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Lesson5

LiquidCrystalAlignmentWZHENGIEOENSYSUTWLesson5

LiquidCrystalAlignm1SurfaceWettingTheshapeofasmalldropofliquidonthesurfaceofasolidisdeterminedby

gSV–gSL=gLVcosa,wheregSV,gSL,andgLVaresurfacetensioncoefficientsatthesolid-vapour,solid-liquid,andliquid-vapourinterfaceandaisthecontactangle.(gLV~20-40erg·cm-2,gSV~50-70erg·cm-2)Inthecaseofanisotropicliquids,allsurfacetensioncoefficientsdependalsoonorientationoftheprincipalaxesofamesophasewithrespecttothesurface.Threepossiblecases:wetting,cosa>0;nonwetting,cosa<0;completewetting,cosa=1.SurfaceWettingTheshapeofa2SurfaceSpreadingIfgSV>gSL+gLV,theequilibriumshapeofthedropisneverreachedandthedropcoversalargeareaofthesurface.Itisacaseofdropspreading.Thespreadingcoefficient

G=gSV–(gSL+gLV).ForavolatileliquidandG>0,theadsorptionofitsvapouratasolidsurfacechangesallg-coefficientssothatcompletewettingisachieved(G=0,cosa=1).ThethicknessoftheliquidisdeterminedbytheVanderWaalsforces

Fornon-volatileliquidwithG>0,suchacaseisimpossibleandthedropisspreading.TheequilibriumthicknessdependsonthespreadingcoefficientwhereLisHamaker’sconstant,risthedensityoftheliquid,andgisthegravityacceleration.Theequationsaretrueforbothisotropicandnematicphases.SurfaceSpreadingIfgSV>gSL3SurfaceWetting

Lowvaluesofqindicatethattheliquidspreads,orwetswell.Highvaluesindicatepoorwetting.q<90:wetting>90:non-wetting=0:completewettingSurfaceWetting

Lowvaluesof4ContactAngle

AHistoryConsideration

Thevalueofstaticcontactanglesaredependentontherecenthistoryoftheinteraction.AdvancedContactAngle thedropletofliquidhasrecentlyexpandedRecededContactAngle thedropletofliquidhasrecentlycontractedAdvancingRecedingContactAngle

AHistoryConsi5ContactAngle

Hysteresis

Thedifferencebetweenthemaximum(advanced/advancing)andminimum(receded/receding)contactanglevaluesiscalledthecontactanglehysteresis.ContactAngle

Hysteresis

The6MeasurementofCA

Goniometry observationofasessiledropoftestliquidonasolidsubstrateTensiometry measuringtheforcesofinteractionasasolidiscontactedwithatestliquidGoniometry Analysisoftheshapeofadropoftestliquidplacedonasolid.Thebasicelements:alightsource,samplestage,lensandimagecapture.Contactanglecanbeassesseddirectlybymeasuringtheangleformedbetweenthesolidandthetangenttothedropsurface.Advantages canuseagreatvarietyofsolidsubstrates,substrateswithregularcurvature,smallquantitiesofliquid,easytotesthightemperatureliquids.Limitations error,especiallysubjectiveerrorbetweenmultipleusers,difficultyinreproducingadvancedandrecededangles.thevelocityofmotioncannotbecontrolled.lesssuitedtoanalysisoftheeffectsofwettingonchangesincontactangle.MeasurementofCA

Goniometry o7MeasurementofContactAngle

GoniometryThebasicelementsofagoniometerincludealightsource,samplestage,lensandimagecapture.Contactanglecanbeassesseddirectlybymeasuringtheangleformedbetweenthesolidandthetangenttothedropsurface.Goiniometer(CAM200,KSV)MeasurementofContactAngle

G8MeasurementofCA(II)

Tensiometry measurestheforcesthatarepresentwhenasampleofsolidisbroughtintocontactwithatestliquid.Asthesolidispushedintotheliquidtheforcesonthebalancearerecorded.Theforcesonthebalanceare Ftotal=wettingforce+weightofprobe-buoyancythewettingforceisdefinedas: Wettingforce=g

