工程材料科学与基础余永宁答案.docx
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工程材料科学与基础余永宁答案.docx
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工程材料科学与基础余永宁答案
Chapter6-ProblemSolutions
1.FIND:
Comparethestructureofaglasstothatoftheliquid.
GIVEN:
Botharenoncrystalline.
SOLUTION:
Thestructureofaglassisessentiallythatofafrozenliquid.ThereisSRObutnoLRO.Sincetheglassisatalowertemperaturethantheliquidofthesamecompositionandmostmaterialscontrastastheyarecooled,thedensityoftheglassisusuallylessthanthatoftheliquid.Thedensityoftheglassisusuallyconsiderablygreaterthanthatofthecrystal,however.Densityismassperunitvolume,andtheunitsweseemostoftenareg/cm3.Themostcommonunitsofreciprocaldensityarecm3/g.Thisisvolumeperunitmass,orspecificvolume.Itisfrequentlyusedbychemicalphysicists,whostudynoncrystallinematerials.
2.
3.FIND:
HowdoesCpofanamorphousmaterialchangeasthetemperatureisincreasedthroughtheglasstransitiontemperature?
SOLUTION:
Heatcapacityisanintensiveproperty,onethatdoesdependonthebulkpropertiesofthematerial.Mostthermodynamicintensivepropertiesbehaveexactlythesameas(molar)volumeinthevicinityoftheglasstransitiontemperature.Hence,heatcapacitychangesslopethroughtheTg.
4.
5.FIND:
Estimatethevolumethermalexpansioncoefficientofaglass.
GIVEN:
Itslinearthermalexpansioncoefficientinthemeltis10x10-6oC-1.
ASSUMPTIONS:
Thematerialbehavestypically,sothatthethermalexpansioncoefficientoftheglassisabout1/3ofthatofthemelt.
SOLUTION:
Thelinearthermalexpansioncoefficientisαthandthevolumetricthermalexpansioncoefficientisαv.
αth(glass)≈αth(melt)/3andαv(glass)≈3αth(glass)
Hence,
αv(glass)≈3αth(melt)=10x10-6oC-1
6.FIND:
Derivetherelationshipbetweenαthandαv:
αth/αv=1/3
SOLUTION:
consideracubeofmaterials,length1onaside.Withheat,thematerialsexpandsisotropicallytolength1+δ1.Wedotheproblemfirstusingdifferentials.
Nowwithdeltas:
V=(ι+δι)3=13+3ι2δι+...⇒∆V≈3ι2δι.Therefore,
9.FIND:
IsTgatemperatureorrangeoftemperatures?
SOLUTION:
Althoughweoftenciteaglasstransitiontemperature,theglasstransitionoccursoverarangeoftemperatures.Tgisratesensitiveandstructuresensitive;itdependsontherateofheatingorcoolingandonthelocalstructurewhichisstatisticallyvariableinaglassormelt.
10.FIND:
Thetemperaturerangefortransitionsthatinvolveunitssmallerthanamer.
SKETCH:
SOLUTION:
Inapolymer,therepeatunitisamer.Iftherepeatunitgainsmobility,thentheentiremoleculeandallofitspartsaremobile.Itrequireslessthermalinput,kT,toexcitesmallerunits,suchasrotationoftheringsidegroupinthepolystyreneshowninthefigure.Hence,suchtransitionaresub-Tg.
COMMENTS:
TransitionsinthecrystallineregionscanoccuraboveTgandbelowTm.
11.FIND:
Designarubbergasketforuseinouterspace.
GIVEN:
Outerspacecanfluctuatebetweencoldandhot,andtheatmospheredependsonthelocationinspace.Solarradiationisverystronginspace.
ASSUMPTIONS:
We'lldesignforspacebeingavacuum.
SOLUTION:
Fortunatelythesealwillprobablyneverseesolarradiation,sothisisnotadesignproblem.Thatisfortunate,sinceflexiblematerials(polymers)donotstanduptoradiation.(Lookatwhathappenstoyourskinwhenyouexposeittobrightsunshine.)Temperaturecanalsobeaproblem.Hightemperaturescansoften,meltordegradepolymers.Lowtemperaturecanchangearubbertoaglass,makingamaterialthatisflexibleatroomtemperaturetobrittleathightemperature.Rubbersealsthathavebecomeglassymaybreakorleak.Metalsealswilldecreaseinvolumeasthetemperatureisdecreased.Ifyourchoiceisarubbergasket,thenitneedstoremainflexibleatusetemperature.Liquidoxygenisverycoldandembrittlesmanymaterials.
12.FIND:
Provideexamplesofmaterialsthatbehavelikesillyputty.
GIVEN:
Sillyputtyisusedatatemperaturethatitsometimesbehavesinafluid-likemannerandsometimesinasolid-likemanner.
SOLUTION:
Therearemanysuchexamples,buttheyaresometimeshardtoidentify.Considerthesematerials:
1.Plumbersputty
2.Rubbermountsforcarenginesandvibratingmachines
3.Rubberbumpers
4.Water.(Considerjumpingoffa100footcliffintoawater-filledquarry)
5.Bullet-proofvest(Textile-likeinordinaryuseandbullet-proofwhennecessary)
COMMENTS:
Foranumberofapplicationsweneedmaterialswithsimilarbutdifferentproperties-amaterialthatflowsunderlowstressbutdoesnotflowunderitsownweight(Binghamplastic).Plumbersputtyisanexample,butitalsoshowsthecharacteristicsofsillyputty.
13.FIND:
Isituniquethatmotoroilsdonotthinwithincreasingtemperature?
SOLUTION:
Recallequation6.3-5b:
=oexp(Q/RT).
