Interplay between Con fi nement, Twist Elasticity, and Intrinsic Chirality in Micellar Lyotropic Nematic Liquid Crystals - Dietrich et a

《Interplay between Con fi nement, Twist Elasticity, and Intrinsic Chirality in Micellar Lyotropic Nematic Liquid Crystals - Dietrich et a》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

pubs.acs.org/LangmuirArticleInterplaybetweenConfinement,TwistElasticity,andIntrinsicChiralityinMicellarLyotropicNematicLiquidCrystalsClarissaF.Dietrich,PerRudquist,PeterJ.Collings,andFrankGiesselmann*CiteThis:Langmuir2021,37,2749−2758ReadOnlineACCESSMetrics&MoreArticleRecommendations*sıSupportingInformationABSTRACT:Recentstudieshaveshownthatlyotropicnematicliquidcrystals(LLCs)areexceptionalintheirviscoelasticbehavior.Inparticular,LLCsdisplayaremarkablesoftnesstotwistdeformations,whichmayleadtochiraldirectorconfigurationsunderachiralconfinementdespitetheabsenceofintrinsicchirality.Thetwistedescapedradial(TER)andthetwistedpolar(TP)arethetworepresentativereflectionsymmetrybreakingdirectorconfigurationsinthecaseofcylindricalconfinementwithhomeotropicanchoring.WedemonstratehowsuchreflectionsymmetrybreakingofmicellarLLCsundercylindricalconfinementisaffectedbyintrinsicchirality,introducedbytheadditionofachiraldopant.Similaritiesanddifferencesbetweentheeffectsofintrinsicchiralityonthedefect-freeTERconfiguration,andontheTPconfigurationincorporatingtwohalf-unittwistdisclinationlines,arediscussed.IntheTPcase,topologicalconstraintsfacilitatestableheterochiralsystemseveninthepresenceofasmallamountofchiraldopant,withunusualregionsofrapidlyreversinghandednessbetweenhomochiraldomains.Atmoderatedopantconcentrations,theTPstructurebecomeshomochiral.Athighdopantconcentrations,forwhichtheinducedcholestericpitchismuchsmallerthanthediameterofthecapillary,thecholestericfingerprintstructuredevelops.210■INTRODUCTIONproportionaltos.Thiswouldbetheplanarpolar(PP)Thenematicliquidcrystal(LC)phaseisanorientationallyconfiguration,depictedinFigure1b.However,inmostcases,5ordered,uniaxialthree-dimensional(3D)liquidandexhibitstheescapedradial(ER)configurationisobtained,forwhichorientationalelasticity.Thelocalaveragedirectionofthedirectorisparalleltothecylinderaxisatthecenter,andcylindricalsymmetry,i.e.,thelocalaverageaxesofthesplay-bendstowardthesurface(Figure1c).TheERanisometricbuildingblocks,isdenotedbythedirectorn̂=configuration,importantly,doesnotcontainanysingularityDownloadedviaBUTLERUNIVonMay16,2021at13:09:51(UTC).n̂(r).Undervariousconfinements,includingspecificboundaryinthen̂field.conditions,thelowest-energyconfigurationcomprisescombi-Ithasbeenobservedthatincertainnematicsystemswithanationsofthethreebasicorientationaldeformations,splay,verysmalltwistmodulus,thenematicdirectorfieldinconfinedtwist,andbend,withcorrespondingelasticconstantsK11,K22,geometriesshowslocalreflectionsymmetrybreakingstruc-Seehttps://pubs.acs.org/sharingguidelinesforoptionsonhowtolegitimatelysharepublishedarticles.andK33.Forsomesurfaceboundaryconditions,K24mayalsotures,i.e.,thelowestelasticenergyisobtainedthrough1playarole.Insomecases,aminimuminthetotalelasticrelievingcostlysplayandbenddeformationwithlesscostlyenergyisobtainedbytheintroductionofoneormore11−17twistdeformation.Interestingly,achiralcylindricalcon-singularitiesinthedirectorfield,so-calleddefectssuchasfinementthenproducesachiraldirectorstructureevenifthedisclinations