LVPcosqwhereg

LVistheliquidsurfacetension,Pistheperimeteroftheprobeandqisthecontactangle.MeasurementofCA(II)

Tensiom9MeasurementofContactAngle

TensiometryThetensiometricmethodformeasuringcontactanglesmeasurestheforcesthatarepresentwhenasampleofsolidisbroughtintocontactwithatestliquid.Iftheforcesofinteraction,geometryofthesolidandsurfacetensionoftheliquidareknownthecontactanglemaybecalculated.Tensiometer(Sigma70,KSV)MakeameasurementofthesurfacetensionoftheliquidusingeitheraWilhelmyplateorDuNouyring.Thesampleofthesolidtobetestedisthenhungonthebalanceandtared.Theliquidisthenraisedtocontactthesolid.Whenthesolidcontactstheliquidthechangeinforcesisdetected.Asthesolidispushedintotheliquidtheforcesonthebalancearerecorded.TheforcesonthebalanceareFtotal=wettingforce+weightofprobe-buoyancy

thewettingforcewhichisdefinedas:Wettingforce=g

LVPcosqgLVistheliquidsurfacetension,Pistheperimeteroftheprobeandqisthecontactangle.MeasurementofContactAngle

T10MeasurementofCA(II)

Tensiometry

AdvantagesAtanypointontheimmersiongraph,allpointsalongtheperimeterofthesolidatthatdepthcontributetotheforcemeasurementrecorded.Allowtheusertoanalyzecontactanglesproducedfromwettingoveranentirerangeofvelocitiesfromstatictorapidwetting.Nopossibilityofsubjectiveerror.Veryusefulinstudyinghysteresis.Variationsofcontactanglesarevisualized.Analysisoffibers,veryproblematicforgoniometry,ishandledeasilybyyourtensiometer.Limitationstheusermusthaveenoughoftheliquidbeingtestedavailablesothathecanimmerseaportionofhissolidinit.thesolidinquestionmustbeavailableinsampleswhichmeetthefollowingconstraints.MeasurementofCA(II)

Tensiom11UseofCAData

Assessingthewettingcharacteristicsofsolid/liquidinteractionsDirectmeasureofwettingOtherexperimentalparametersmaybederiveddirectlyfromcontactangleandsurfacetensionresults.WorkofAdhesion:theworkrequiredtoseparatetheliquidandsolidphases,orthenegativefreeenergyassociatedwiththeadhesionofthesolidandliquidphases.Usedtoexpressthestrengthoftheinteractionbetweenthetwophases.TheworkofAdhesionisgivenbytheYoung-Dupreequationas: Wa=g(1+cosq)WorkofCohesion:theworkrequiredtoseparatealiquidintotwoparts,itisameasureofthestrengthofmolecularinteractionswithintheliquid.Itisgivenby; Wc=2gUseofCAData

Assessingthew12UseofCAData

WorkofSpreading:thenegativefreeenergyassociatedwithspreadingliquidoversolidsurface.AlsoreferredtoasSpreadingCoefficientitisgivenas: Ws=g(cosq-1)WettingTension:ameasurementofforce/lengthdefinedas:

t=Fw/P=g

LVcosqThisvalue,wettingforcenormalizedforlength,alsorepresentstheproductofthecosineofthecontactangleandthesurfacetension.Itallowsforacharacterizationofthestrengthofthewettinginteractionwithoutseparatemeasurementofsurfacetension.Mosthelpfulinsituations,suchasmulticomponentsystems,wheresurfacetensionatinterfacemaynotequalequilibriumsurfacetension.AlsoreferredtoasAdhesionTensionorWorkofWetting.CharacterizationoftheSolidSurfaceMeasurementsofsurfacetensionyielddatawhichdirectlyreflectthermodynamiccharacteristicsoftheliquidtested.Measurementofcontactanglesyielddatawhichreflectthethermodynamicsofaliquid/solidinteraction.UseofCAData

