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JournalofAdhesionScienceandTechnology24(2010)2681–2692 MicrochannelInducedSurfaceBulgingofaSoftElastomericLayerAbhijitMajumderAnuragKumarTiwariKrishnaraoKoradaandAnimangsuGhatakDepartmentofChemicalEngineering,IndianInstituteofTechnology,Kanpur,UP208016,India WhenawettingliquidÞllsinmicrochannelsembeddedinsideathinelastomericlayer,thesurfaceofthelayerdoesnotremainsmoothbutbulgesoutinthevicinityofthechannels.Theheightofthebulgedependsonthedeformabilityofthelayerandthesurfacetensionofliquid;inaddition,itdependsalsoontheverticallocationofthechannelfromthesurfaceofthelayerandthechanneldiameter.While,forliquidsoflow500cPbulgingoccursinstantaneously,forliquidsofhighviscosity4000cP,itoccursoveraperiodoftime.Concomitanttobulgingofthelayer,thecrosssectionofthechannelalterstooinitsshapeandsizesuggestingthattheelasticenergypenaltyassociatedwiththebulgingofthelayerissuppliedbytheinterfacialenergyoftheliquidÐairandliquidÐsolidinterfaces.Localbulgingofthelayeraltersalsoitslocaldeformabilitywhichisdemonstratedbycontactmechanicsexperiments:indentationwithasphericalindenteryieldsanon-circularcontactarea,theshapeandsizeofwhichvarywiththedepthofindentation.Thus,sub-surfacemicrochannelscanbesuitablyusedforgeneratingsurfacepatternsontheelastomerandalsoformodulatingitsmodulus.KoninklijkeBrillNV,Leiden,2010KeywordsMicrochannel,bulging,indentation,modulationofmodulus,non-circularcontactarea1.IntroductionNanotomicro-scalepatterningofthesurfaceofasoftelastomericlayerisimportantforvarietyofpracticalandtechnologicalapplications,e.g.,forcreatingsuper-hydrophobicsurfaces[1,2];generatingstructuralcolour[3];biological[4]andchemicalsensors[5];scaffoldsfortissueengineering[6];micro-electromechanicalsystems[7];patternedadhesives[8];andsoon.Manyoftheseapplicationsdemandnotjustpatterningofthematerialsurfacebuthierarchicalpatterningandinmanycasesitisnotjustphysicaltexturingofthematerialbutspatialmodulationofoneormorephysicalproperties[9]alsobecomesimportant.Theseapplicationsdemandnovelfabricationmethodswhichcangeneratepatternswithcontrolledgeometric Towhomcorrespondenceshouldbeaddressed.E-mail:aghatak@iitk.ac.inKoninklijkeBrillNV,Leiden,2010DOI:10.1163/016942410X508190 A.Majumderetal./JournalofAdhesionScienceandTechnology24(2010)2681–2692 Figure1.TheschematicofatypicalelastomericÞlmofthicknesswithmultiple,uniformlyspacedmicrochannelsofdiameterburiedataverticaldistancefromthesurface.TheÞlmremainsbondedtotherigidsubstrate.PDMSsothatitcanbeeasilywithdrawnfromthecrosslinkedÞlmonapplicationofagentlepull[17].Straightmicrochannels,whichspanthroughthewholewidthoftheÞlmsarethusgeneratedasmonolithicstructuresinsidePDMSelastomeric3.SurfaceDeformationsThesechannelsareÞlledwithliquidswhichwetthesurfaceofthechannelwallcompletely,e.g.,siliconeoilsofdifferentviscosities100Ð1000cP,surfaceten-20mN/m.TheseliquidsÞllinthechannelsbycapillaryaction,thereforenopumpisrequiredforthispurpose.Figure2(a)showsthetopviewofthepartiallyÞlledchannel.Themolecularweightsoftheseoilsaresuchthattheydonotdiffuseintothecrosslinkednetworkwithinthetimedurationofmostofourexperiments.ThiswasconÞrmedbyplacingablockofPDMSinapooloftheoilwhichdidnotswellthePDMSevenafteraverylongtime.Interestingly,astheliquidÞllsinthechannel,thethinskincoveringitspontaneouslybulgesoutformingsurfaceundulations,withmaximumheightoftheundulationoccurringatthelocationofleastthicknessoftheskin.Whileforlowerviscosityofoil,100Ð400cPtheequilibriumdeformationisreachedwithin5Ð10min,fortheoneswithhighervis-cosity,400Ð4000cPtheÞlmdeformsoveralongerperiodoftime4Ð5hours.WhilethisdeformationcanbefeltbyslidingaÞngeroverthesurfaceoftheÞlmandcanbecharacterizedqualitativelybyopticalproÞlometry,itscross-sectionalimageisobtainedbycuttingasliceoftheÞlmusingasharprazorbladeandview-ingitunderanopticalmicroscope.AnalysisofthechannelcrosssectionbythisprocessrequiresthatafterÞllingitwithoil,thechannelbepermanentlysetatits A.Majumderetal./JournalofAdhesionScienceandTechnology24(2010)2681–2692 Figure2.