.Closetoasingularity,theelasticenergydensityLCmaterialitselfisintrinsicallyachiral.11,13,15,17Therefore,divergesandcontinuumelasticitythereforebreaksdown.OneboththeERandaconfigurationwithtwodisclinationsarewaytoavoidthedivergenceintheelasticenergyisforthereplacedbychiralstructures,withthesameprobabilityformaterialtoadoptastructureinwhichtheorderparameterofright-andleft-handedconfigurations.Recently,wereported2−4thephaseapproacheszerointhecoreofthedefect.reflectionsymmetrybrokenconfigurationsinlyotropicliquidAnotherpossibility,alsoexperimentallyobserved,isthat,ifcrystals(LLCs)ofdisklikemicellesundercylindricalconfine-5,6possible,thedefectinstead“escapesinthethirddimension”.ConsideracylindricalcapillarywithhomeotropicboundaryconditionsfilledwithanematicLC;cf.Figure1.Ifn̂isnormalReceived:December9,2020tothesurfaceattheboundary,thedirectorfieldmightRevised:January31,2021compriseans=+1linesingularityatthecenter.ThisiscalledPublished:February12,2021theplanarradial(PR)configuration;Figure1a.Intheory,thes=+1defectislikelytosplitupintotwos=1/27−9disclinations,astheelasticenergyarounddisclinationsis©2021AmericanChemicalSocietyhttps://dx.doi.org/10.1021/acs.langmuir.0c035002749Langmuir2021,37,2749−2758

1Langmuirpubs.acs.org/LangmuirArticleStartingfromtheERconfiguration,afiniteamountofchiraldopantinducesthetwistedescapedradial(TER)config-uration,whichwithincreasingdopantconcentrationbecomesunstabletohelicalundulationsalongthecylinderaxiswithapitchsignificantlylargerthanp.Whenstartingfromthetwistedpolar(TP)structure,wefindseveraldistinctregimes,forwhichthecapillaryconfinementimposeseitheralargerorsmallermacroscopictwistcomparedtotheintrinsiccholesterictwistexpectedfromthetwistingpowerofthechiraldopant.WhilethedisclinationfreeTERconfigurationisalwayshomochiralwithaddedchiraldopant,wefindthattheTPconfigurationmaybeheterochiralatsmallconcentrationsofchiraldopantwhenconfinementeffectsgovernthestructure.Thestructureinthisregimeisfurtherstabilizedbytopologicalconstraints.Butathigherdopantconcentrationswhereintrinsicchiralitybecomessignificant,theTPstructurebecomeshomochiral,asonehandednessofthetwistdeformationsisfavoredduetothedopant.Asexpected,whenpismuchsmallerthantheinnerdiameterDoftheFigure1.Possibleachiralnematicdirectorstructuresincylindricalcapillary,theconfinementlosesitsinfluenceonthestructurecapillariesunderhomeotropicboundaryconditions.Theradial(a)andthecharacteristic(bulk)fingerprinttextureoftheandplanarpolar(b)configurationscontainlinedefects(red),whilecholestericliquidcrystalisobserved.theescapedradialconfiguration(c)isfreefromdisclinations.Reprintedfromref11.■MATERIALSANDMETHODSThelyotropicliquidcrystal(LLC)usedasahostphaseinthisstudyis11mentaftermagneticfieldtreatment.Inparticular,wecouldaternarysystemcontainingN,N-ethylhexadecylammoniumbromideexplainthepeculiartwistedpolar(TP)configuration,where(CDEAB)asthesurfactant,decan-1-ol(DOH)asthecosurfactant,thetwohalf-unitdisclinationlinesmakeaseeminglyperfectanddoublydistilledwaterasthesolvent.Thecompositionofthehostdoublehelixalongthecapillary.Weproposedthatthereasonphaseis32.0wt%CDEAB,4.8wt%DOH,and63.2wt%water,asfortheobservedreflectionsymmetrybreakingwastheusedinref11.Atthisconcentration,thesurfactantandcosurfactantformationof(chiral)twistdisclinationsinsteadof(achiral)moleculesassemblethemselvesintodisk-shapedmicellesforminganematicNDphase;cf.Figure2a,b.Theshortaxesofthedisk-shapedwedgedisclinations,asaresultofapresumed,verysmallvalueofthetwistelasticconstantofthemicellarliquidcrystalsystem.Ourveryrecentmeasurementsoftheelasticconstantsofthismicellarlyotropicsystembymeansofdynamiclightscatteringmeasurementsrevealedthatthetwistconstantisindeedverysmall,about1orderofmagnitudesmallerthanthesplayandabout2ordersofmagnitudesmallerthanthebend18constant.Here,westudytheeffectsofchiraldopingonthereflectionsymmetrybrokenconfigurationsinthecaseoflyotropicdiscoticmicellarLCsconfinedtocylindricalcapillaries.SincethemicellarnematicLLCsystemofN,N-ethylhexadecylam-moniumbromide(CDEAB)/decan-1-ol(DOH)/water(H2O)isachiral,thereisnoenergeticbiasforeitherhandednessintheabsenceofachiraldopant.Hence,allreflectionsymmetrybrokendirectorconfigurationsundercapillaryconfinementcontainleft-andright-handeddomainswiththesameprobability.Thisdegeneracyisliftedwhenaddinganenantiomericchiraldopantofonehandedness,like(R)-mandelicacid((R)-MA).Generally,atverysmallconcen-trationsofadopant,thedirectorstructureisgovernedbyconfinement,whereasathighdopantconcentrations,thestructureisgovernedbytheintrinsicLCchirality.Withincreasingdopantconcentration,weseeaspectacularsetoftexturesrelatedtotheERandtwistedescapedradial(TER)configurationsorthemagneticallymediatedTPstructure.AtFigure2.(a)SchematicsofCDEAB,(b)disk-shapedmicellarbuildingblocks,(c)perspectiveviewofthehomeotropicboundarydopantconcentrationsforwhichthecholestericpitchpisconfinementinthecapillary,schematicallyshowingthemicellarequalorslightlylargerthanthecapillarydiameterD,thepitchorientationatthecapillarysurface,and(d)themolecularstructureofoftheresultinghelicalstructureisaresultofadelicate(R)-MA(d).Reprintedfromref11.(e)Phasetransitiontemperaturesinterplayamongconfinement,twistelasticity,andintrinsicasafunctionof(R)-MAconcentration.19Thestudiedregimeischirality.Forsimplicity,weusetheinversepitch,1/p,asamarkedinyellow;s=isotropicphase,c=crystallinephase,N*D=measureofthetwistofthestructure.chiraldiscoticnematicphase,andΦ=twophaseregions.2750https://dx.doi.org/10.1021/acs.langmuir.0c03500Langmuir2021,37,2749−2758

2Langmuirpubs.acs.org/LangmuirArticlemicellesarelong-range-orderedalongthedirectorn̂,whichcoincidesparticularlylow-energypenaltyrelatedtotwistdeformations,withtheopticalaxisoftheuniaxialNDphase,havingpositiveopticalwhichconformswellwiththeverylowvalueofthetwistelasticanisotropyandnegativemagneticanisotropy.CDEABandDOHwereconstantK22measuredinref18.Figure3showsacapillarypurchasedfromMerckKGaAandusedwithoutanyfurtherpurification.Thechiraldopantusedinthisstudyisthe(R)-enantiomerofα-hydroxyphenylaceticacid(=(R)-mandelicacid,abbreviatedas(R)-MA),purchasedfromAlfaAesarwith>99%purityand>99%enantiomericexcess.Thecapillarywallsprovidehomeotropicboundaryconditions,i.e.,thedirectorn̂alignsnormaltothecapillarywalls(Figure2c)withoutanysurfacemodificationneeded.Themolecularstructureof(R)-MAisshowninFigure2d.Notethatthecalculationofthemolarfractionoftheaddedmandelicacidincludesthewatercontentofthesystem.Sincemostofthemolarfractionsunderstudywereinthemillimolarregime,apossibledecreaseinthenematic-to-isotropicphasetransitiontemperaturesofthevariousmixturesupto0.1mol%canbeneglected(seethephase19diagraminFigure2e).Therefore,itwaspossibletocarryouttheexperimentsatroomtemperature.First,CDEABand(R)-MAweredissolvedindoublydistilledwater,afterwhichDOHwasadded.Forstirringthemixture,aglassvialwithascrewcapwasusedandsealedwithparafilmtopreventsolventFigure3.