WorkofSpreadi13UseofCAData

Twobasicapproaches

CriticalSurfaceTension:Usingaseriesofhomologousliquidsofdifferingsurfacetensionsagraphofcosqvsgisproduced.Itwillbefoundthatthedataformalinewhichapproachescosq=1atagivenvalueofg.Thisisthemaximalsurfacetensionofaliquidwhichmaycompletelywetyoursolid.Thisvalue,calledthecriticalsurfacetension,canbeusedtocharacterizeyoursolidsurface.FreeSurfaceEnergy:Anotherwaytocharacterizeasolidsurfaceisbycalculatingfreesurfaceenergy,alsoreferredtoassolidsurfacetension.Theliquidsusedmustbecharacterizedsuchthatthepolaranddispersivecomponentsoftheirsurfacetensionsareknown.TherelevantequationisgivenbyOwensandWendtas:

g

l(1+cosq)/(g

ld)1/2=(g

sp)1/2[(g

lp)1/2/(g

ld)1/2]+(g

sd)1/2whereqisthecontactangle,g

lisliquidsurfacetensionandg

sisthesolidsurfacetension,orfreeenergy.Theadditionofdandpinthesubscriptsrefertothedispersiveandpolarcomponentsofeach.UseofCAData

Twobasicappro14SurfaceTension&SurfaceFreeEnergy

Surfacetensionformforce:Theforce,F,involvedinstretchingafilmis:F=γLγ=surfacetension(constant)Thismeans:γ=F/Li.e.force/unitlengthUnits:N/mormN/m(=dyn/cminc.g.sunits)Surfaceenergy

fromwork:Thework,dW,involvedinincreasingthesurfacebyalengthdxis:dW=dG=γLdx=γdAThismeans:γ=dG/dAi.e.freeenergy/unitareaUnits:J/m2=N/mSurfacetensionandsurfaceenergyareinterchangeabledefinitionswiththesameunitsSurfaceTension&SurfaceFree15ContactAngle

SurfaceTension

Theinterfacialfreeenergiesbetweenthethreephasesglvcosq=g

sv–g

slwhereg

lv,g

svandg

slrefertotheinterfacialenergiesoftheliquid/vapor,solid/vaporandsolid/liquidinterfaces.ContactAngle

SurfaceTension16SurfaceEnergyTheenergy,whichisneededtodeviatetheliquidcrystalmolecules(thedirector)fromthepreferredorientationatthesurface,iscalledanchoringenergy.Theenergyofadhesionofliquidcrystalwiththesolidsurfaceandthesurfaceenergyoftheliquidcrystal-solidinterfaceareoftheorderof20-40erg/cm2;thatis,severalordersofmagnitudehigherthantheanchoringenergyofthedirectorreorientationatthesurface(10-3~1erg/cm2).Theanchoringenergy(bytheRapinipotential):ThemoregeneralexpressionThe“polar”and“azimuthal”anchoringenergies:SurfaceEnergyTheenergy,whic17SurfaceEnergyofSolidSurfaceEnergyofSolid18SurfaceEnergyofSolidSurfaceEnergyofSolid19SurfaceEnergyofSolidSurfaceEnergyofSolid20SurfaceEnergyofSolidSurfaceEnergyofSolid21SurfaceEnergyofSolidSurfaceEnergyofSolid22MeasurementofAnchoringEnergy

I.Field–offTechniqueTheazimuthal(Wf)andpolar(Wq)anchoringenergiescanbedeterminedfromthecorrespondingthicknessrofthedomainwallwhichseparatesregionsofnematicLCwithdifferentdirectororientations,

r

Kiid/WwhereKiiisaneffectiveelasticconstant,Wisthecorrespondingelasticenergy,anddthethicknessofthecell.

