Dr Stefan W Hell - Laboratoire de physique des solides地狱博士Stefan W固态物理实验室

THE

PHYSICSOFFOAMBoulderSchoolforCondensedMatterandMaterialsPhysics July1-26,2002:PhysicsofSoftCondensedMatter1.IntroductionFormationMicroscopics2.StructureExperimentSimulation3.StabilityCoarseningDrainage4.RheologyLinearresponseRearrangement&flowDouglasJ.DURIANUCLAPhysics&AstronomyLosAngeles,CA90095-1547<durian@>Princen-Prud’hommemodelsheara2Dhoneycomb,alwaysrespectingPlateau’srulesdeformationisnotaffine:verticesmustrotatetomaintain120-120-120stress,sstrain,gslope,Gogyshearmodulus:Go=gfilm/Sqrt[3]ayieldstrain:gy=1.2agfilmetc.Yes,but…Princen-Prud’hommeisfor2D

periodic

static

dryfoamdimensionality?generallyexpectG~Laplacepressure(surfacetension/bubblesize)wetness?shearmodulusmustvanishforwetfoamsdissipation?nonzerostrainrateoroscillationfrequency?disorder?smallerrearrangementsize(notsystem)?smalleryieldstrain?small-strainnon-affinemotionbubblemotionisup&downaswellasmore&lesscomparebondsanddisplacements(normalizedtoaffineexpectation)trendsvspolydisersityandwetness(DJD)f=1f=0.84width=0.75width=0.1Frequencydependence,G*(w)Simplestpossibility:Kelvinsolid G*(w)=G0+ihw{i.e.G’(w)=G0andG〞(w)=hw}Buttypicaldatalooksmuchdifferent:G’(w)isn’tflat,andincreasesathighw…G〞(w)doesn’tvanishatloww…(A.Saint-Jalmes&DJD)High-wrheologyDuetonon-affinemotion,anothertermdominates: G*(w)=G0(1+Sqrt[iw/wc])** shownbydottedcurvefore=0.08foam:[**seenandexplainedbyLiu,Ramaswamy,Mason,Gang,WeitzforcompressedemulsionusingDWSmicrorheology](A.D.Gopal&DJD)NB:ThisgivesarobustwaytoextracttheshearmodulusfromG*(w)vswdata.HereGo=2300dyne/cm2

Short-tDWSlong-t:rearrangementsgiveexponentialdecayshort-t:thermalinterfacefluctuations(Y=<Dr2(t)>)amplitudeoffluctuations:microrheology:UnjammingvsgasfractionDataforshearmodulus:symbols:polydispersefoamsolidcurve:monodisperseemulsion(Mason&Weitz)dashedcurve:polydisperseemulsion(Princen&Kiss)unjammedjammedpolydispersitymakeslittleornodifference!(A.Saint-Jalmes&DJD)Behaviornearthetransitionsimulationof2Dbubblemodelshearmoduluscoordinationnumberstress-relaxationtime

trappearstodivergeatfrcp~0.84better“pointJ〞statisticsbyO’Hern,Langer,Liu,Nagel(DJD)Unjammingvstimeelasticityvanishesatlongtimes…stressrelaxesasthebubblescoarsentimescaleissetbyfoamageiehowlongforsizedistributiontochangenotsetbythetimebetweencoarsening-inducedrearrangements(20s)Eventhoughthisisnotathermallyactivatedmechanismlikediffusionorreptation,therheologyislinearG*(w)andG(t)dateareindeedrelatedbyFouriertransform(A.D.Gopal&DJD)Unjammingvsshearmakebubblesrearrange&explorepackingconfigurationsslowshear:suddenavalanche-likerearrangementsofafewbubblesatatimefastshear:rearrangementsmergetogetherintocontinuoussmoothflowslow&jerkyfast&smoothRearrangementsizeseventhelargestareonlyafewbubblesacrosspictureofaverylargeeventdistributionofenergydrops(before-after)hasacutoff {butitmovesoutonapproachtofc“pointJ〞}NB:sheardeformationisuniformUCLA:directobservationoffreesurfaceinCouettecellviscosityandG*(w)areindep.ofsamplethickness&cellgeometryDWSgivesexpecteddecaytimeintransmissionandbackscatteringviscousfingeringmorphologyHohler/Cohen-Addadlab(Marne-la-Vallee):multiplelightscatteringandrheologyDenninlab(UCIrvine):2DbubbleraftsandlipidmonolayersWeitzlab(Exxon/Penn/Harvard):RheologyofemulsionsComputersimulations:bubblemodel(DJD-Langer-Liu-Nagel)Surfaceevolver(Kraynik)2D(Weaire)vertexmodel(Kawasaki)

uniformshear-bandexponentialimportantscalesnotation:valuesforFoamy:bubblemotionviaDWS lowshearhighshearto=timebetweenrearrangementsateachscatteringsitetimeforadjacentscatteringsitestoconvectapartbyl

(A.D.Gopal&DJD)DWStimesvsstrainratebehaviorchangesatexpectedstrainratescalesdiscreterearrangementsjammed/solid-likelaminarbubblemotionunjammed/liquid-like(A.D.Gopal&DJD)Rheologicalsignature?simplestexpectationisBinghamplastic:but1/gisn’tseenineitherdataorbubble-model:norealsignatureofgmindata..(A.D.Gopal&DJD)Superimposestep-strain!StressjumpandrelaxationtimebothmeasureelasticityG(0)tRStress(dyne/cm2)StraintransientrelaxationshearmodulusbubblemotionvsrheologyAllmeasuresofelasticityvanishatsamepointwhererearrangementsmergetogetherintocontinuousflow“unjamming〞shearrate=yieldstrain/eventdurationThiscompletestheconnectionbetweenbubble-scaleandmacroscopicfoambehaviorJammingWe’venowseenthreewaystounjamafoamieforbubblestorearrangeandexploreconfigurationspacevsliquidfraction(gasbubblepacking)vstime(asfoamcoarsens)vsshearTrajectoriesinthephasediagram?doesshearplayroleoftemperature?(A.J.Liu&S.R.Nagel)ThreeeffectivetemperaturesCompressibility&pressurefluctuationsViscosity&shearstressfluctuationsHeatcapacity&energyfluctuationsT’sallreduceto(dS/dU)-1forequilibratedthermalsystemsWhatistheirvalue&shearratedependence;aretheyequal?Difficulttomeasure,soresorttosimulation…(I.K.Ono,C.SO’Hern,DJD,S.A.Langer,A.J.Liu,S.R.Nagel)ThethreeTeff’sagree!N=400bubblesin2Dboxatf=0.90areafractionTeffapproachesconstantatzerostrainrateTeffincreasesveryslowlywithstrainrateg.TpTxyTUTT0.0060.0040.00200.0080.0040bidispersepolydisperse0.00010.0010.010.11…alsoagreewithT=(dS/dU)-1

Monte-CarloresultsforW(U),theprobabilityforarandomlyconstructedconfigurationtohaveenergyUForthissystem,theeffectivetemperaturehasalltheattributesofatruestatisticalmechanicaltemperature.TU=U/0.65N=U/(f/2)NS=TUfromshearingrunsMini-conclusionsStatisticalMechanicsworksforce