(a)TopviewofamicrochannelÞlledwithoilshowsconcavemeniscusofoil.(b)Ð(d)OpticalmicrographsofthecrosssectionoftheÞlmshowthebulgingeffectofthethinskinabovethechannel.(b)EmptychannelembeddedinsideanelastomericÞlmataverticaldistance30µmfromthesurface.(c)Ð(d)DeformationofthechannelcrosssectionsintwodifferentelastomericÞlmswithskin25and40µmrespectively,duetoÞllingwithoil.Scalebarrepresents200µm.deformedform;however,thesiliconeoilwithoutanyfunctionalizedgroupsinitsmolecularstructureisnotamenabletocrosslinking.Therefore,inordertoexam-inethedeformationofthechannel,itisÞlledwithSylgard170elastomer(aDowCorningproduct)mixedwiththecuringagentfollowedbycuringitatSince,viscosityofSylgard170pre-polymerliquidis4000cP,sufÞcienttimeisgivenfortheequilibriumdeformationtobereachedbeforecrosslinkingtheliquid.InFig.2(b)Ð(d)wepresenttypicalcross-sectionalviewsoftheÞlmswhichshowanemptychannelanditsdeformedformafteritisÞlledwiththeoil.NoticethatheretheelasticÞlmremainsbondedtotherigidplate,sothatitcandeformonlyonitsfreesurface.However,ifweusechannelembeddedfreeÞlm,whichremainssupportedonlyatitsedges,bulgingoccursonitsbothsurfaces,albeittodifferentdegreesdependingonthethicknessoftheskin.OpticalproÞlometryofthesurfaceoftheseÞlmsshowsthatincreaseswithofthechannelbutdecreaseswithskinthicknessoftheÞlm.Bycarry-ingoutexperimentswithalargenumberofÞlmswithdifferentchanneldiameters50Ð900µmandskinthickness10Ð80µm,ithasearlierbeenshownthatscales[18]as  .IntheabsenceofanyexternalmechanicalÞeld,thebulgingpossiblyoccursbecauseofsurfaceeffects,tobespeciÞc,becauseofthewettingof A.Majumderetal./JournalofAdhesionScienceandTechnology24(2010)2681–2692thePDMSsurfacewithoil.Since,thePDMSsurfaceisoleophilic,itleadstonega-tiveLaplacepressureatthemeniscus,i.e.,attheinterfaceoftheoilinthechannelandatmosphere;asaresult,thepressureinoildecreasesbelowtheatmospheric.Thedeformabilityofthematrix,i.e.,thechannelwall,however,bringsincomplications.Forexample,theliquidinsidethechannelissubjectedtotwoopposingforces:theforceattheopenendsgivenas4whichshouldsqueezeinmoreliquidinsidethechannelandtheforcealongthelengthofthechannel:whichtendstosqueezeouttheliquid;hereisthelengthofthechannel.Sinceinexperiments,,itisthelatterforcethatshoulddominateleadingtosqueezingoutoftheliquid,butsuchaneffectwouldbeaccompaniedalsobythebendingofthechannelwallrequir-inglargeelasticenergypenalty.Infact,thechannelindeedgetscompressed,butonlyveryslightlyintheportionwherewallthicknessisinÞnitelylarge;however,itbulgesoutclosetothethinskinabovethechannel.Figure3showstheopticalmicrographofthecrosssectionofaPDMSÞlminwhichachannelofdiameter710µmisembeddedtothemaximumdepthsothattheskinthicknessismaintainedat50µm.ThechannelisÞlledwithSyl-gard170pre-polymerliquidmixedwithcrosslinkerandisallowedtocure.While Figure3.ThecrosssectionofanelastomericÞlmembeddedwiththemicrochannelÞlledwithSylgard170.Thediameterofthechannelandtheskinthicknessare570µmand50µm,re-spectively.ThedottedcirclerepresentsthetraceoftheemptychannelandthesolidlineeÐfrepresentstheundeformedfreesurfaceoftheÞlm.TheblackarrowsindicatethatthechannelgetscompressedalongaÐbandcÐdanditexpandsalongdÐa.AlongbÐc,thechannelwallremainsunaltered.Thescalebarrepresents100µm.Percentageincreaseincross-sectionalareaofthechannelisplottedagainsttheofthethinskinabovethemicrochannel.Thesymbols()representchanneldiameters550µmand690µm,respectively. A.Majumderetal./JournalofAdhesionScienceandTechnology24(2010)2681–2692thedottedcirclerepresentsthetraceoftheundeformedchannel,theblackpor-tionrepresentsthedeformedcrosssectionofthechannel.TheÞgureclearlyshowsthatthechannelgetscompressedalongaÐbandcÐd;itbulgesoutalongdÐa;nosigniÞcantdeformationisobservedalongbÐc.Thisobservationsuggeststhatthedifferentialpressureactsdifferentlyindifferentportionsofthechannelwall.Forexample,inthethinskincoveringthechannel,thepressurevariesgradu-allyfromatthewallofthechanneltoatthePDMSÐairinterface.Hence,thereisadistributionofpressurewhichmaybeassumedtobelinear,sothat,theaveragepressureattheskincoveringthechannel2islessthantheatmosphericpressure.Thus,theskinactslikeathinplatebeingsubjectedtoacompressiveaxialstressof2whichresultsinitsbuckling.Bucklingofthinplatesandrodsfollowsasetoffunctionalformsknownasellipticcurvesgeneratedbysolvingthefollowinggenericequationandthecorre-spondingboundaryconditions[20]: ds2+a=0;=00 ds=d0 deÞnesthecontourlengthofthecentrelineoftheplateand(s)angleofthetangenttothecentreline;parameteristheratiooftheaxialloadperunitwidthoftheplateanditsbendingrigidity, are,respectively,thetangenttothecentrelineandrateofchangeoftangentwiththecontourlength.Whileequation(1)accountsonlyforsmallbendingofathinplate,moreinvolvedanalysisforlargebendingdeformationofaÞnitelythickelasticblockhasbeenderived.However,forthesakeofsimplicity,weexamineifthesurfaceproÞleofthedeformedÞlmmatcheswiththatofanelasticainthelightofequation(1).InFig.4,thetracesofthesurfaceproÞlesforÞlmsofthicknessand500µmallwithembeddedchannelsofdiameter50µmareusedtoÞttoequation(1).ForallthesecasesthechannelsremainmaximallyburiedwithintheÞlmsothattheskinthicknessoftheÞlmcoveringthechannelincreasesfrom10to450µmfortheabovesetofÞlms.Curve1showsthatwhentheskinthicknessissmall,e.g.,10µm,itbulgesouttoformanarrowpeakwhichisnotcapturedwellbyequation(1).However,forÞlmsoflargerskinthickness,e.g.,250and450µm,thedeformationproÞlesarerepresentedreasonablywellbyequation(1)asshownbycurves2Ð4implyingthatthesurfacedeformationofÞlmsmayindeedoccurbucklingoftheskin.Whileequation(1)approximatesthebucklingphenomenonratherwell,itdoesnotincorporatetheeffectofthicknessofthethinskinwhichinthepresentproblemdoesnotremainuniformbutvariesspatially.Thisvariationbecomesmoreprominentforthinnerskins,andasaresultequation(1)failstocapturethecorrespondingopticalproÞles.4.DeformationofMicrochannelEquation(1)isnotadequateforanotherreason:closeexaminationofthechannelcrosssectionsuggeststhatitnotonlydeformsfrombeingcircularbutitsperimeter A.Majumderetal./JournalofAdhesionScienceandTechnology24(2010)2681–2692ofthechannelwall.ThusÞnitepositivevaluesof%suggestthatbulgingdefor-mationofthethinskinoccursnotonlyduetotheLaplacepressureatthemeniscusoftheliquidinsidethechannelbutalsoduetoconversionofsurfaceenergytotheelasticenergyofthechannelwall.5.ContactMechanicsExperimentBesidescausingsurfacedeformation,theliquidÞlledsub-surfacemicrochannelsal-teralsotheeffectivelocalmodulusoftheelasticÞlminthevicinityofthechannels.WhileitisexpectedthatthepresenceoftheburiedmicrochannelshoulddecreasethelocalmodulusoftheÞlmenhancingitsdeformability,thebulginginducedbytheliquidinsidethechannelcanfurtheramplifyit.Thealterationinlocaldeforma-bilitycanbeprobedbycontactmechanicsexperimentsaspresentedinFig.5.HeretheelasticÞlmremainsstronglybondedtotherigidsubstrateandasofthemi-sphericalindentermadeofPDMSofradiusofcurvature442mmispressedagainstitindisplacementcontrolledmode.WhentheindenterisloadedagainstthesmoothportionoftheÞlm,devoidofanysubsurfacemicrostructure,acircularcontactareaappearsthediameterofwhichincreaseswiththedepthofindentation.However,whenindentedatthelocationofthesub-surfacemicrochannelsÞlledwithliquid,anon-circularcontactareaappears,thegeometricshapeandsizeofwhichvarywiththeskinthicknessabovethechannelandthedepthofindentation.Fig-ure6showstheopticalmicrographsofthecontactareainexperimentsinwhich