Anchoringenergycanalsobecalculatedfromthemeasurementsoftheangulardependenceoftheintensityofthesmallanglelightscatteringbydirectorfluctuations.Thewavevectorqofdirectorfluctuationsdependsonanchoringenergy,Forstronganchoring,Wthelowestenergycurvaturemodehasq=p/d.ForfiniteW,thewavevectorissmaller: qw=p/(d+2b)wherebistheso-calledextrapolationlength,

b=Ki/W,whereKiistheelasticmoduluscorrespondingtogeometryofexperiment.MeasurementofAnchoringEnerg23MeasurementofAnchoringEnergy

II.Field–onTechniqueTheclassicalmethodfordeterminingtheanchoringenergyistheFreedericksztransition.Theorientinginfluenceofthesurfaceresultsinadeformationofthedirectorprofileinapreviouslyhomogeneousorhomeotropicliquidcrystalcell,hinderingitsfreerotationparallelorperpendiculartotheexternalfieldduetothedielectricinteraction.Thevalueofthethresholdfield,theshapeofelectricoropticalliquidcrystalresponseabovethethreshold,andthedynamicsoftheFreedericksztransitionmakeitpossibletodeterminethecorrespondinganchoringenergyW.Inthefirstapproximation,wemayusethesameconsiderationsonthewavevectorsofthedeformationsaswealreadystatedabove.ThecorrespondingratioofthedisturbingfieldHwtothethresholdfieldsH

Hw/H=1–2/wi

.wherethecharacteristicparameterwi>>1isdefinedfrom

wi

=d/bi=d

Wi/Ki

MeasurementofAnchoringEnerg24MeasurementofAnchoringEnergyAnexampleshowntheshapeofthesurfacepotentialW(q)wellforplanar-orientedMMBAmeasuredbytheFreedericksztransitiontechnique.MeasurementofAnchoringEnerg25TheMechanismofLCAlignmentHomogenousandhomeotropicalignmentsaremainlydeterminedbythephysicochemicalinteractionsbetweenliquidcrystalandsurface.Thesurfaceenergiesofhomogeneousandhomeotropicalignmentsareexpressedasfollows;

gLS(//)=gS+gL(//)–Wa(//),

gLS()=gS+gL()–Wa(). wheregLS,gS,gLandWaarethesurfaceenergyofliquidcrystal-solid,solid,liquidcrystalandtheworkofadhesion,respectively.Thealignmentofliquidcrystaloccurstoreducethesurfaceenergy,dependingonthemagnitudebetweengLS(//)andgLS(),orWa(//)andWa().Creagh’stheory:Homeotropicalignmentisinducedonalowenergysurface.Buttheconverseisnottrue.Planeralignmentisusuallyobtainedaslongasthesurfaceismicroscopicallyflatandtheliquidcrystaldoesnotcontainanyamphiphilicimpuritywithinefficiencylowsurfacepolarity.Stableparallelalignmentisobtainedbydecreasingthesurfacepolaritybymeansofacoatingpolymerorasurfacecouplingagent,whosemoleculestendtoadsorbparalleltothesurface.

Inordertoobtainhomogeneousalignment,unidirectionalrubbingisnecessary.ThemechanismofparallelalignmenttotherubbingdirectionisanalysedbyBerremanD.W.Berreman,Phys.Rev.Lett.,28:1683,1972..Heestimatedthedifferenceofelasticenergiesbetweenparallelandperpendicularalignmentstothegroovestobeabout5x105erg/cm3forthefusedquartzsurfacewithdiamondpastes.Butfortheusualcloth-rubbedsurface,thegroovesarenotobservedevenbytheelectronmicroscope.Thereforethemechanismofhomogeneousalignmenttotheusualrubbedsurfacemightnotbegrooves,butisconsideredtobeduetostatisticallyparallelalignmentofsomeimpuritiescoatedontothesurfacebyrubbingorofsurfacemoleculesoftheorientationlayer.TheMechanismofLCAlignmentH26MechanismofLCAlignment(cont.)

