is such the PbO is the oxide predicted. Hence, PbO is not a good glass former. It is an intermediate.FIND: Are epoxies and thermoset polyesters semicrystalline or noncrystalline?GIVEN: Both are highly crosslinked, transparent, hard and brittl

47、e.SOLUTION: Highly crosslinked polymers are always noncrystalline andbelow Tg at room temperature.They are glasses. The crosslinks preventcrystallization.COMMENTS: On of the problems with some composite matrices is that they are brittle and not tough. Thermoplastic matrices are being developed for v

48、arious demanding applications. High molecular weight thermoplastics, which are semicrystalline polymers, have high viscosity. It is difficult to get them to flow into the spaces between fibers.FIND: How can you detect when a glassy metal crystallizes?SOLUTION: Heat is released when crystallization o

49、ccurs. If the metal were like a coin in your pocket, it might burn you. Use a calorimeter to quantify the effect. X-ray diffraction will also show when crystallization occurs. The density or specific volume of the material changes with crystallization.COMMENTS: Many other techniques can also be used

50、 to detect crystallization.FIND: Will mixtures, actually solutions, of PbO and SiO2 be good glass formers?GIVEN:SiO2 is a good glass former; PbO is not.SOLUTION: Since they form a solution, we expect the solution, which is even more complex than either component, to be even slower to crystallize. Th

51、us, PbO-SiO2 mixtures should be excellent glass formers so long as the PbO content is not high.FIND: Explain the role of B and Si in Metglas?.GIVEN: Metglas? is an iron based amorphous metal alloy.8 / 13SOLUTION: The additives hinder crystallization, by increasing the viscosity of the melt, thereby

52、reducing the diffusion coefficient, and by increasing the size of the unit cell, thereby making it necessary for atoms to move farther to their crystallographic positions.34.FIND: How does modulus change as molecules are aligned along a fibers axis? GIVEN: A single molecule is bonded by covalent for

53、ces. A collection of molecules is boned by both primary and weaker secondary bonds.In a fiber with all molecules aligned along the fiber axis, forces are transmitted along covalent bonds only.SKETCH:Modulus Molecular Misalignment along Fiber AxisSOLUTION: The figure can best be read by beginning a l

54、arge values on the abscissa. As the alignment increases, the modulus increases.With near zero misalignment, the molecules are packed together in a parallel fashion and stresses are carried by covalent bonds. The fiber requires a large stress to achieve significant deformation.COMMENTS: Pound for pou

55、nd, organic fibers with this morphology have better mechanical properties than do metals.FIND: What polymer would you select for use as a flexible gasket on a liquid nitrogen tank?GIVEN: Liquid nitrogen boils at a very low temperature.SOLUTION: You need a material that remains flexible even down to

56、liquid nitrogen temperatures and one that does not react with nitrogen.Some silicone rubbers (thermoset elastomers) are currently used for this application.FIND: Why is the modulus of Spectra PE roughly 30 times greater than that of sandwich bag PE?GIVEN: Both are PE.SOLUTION: The difference is modu

57、lus is chiefly a result of the very high molecular orientation in Spectra PE fiber and virtually no molecular orientation in sandwich bag PE.FIND: Predict interesting properties of poly(dimethyl siloxane).9 / 13SKETCH:SOLUTION: The polymer contain no carbon in the backbone. It is inorganic. The meth

58、yl side groups preclude crystallization, so the material is amorphous. The molecule is symmetric and its Tg is well below room temperature. Hence, it is a rubber. Lightly crosslinked, it has excellent elastomeric properties. Because of its chemistry, it is chemically inert in most environments, as w

59、ell as stable to moderate temperatures.COMMENTS: A low grade of the materials is sold as RTV silicone rubber.FIND: Calculate the end-to-end separation of PS molecules. GIVEN: The DP is 5000DATA: 1 = 1.54ASKETCH:SOLUTION: We use equation 6.6-2: L = m12(1 + cos )? to approximate the end-to-end separat

60、ion. There are 2 bonds, each 1 = 1.54A per mer. The backbone is all carbon, so the factor (1 +cos)/(1-cos ) is 2. Substituting gives:L = 2 x 5000 x 1.542 x 21/2 = 218ACOMMENTS: This is a lower bound, largely because of the terms neglected in equation 6.6-2. A more sophisticated calculation shows the