Figure5.SchematicoftheexperimentinwhichanindenterisbroughtincontactwiththeÞlminadisplacementcontrolledmodeusinganano-positioner.ThecorrespondingloadismeasuredusingaweighingbalanceinterfacedwithacomputerandthecontactareaisvisualizedwithamicroscopeÞttedwithadigitalcamera. A.Majumderetal./JournalofAdhesionScienceandTechnology24(2010)2681–2692 Figure6.OpticalmicrographsshowthecontactareaoftheindenterandtheelasticÞlmwithasinglemicrochannelofdiameter50µmembeddedinside.ThechannelisÞlledwithsiliconeoilofvis-cosity380cPandsurfacetension20mN/m.Micrographs(a)Ð(d)representtheexperimentsinwhichwesubjectedaÞlmwithskinthickness5µmtoindentationdepths101µm,respec-tively.Micrographs(e)Ð(h)representÞlmswithskinthickness80µm,respectively;theindentationdepthismaintainedat11µm.Thescalebaris100µm.thehemisphericallensissymmetricallyalignedwithsub-surfacechannelsofdi-50µmburiedtodifferentskinthicknesses50Ð100µmwhilethedepthofindentationisvariedfrom6to100µm.Theseriesofopticalmicro-graphsshowthatthepresenceofthemicrochannelaltersthelocalmechanicsasaresultofwhichnon-circularcontactareawithnarrowcornersappears.Forsmallerindentationdepths,theeffectofthechannelbecomesmorepronouncedthanthatofthesmoothportionoftheÞlm:asaresult,theheightofthecontactissigniÞ-cantlylargerthanitswidth.Withincreaseintheindentationdepth,thefractionofcontactwiththesmootherportionoftheÞlmincreasesandasaresulttheratiodecreases.InFig.7,weplotasafunctionofforÞlmsinwhichtheskinthicknessvaries:5Ð25µm.AlargevalueofratioshowsthattheÞlmismoredeformablealongtheaxialdirectionofthechannelsthanperpendiculartoit.WecanrationalizethisobservationbyconsideringtheJKR(Johnson,KendallandRoberts)theory[21]ofadhesionwhichsuggeststhatforcontactofahemi- A.Majumderetal./JournalofAdhesionScienceandTechnology24(2010)2681–2692 Figure7.Theratioofheightandwidth,asobtainedfromopticalmicrographsinFig.6forÞlmsofvariousskinthicknesses:45and80µm(representedbysymbols,respectively)isplottedwithrespecttodepthofindentationnormalizedwiththediameterofthesphericalindenterwithasemi-inÞniteelastichalf-space,atzerocontactload,theradiusofthecontactareavarieswitheffectiveelasticmodulusoftheadheringbodiesas.Hencefortwodifferenteffectiveelasticmoduli,theratioofcontactareais.Drawinganalogytothisproblem,theeffectiveshearmodulusoftheÞlminthevicinityofthechannelcanbeobtainedintermsoftheratio,whereistheeffectiveshearmodulusofthelayerinthevicinityofthechannelforcontactalongthedirectionoftheaxisofthechannelandisthesameinadirectionperpendiculartoit.Usingrepresentativenumbers,e.g.,5forskinthickness5µm,isestimatedtobe1000.Theratiodecreasesasymptoticallyto1withincreaseinthicknessoftheskin,andthus,theratioincreaseswithincreaseintheskinthickness.AmoreexacttheoreticalanalysiswillberequiredtopredictcorrectlytheeffectiveelasticmodulusoftheÞlminthevicinityofthechannels.6.SummaryWehavepresentedhereanexampleofwettinginduceddeformationofasoftelastomericsubstrateinwhichsurfaceenergygetsconvertedtoelasticenergy.Inparticular,wehaveshownthatthesoft,thinwallofamicrochannel,embeddedin-sideasoft,ßatandelasticlayer,e.g.,PDMSbulgesoutwhenthechannelisÞlledwithaliquid,e.g.,siliconeoilwhichwetsitssurface.Butthesamedoesnothap-penwhenanon-wettingliquidlikewaterisused,asitdoesnotÞllinthechannelspontaneously.Inthecontextofwettingliquid,thebulgingoccursbytheinterplay A.Majumderetal./JournalofAdhesionScienceandTechnology24(2010)2681–269219.A.Ghatak,L.MahadevanandM.K.Chaudhury,,1277(2005).20.A.E.H.Love,MathematicalTheoryofElasticity.DoverPublishingLtd.,NewYork(1944).21.K.L.Johnson,K.KendallandA.D.Roberts,Proc.R.Soc.Lond.A,301(1971).