Whatisthetruemechanismofliquidcrystalalignment?Onefactoristheeffectofimpurities.Insightintotheireffectisprovidedbythefollowingfact.Wesometimesexperienceadeteriorationofthealignmentinliquidcrystaldisplaycells.Haller,KmetzandIshikawaexplainedthereasonforthisphenomenonastheeffectoftheadhesionofamolecularlayeronthesurface.Itisthoughtthattheadhesionlayerconsistsofanimpurity.Inordertoexaminetheintrinsicorientationofliquidcrystalwithouttheinfluenceofanyimpurity,theimpuritymustbeeliminatedfromtheliquidcrystal. Whydoespureliquidcrystalalwaysalignhomogenouslyonsmoothinorganicmaterials?Okanoshowedbyconsideringexcludedvolumeinteractionthattheelongatednematicmoleculesalwaysfavourtheplanaralignmentonthecellwalls. Theexperimentsusingtheliquidcrystalchromatographyshowedthathomeotropicalignmentiseasilyinducedwhenthepolarityofthesubstrateisstrongandamphiphilicimpuritiesarecontainedinliquidcrystal.Becausetheimpuritiesareadsorbedonthesubstrateandinducehomeotropicalignment.Therefore,theweakpolarityofthesubstrateiseffectiveonthehomogeneousalignment.MechanismofLCAlignment(con27Lesson5

LiquidCrystalAlignmentWZHENGIEOENSYSUTWLesson5

LiquidCrystalAlignm28SurfaceWettingTheshapeofasmalldropofliquidonthesurfaceofasolidisdeterminedby

gSV–gSL=gLVcosa,wheregSV,gSL,andgLVaresurfacetensioncoefficientsatthesolid-vapour,solid-liquid,andliquid-vapourinterfaceandaisthecontactangle.(gLV~20-40erg·cm-2,gSV~50-70erg·cm-2)Inthecaseofanisotropicliquids,allsurfacetensioncoefficientsdependalsoonorientationoftheprincipalaxesofamesophasewithrespecttothesurface.Threepossiblecases:wetting,cosa>0;nonwetting,cosa<0;completewetting,cosa=1.SurfaceWettingTheshapeofa29SurfaceSpreadingIfgSV>gSL+gLV,theequilibriumshapeofthedropisneverreachedandthedropcoversalargeareaofthesurface.Itisacaseofdropspreading.Thespreadingcoefficient

G=gSV–(gSL+gLV).ForavolatileliquidandG>0,theadsorptionofitsvapouratasolidsurfacechangesallg-coefficientssothatcompletewettingisachieved(G=0,cosa=1).ThethicknessoftheliquidisdeterminedbytheVanderWaalsforces

Fornon-volatileliquidwithG>0,suchacaseisimpossibleandthedropisspreading.TheequilibriumthicknessdependsonthespreadingcoefficientwhereLisHamaker’sconstant,risthedensityoftheliquid,andgisthegravityacceleration.Theequationsaretrueforbothisotropicandnematicphases.SurfaceSpreadingIfgSV>gSL30SurfaceWetting

Lowvaluesofqindicatethattheliquidspreads,orwetswell.Highvaluesindicatepoorwetting.q<90:wetting>90:non-wetting=0:completewettingSurfaceWetting

Lowvaluesof31ContactAngle

AHistoryConsideration

Thevalueofstaticcontactanglesaredependentontherecenthistoryoftheinteraction.AdvancedContactAngle thedropletofliquidhasrecentlyexpandedRecededContactAngle thedropletofliquidhasrecentlycontractedAdvancingRecedingContactAngle

AHistoryConsi32ContactAngle

Hysteresis

Thedifferencebetweenthemaximum(advanced/advancing)andminimum(receded/receding)contactanglevaluesiscalledthecontactanglehysteresis.ContactAngle

Hysteresis

The33MeasurementofCA

Goniometry observationofasessiledropoftestliquidonasolidsubstrateTensiometry measuringtheforcesofinteractionasasolidiscontactedwithatestliquidGoniometry Analysisoftheshapeofadropoftestliquidplacedonasolid.Thebasicelements:alightsource,samplestage,lensandimagecapture.Contactanglecanbeassesseddirectlybymeasuringtheangleformedbetweenthesolidandthetangenttothedropsurface.Advantages canuseagreatvarietyofsolidsubstrates,substrateswithregularcurvature,smallquantitiesofliquid,easytotesthightemperatureliquids.Limitations error,especiallysubjectiveerrorbetweenmultipleusers,difficultyinreproducingadvancedandrecededangles.thevelocityofmotioncannotbecontrolled.lesssuitedtoanalysisoftheeffectsofwettingonchangesincontactangle.MeasurementofCA