Thisequationtellsyouthatastemperatureincreases,viscositydecreasesexponentially.Ifmotoroildoesnotbehavethisway,thenitbehavesinanunusualmanner.
COMMENTS:
Motoroil,infact,doesbehaveinanunusualmanner.It'sviscosityisessentiallyconstantwithtemperature!
Letmetrytoexplainhowthisisaccomplished.Oilcontainspolymermoleculesinasolvent.Themoleculesdonotlikethesolventallthatmuch,sotheytendtoballuporcoilsomewhattightlyonthemselves.Asthetemperatureisincreased,theinteractionbetweensolventandpolymerchanges.Thepolymerbeginstolikethesolvent,soituncoils.Thepolymermoleculesthenbecomeentangledinoneanother,raisingtheviscosity,whichcounteractsthenormaldecreasewithincreasingtemperature.
14.FIND:
WhetheritismoredifficulttoobtainaGIVEN:
shearstrainratewithahighviscosityfluidoralowviscosityfluid.
ASSUMPTIONS:
Theoilsbehaveinasimilarfashioninastressfield.
SKETCH:
SOLUTION:
Newton’sLawofViscositystatesthatshearstressisproportionaltovelocitygradient.Theconstantofproportionalityisviscosity:
τ=η(dv/dx).Sincethevelocitygradientisinvariantinthisproblem,theshearstressvarieswithviscosity.Thehigherviscosityoilwillrequirealargerstresstomaintaintheplatevelocity.Skotch®tapeisapolymerfilmwithathincoatingofanoil-likematerial.Itissimplythethinnessoftheoilfilmanditsviscositythatpreventsslippagebetweensubstrateandfilm.
COMMENTS:
Whenalargestressisrequiredtoshearafluid,thenmuchworkislostsothatheatisgeneratedinthefluid.
15.FIND:
Explainhowviscositychangesasamaterialiscrystallizedorsolidifiesasaglass.
SOLUTION:
Letusfirstconsiderwhatoccurswhenamateriallikemolassesorhoneyiscooled.Ascoolingproceeds,thematerialgets"thickerandthicker".Technically,wemeanthattheviscositydecreaseswithtemperature.Eventuallythematerialissohardthatwesayitisfrozen.Whatwemeanreallyisthatwearebelowtheglasstransitiontemperature.Thus,viscositydecreasesmanyordersofmagnitudeasmolasses,oranymaterialsthatdoesnotcrystallize,iscooledfromthefluid-likestatetotherock-hardstate.Nowconsideramaterialthatcrystallizes,say,water,sinceweareallfamiliarwithit.Aswateriscooled,itchangesviscosityverylittle.At0Cbothwaterandicecoexist.Below0Conlyiceexists.Thus,theviscosityofH2Ochangesordersofmagnitudeat0C.Unlikematerialsthatdonotcrystallize,viscositychangesordersofmagnitudeoveraverynarrowtemperaturerange-lessthanadegree.
16.FIND:
ShowtheatacticandisotacticconfigurationsofPP.Whichismorelikelytobesemicrystalline?
GIVEN:
ThestructureofPPisshowninTable6.4-1.ThestructureofatacticandisotacticpolymerisshowninFig.6.4-5.
SKETCH:
i-PPhasthemethylgroupsallonthesameside.(TheHsidegroupsarenotshown,buteachcarbonisbondedto4atoms.YoushouldmentallyvisualizealltheHatoms.)
a-PPhasthemethylgroupsappearingrandomlyononesideortheother.
SOLUTION:
Sincethemethylgroups,whicharelargeandbulky,areallonthesamesideini-PP,themoleculescanbeefficientlypackedtogether(whenthemoleculesarestretchedout).Hence,i-PPissemicrystalline.Itmechanicalpropertiesaregenerallygooduptoaboutthemeltingtemperature,160C.a-PPisnoncrystalline,sincethemoleculescannotbepackedtogetherintoaunitcell.It'spropertiesarelimitedbyitsglasstransitiontemperature,whichisabout0C.
COMMENTS:
A-PPisauselessgummysubstance.AllthePPinusetodayisi-PP.Itisusedinhugequantities.
17.FIND:
ShowthestereoisomersofPAN.
GIVEN:
:
PANispoly(vinylcyanide).
SKETCH:
(Harenotshown)
isotactic
syndiotactic
atactic
COMMENTS:
CommerciallyavailablePANisatactic.
18.FIND:
Whichpolymerismorelikelytobesemicrystalline,PVdF(whichhas2F's)orPVF(avinylpolymer,whichhas1F)?
SOLUTION:
NotethatthePVdF[poly(vinylidenefluoride)]issymmetric.Symmetricmoleculesareeasiertopackthannonsymmetricones.PVdFissemicrystalline.PVF,likePVC,isnoncrystalline.
19.FIND:
EstimatetheglasstransitiontemperatureofPET.
GIVEN:
It'smeltingtemperatureisabout255C=528K.
SOLUTION:
Themeltingtemperatureofnonsymmetricpolymersisabout2/3Tm,whenthemeltingtemperatureisinabsolutedegrees.Hence,Tg2/3x528K=353K=79C.
COMMENTS:
TheTgofPETisupto40Chigherthan80C,dependingonthespecificpolymercharacteristics.
20.FIND:
CalculatethenumberofmersordegreeofpolymerizationisasampleofPPwithamolecularweightof150,000g/mole.
DATA:
PPisavinylpolymerwithamethylsidegroup.
SOLUTION:
Thereare3Cand6Hperrepeatunit⇒MW=3x12+6x1=42g/mer.Hence,numberofmers=150,000g/mole/42g/moleofmers=3571mers.
COMMENTS:
Wealwaysignorechainendgroupsinthesesortsofcalculat
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