Goniometry o34MeasurementofContactAngle

GoniometryThebasicelementsofagoniometerincludealightsource,samplestage,lensandimagecapture.Contactanglecanbeassesseddirectlybymeasuringtheangleformedbetweenthesolidandthetangenttothedropsurface.Goiniometer(CAM200,KSV)MeasurementofContactAngle

G35MeasurementofCA(II)

Tensiometry measurestheforcesthatarepresentwhenasampleofsolidisbroughtintocontactwithatestliquid.Asthesolidispushedintotheliquidtheforcesonthebalancearerecorded.Theforcesonthebalanceare Ftotal=wettingforce+weightofprobe-buoyancythewettingforceisdefinedas: Wettingforce=g

LVPcosqwhereg

LVistheliquidsurfacetension,Pistheperimeteroftheprobeandqisthecontactangle.MeasurementofCA(II)

Tensiom36MeasurementofContactAngle

TensiometryThetensiometricmethodformeasuringcontactanglesmeasurestheforcesthatarepresentwhenasampleofsolidisbroughtintocontactwithatestliquid.Iftheforcesofinteraction,geometryofthesolidandsurfacetensionoftheliquidareknownthecontactanglemaybecalculated.Tensiometer(Sigma70,KSV)MakeameasurementofthesurfacetensionoftheliquidusingeitheraWilhelmyplateorDuNouyring.Thesampleofthesolidtobetestedisthenhungonthebalanceandtared.Theliquidisthenraisedtocontactthesolid.Whenthesolidcontactstheliquidthechangeinforcesisdetected.Asthesolidispushedintotheliquidtheforcesonthebalancearerecorded.TheforcesonthebalanceareFtotal=wettingforce+weightofprobe-buoyancy

thewettingforcewhichisdefinedas:Wettingforce=g

LVPcosqgLVistheliquidsurfacetension,Pistheperimeteroftheprobeandqisthecontactangle.MeasurementofContactAngle

T37MeasurementofCA(II)

Tensiometry

AdvantagesAtanypointontheimmersiongraph,allpointsalongtheperimeterofthesolidatthatdepthcontributetotheforcemeasurementrecorded.Allowtheusertoanalyzecontactanglesproducedfromwettingoveranentirerangeofvelocitiesfromstatictorapidwetting.Nopossibilityofsubjectiveerror.Veryusefulinstudyinghysteresis.Variationsofcontactanglesarevisualized.Analysisoffibers,veryproblematicforgoniometry,ishandledeasilybyyourtensiometer.Limitationstheusermusthaveenoughoftheliquidbeingtestedavailablesothathecanimmerseaportionofhissolidinit.thesolidinquestionmustbeavailableinsampleswhichmeetthefollowingconstraints.MeasurementofCA(II)

Tensiom38UseofCAData

Assessingthewettingcharacteristicsofsolid/liquidinteractionsDirectmeasureofwettingOtherexperimentalparametersmaybederiveddirectlyfromcontactangleandsurfacetensionresults.WorkofAdhesion:theworkrequiredtoseparatetheliquidandsolidphases,orthenegativefreeenergyassociatedwiththeadhesionofthesolidandliquidphases.Usedtoexpressthestrengthoftheinteractionbetweenthetwophases.TheworkofAdhesionisgivenbytheYoung-Dupreequationas: Wa=g(1+cosq)WorkofCohesion:theworkrequiredtoseparatealiquidintotwoparts,itisameasureofthestrengthofmolecularinteractionswithintheliquid.Itisgivenby; Wc=2gUseofCAData

Assessingthew39UseofCAData

WorkofSpreading:thenegativefreeenergyassociatedwithspreadingliquidoversolidsurface.AlsoreferredtoasSpreadingCoefficientitisgivenas: Ws=g(cosq-1)WettingTension:ameasurementofforce/lengthdefinedas:

t=Fw/P=g

LVcosqThisvalue,wettingforcenormalizedforlength,alsorepresentstheproductofthecosineofthecontactangleandthesurfacetension.Itallowsforacharacterizationofthestrengthofthewettinginteractionwithoutseparatemeasurementofsurfacetension.Mosthelpfulinsituations,suchasmulticomponentsystems,wheresurfacetensionatinterfacemaynotequalequilibriumsurfacetension.AlsoreferredtoasAdhesionTensionorWorkofWetting.CharacterizationoftheSolidSurfaceMeasurementsofsurfacetensionyielddatawhichdirectlyreflectthermodynamiccharacteristicsoftheliquidtested.Measurementofcontactanglesyielddatawhichreflectthethermodynamicsofaliquid/solidinteraction.UseofCAData

WorkofSpreadi40UseofCAData

Twobasicapproaches

CriticalSurfaceTension:Usingaseriesofhomologousliquidsofdifferingsurfacetensionsagraphofcosqvsgisproduced.Itwillbefoundthatthedataformalinewhichapproachescosq=1atagivenvalueofg.Thisisthemaximalsurfacetensionofaliquidwhichmaycompletelywetyoursolid.Thisvalue,calledthecriticalsurfacetension,canbeusedtocharacterizeyoursolidsurface.FreeSurfaceEnergy:Anotherwaytocharacterizeasolidsurfaceisbycalculatingfreesurfaceenergy,alsoreferredtoassolidsurfacetension.Theliquidsusedmustbecharacterizedsuchthatthepolaranddispersivecomponentsoftheirsurfacetensionsareknown.TherelevantequationisgivenbyOwensandWendtas:

g

l(1+cosq)/(g

ld)1/2=(g

sp)1/2[(g

lp)1/2/(g

ld)1/2]+(g

sd)1/2whereqisthecontactangle,g

lisliquidsurfacetensionandg

sisthesolidsurfacetension,orfreeenergy.Theadditionofdandpinthesubscriptsrefertothedispersiveandpolarcomponentsofeach.UseofCAData

Twobasicappro41SurfaceTension&SurfaceFreeEnergy

Surfacetensionformforce:Theforce,F,involvedinstretchingafilmis:F=γLγ=surfacetension(constant)Thismeans:γ=F/Li.e.force/unitlengthUnits:N/mormN/m(=dyn/cminc.g.sunits)Surfaceenergy

fromwork:Thework,dW,involvedinincreasingthesurfacebyalengthdxis:dW=dG=γLdx=γdAThismeans:γ=dG/dAi.e.freeenergy/unitareaUnits:J/m2=N/mSurfacetensionandsurfaceenergyareinterchangeabledefinitionswiththesameunitsSurfaceTension&SurfaceFree42ContactAngle

SurfaceTension

Theinterfacialfreeenergiesbetweenthethreephasesglvcosq=g

sv–g

slwhereg

lv,g

svandg

slrefertotheinterfacialenergiesoftheliquid/vapor,solid/vaporandsolid/liquidinterfaces.ContactAngle

SurfaceTension43SurfaceEnergyTheenergy,whichisneededtodeviatetheliquidcrystalmolecules(thedirector)fromthepreferredorientationatthesurface,iscalledanchoringenergy.Theenergyofadhesionofliquidcrystalwiththesolidsurfaceandthesurfaceenergyoftheliquidcrystal-solidinterfaceareoftheorderof20-40erg/cm2;thatis,severalordersofmagnitudehigherthantheanchoringenergyofthedirectorreorientationatthesurface(10-3~1erg/cm2).Theanchoringenergy(bytheRapinipotential):ThemoregeneralexpressionThe“polar”and“azimuthal”anchoringenergies:SurfaceEnergyTheenergy,whic44SurfaceEnergyofSolidSurfaceEnergyofSolid45SurfaceEnergyofSolidSurfaceEnergyofSolid46SurfaceEnergyofSolidSurfaceEnergyofSolid47SurfaceEnergyofSolidSurfaceEnergyofSolid48SurfaceEnergyofSolidSurfaceEnergyofSolid49MeasurementofAnchoringEnergy

I.Field–offTechniqueTheazimuthal(Wf)andpolar(Wq)anchoringenergiescanbedeterminedfromthecorrespondingthicknessrofthedomainwallwhichseparatesregionsofnematicLCwithdifferent

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