(a)SchematicsoftheTERstructuredrawnwithaleft-evaporation.Tohomogenizethemixtures,thesampleswerestirredinhandedtwistalongthecapillarydiameter.(b)Microphotographofathermoshaker(Biosan,PST-60HL)at40°Candputonarollerthecapillarywithleft-andright-handedTER(yellow)andER(black)(PhoenixInstruments,RS-TR05).Thehomogenizationtook5daysregionsintheachiralLLC.withalternatinguseofthethermoshakerandtheroller.Goodhomogenizationwasverifiedbyrotatingthevialtocheckforuniformviscosityandhomogenousflowandbyobservinguniformopticalwithcoexistingright-andleft-handedTERregionsintheretardationwithcrossedpolarizers.Themixtureswerefilledintothin-achiralLLCduringtheslowrelaxationtowardtheachiralERwalledglasscapillarieswithadiameterof700μmasusedinref11byconfiguration.Thechangesbetweenright-andleft-handedawaterpumpjet.Afterthecapillarywasfilled,bothendsweresealedregionsalongthecapillaryarecontinuousastherearenobymeltingtheglasswithalighter,andthesealwascarefullychecked.topologicalconstraintsbetweenthetwo.IntheTERAfterfillingthecapillaries,theLLCwasheatedintotheisotropicconfiguration,thesuperimposedtwistgoesalongthecapillaryphase(around50°C)sothatanypossibleeffectsofshearalignmentdiameter(Figure3a),whichcanbeseenbyabrighteningofduringthefillingprocesscouldberuledout.Photographsweretakenthedarkbrushalongtheaxisofthecapillaryundercrossedatroomtemperatureapproximately2weeksafterfillingandafterheatingto,andcoolingfrom,theisotropicphase.Apossibledemixingpolarizers(Figure3b).IntheachiralLLC,thetwosensesofofthephaseinacapillarywasruledoutbycheckingthetextureswithTERtwistareofcoursedegenerateandthereforeoccurwith(polarized)opticalmicroscopy.equalprobability.ThelocalsenseoftwistcanbecheckedbyFurthermore,polarizedopticalmicroscopywasusedtoanalyzethe11decrossingthepolarizers.InthecapillaryshowninFigure3,directorfieldswithinthefilledcapillaries.AsampleholderthattheTERconfigurationisdefect-freeoverthewholecapillaryallowedrotationofthecapillariesunderthemicroscopewasused(seeexceptnearthetwoendsofthecapillary.FigureS1aintheSupportingInformation).ToresolvetheLLCFigure4a−gshowshowtheERconfigurationisaffectedbytexturesundercapillaryconfinement,waterwasusedasanindexchiraldopingintheformof(R)-mandelicacidatdifferentmatchingfluid(IMF)tominimizetherefractioneffectsoftheglass,dopantconcentrations.Weknowthatatzerodopantallowingforobservationofthetextureacrosstheentirecapillary;seeFigureS1b,c,SupportingInformation.Thecapillarieswereplacedonconcentration,thegroundstateisER,butatfinitedopantamicroscopeslideunderthemicroscope,adropofwaterwasputonconcentrations,thegroundstateimmediatelybecomestop,andtheareawascoveredbyacoverslip.Microphotographswere(homo-)chiral,i.e.,TER.Forexample,at0.006mol%(FiguretakenwithaNikonD40camera.4a),thecenterregionalreadyappearshomogeneouslybrightABrukerB-E25Velectromagnetwithamaximummagneticfieldduetotheinduceddirectortwistalongthecapillarydiameter.strengthof1TwasusedfortheexperimentsinwhichamagneticfieldTherefore,ifthereisathresholdforanyreason,itmustbewasapplied.Thecapillarieswereinsertedwiththeirlongaxesparallelbelow0.006mol%,whichwouldcorrespondtosixchiraltothemagneticfield.Bymeansofahomemadetemperature-moleculesper100000nonchiralmolecules.Atdopantcontrolledsampleholder(seeFigureS1dintheSupportingconcentrationsbetween0.02and0.04mol%(Figure4b,c),Information),thesampleswereheatedintotheisotropicphaseandcooledslowly(0.2K/h)inthemagneticfield.theTERconfigurationisunstabletoundulationsalongthecapillary.Theundulationsgrowinamplitude(Figure4d−f)■andbecomeperiodic,adoptingasinusoidalappearance.RESULTSANDDISCUSSIONFurthermore,theperiodicitydecreaseswithincreasingdopantResults:TwistedEscapedRadialDirectorConfigu-concentration.Whenrotatingthecapillaryaboutitsaxis,theration.Aftercoolinganundopedsamplefromtheisotropicundulatedstructureappearstomovetotheright/leftphase,aninhomogeneousstructure,reminiscentofanematicdependingonthedirectionofrotation.Thissuggeststhatschlierentexture,isadopted,whichveryslowly(overweeks)theescapedirectionspiralsaroundthecapillaryaxis,relaxestowardtheERconfiguration.Inthelatterstageofthisreminiscentofaphonecordlikestructuregivingasinusoidalrelaxationprocess,TERregionsarereadilyobserved,buttheseappearance(Figure5).ThepitchofthespiralingescapeareeventuallyandcontinuouslyturnedintotheachiralERdirectionistherefore2timestheapparentperiodicityinthestructure.Theverylongrelaxationtimeisduetothelongpicture.Thestructureisnowtwistedbothalongthediameterwavelengthofthedeformations(∼1mm).Furthermore,theandalongthecylinderaxis,andwerefertothisconfigurationlong-termcoexistenceoftheTERandERstructuresindicatesaasthedoublytwistedescapedradial(DTER)configuration.In2751https://dx.doi.org/10.1021/acs.langmuir.0c03500Langmuir2021,37,2749−2758

3Langmuirpubs.acs.org/LangmuirArticleFigure5.EffectofchiraldopantontheERconfiguration;cf.Figure4.Thedirectorfieldistangentialtotheblue“witchhat”surfaceandpointstowardthetipofthehat.(a)Nodopant:the(ER)structureisachiralandtheescapedirectionisalongthecylinderaxis;cf.Figure1c.(b)Undulatedstructure,inwhichtheescapedirectionspiralsaboutthecapillaryaxisandadoptsa“phonechord”arrangement(c);cf.Figure4d,e.Thisisthedoublytwistedescapedradial(DTER)structure.(TheDTERstructurewascalledthe“twistedescapedradial20structure”intheworkofKitzerowetal.Here,weusethenotation“twistedescapedradialstructure”fortheconfigurationshownin13Figure4,asintroducedintheworkofJeongetal.ThisshouldnotFigure4.Observedtexturesoftheinvestigatedmicellarnematicbeconfusedwiththedoubletwiststructurescharacteristicofblueliquidcrystalwithdifferentchiraldopantconcentrationsincapillaries.phases.)Thebluecylindersin(c)representthedirectorfield.Thecapillarieswereslowlycooledfromtheisotropicphase.ourcase,wefindthatthephonecordlikestructureisalsoleft-handed,thesamehandednessinducedbythehelicaltwistingpower(HTP)inbulksamples.At∼0.070mol%(Figure4f),theperiodicityoftheaxiallyspiralingdirectorfieldapproximatelyequalstheinnerdiameterofthecapillary.Somewherebetween0.07and0.09mol%,thisperiodictexturebecomesunstableandtheLCadoptsarandomlyalignedcholestericfingerprinttexturewithahelixpitchofabout200μm;cf.Figure4g.ThegraphinFigure6depictstheinversepitchoftheDTERstructureasafunctionofthedopantconcentrationcomparedtotheintrinsiccholestericinversepitchofthedopedsystems.Evidently,theFigure6.Inversepitch(1/p),alsocalledtwist,oftheDTERstructuremacroscopictwistoftheDTERstructureissignificantlyasafunctionoftheconcentrationof(R)-mandelicaciddopant.Inasmallerthantheintrinsiccholesterictwist.bulksampleattheselowconcentrations,theinversepitchisResults:TwistedPolarDirectorConfiguration.Whenproportionaltotheconcentration(dashedline).thecapillariesareslowlycooled(0.2°C/h)fromtheisotropicphaseundertheapplicationofanaxial1Tmagneticfield,weseeacompletelydifferentsetofdirectorstructures.Withnomuchlessdefined(see,forinstance,therightmostpartofthechiraldopantadded,wereadilyobservetheformationoftwocapillaryinFigure7).Adetailedobservationofthelatterhalf-unitdisclinationlines;cf.Figure7.Inmajorpartsoftheregions(Figure8)revealsthepresenceofsharpkinksinthecapillaries,thetwolinesformawell-defineddoublehelixdisclinationlineswithaspacingofabout100μmalongthestructure.Thisisthetwistedpolar(TP)structure,describedinlines.Inthesmooth,puredouble-helixTPregions,thereareref11.ThepitchoftheTPstructure,pTP,oftheconfinednosuchkinks.AslightdecrossingofthepolarizersrevealsaachiralLCisabout5−10mm,i.e.,about10timeslongerthanlocalopticalactivity,whichchangessignatthesekinks.Hence,thecapillarydiameterof700μm.Asexpected,left-andright-whentheregionatonesideofakinkturnsorange/blueforonehandedTPregionsoccurwiththesameprobability.senseofpolarizerdecrossing,itturnsblue/orangefortheHowever,domainswithwell-definedTPheliceswithpitchoppositesignofdecrossing(seeFigure8c,d).pTParesometimesseparatedbyregionswherethereisWiththechiraldopantadded,wefindfourdifferentregimesseeminglynodoublehelixorwhereanyhelixisatleastintermsofthemacroscopicdirectorperiodicityofthehelical2752https://dx.doi.org/10.1021/acs.langmuir.0c03500Langmuir2021,37,2749−2758

4Langmuirpubs.acs.org/LangmuirArticleFigure7.Twistedpolar(TP)structurewithsmoothdouble-helixdomainsandregionswithcloselyspacedkinksinthetwodisclinationlines.waterintoaccount.ThecorrespondingHTP(takingwaterintoaccount)givesapproximately−0.09μm−1(mol%)−1.Forcomparison,weshowthevaluesoftheobservedTPpitch,pTP,andathigherconcentrations,thepitchdeterminedfromthecholestericfingerprintstructureinsidethecapillaries.First,atverylowchiraldopantconcentrations(0.006−0.025mol%),thestructureisTPandheterochiral;theTPconfigurationstillexhibitsleft-andright-handeddoublehelixdomains,oftenseparatedbyshorterregionswithkinks.AtFigure8.(a,b)Close-upofthekinksofthedisclinationlinesinanon-TPregion.Decrossing±10°ofthepolarizers(c,d)revealsthe0.025mol%chiraldopantconcentration,theintrinsicoppositesign(orange/blue,blue/orangeappearance)ofopticalcholestericpitchpisalreadymuchsmallerthanpTP,butthisactivitybetweenkinks.isnotreflectedinpTP.Hence,inthisregime,theintrinsiccholesterictwistiscounteractedbythecapillaryconfinement.structureinthecapillaries,dependingonthedopantAtaconcentrationof0.030mol%(correspondingto0.16concentration.Figure9adisplaysmeasuredvaluesfromwt%(R)-mandelicacid),thesystementersasecondregimeby21Hiltropetal.ofthecholestericpitchpandtheinversebecominghomochiral,left-handedTP.Furthermore,therearepitchintheabsenceofconfinementeffects,i.e.,thepitchnoregionswithkinksinthedisclinationsanymore.Evenwhenresultingfromthehelicaltwistingpower(HTP)ofthedopantusingstatisticsfrommanysamples,wecouldnotconfirmanforthesamematerialsystem.Thetwistsenseinducedby(R)-increaseinthepresenceofleft-handedtwistdomainsatthemandelicacidinthissystemisleft-handed.NotethatHiltropetal.calculatedtheHTPfromthemolarratioofthedopanttoexpenseofright-handedonesatincreaseddopantconcen-thesurfactantandcosurfactant,nottakingtheamountofwatertrationsrangingfrom0to0.025mol%.Inthehomochiralintoaccount.ThepinkdatapointsinFigure9awereregime,theTPdoublehelixisleft-handedovertheentirerecalculatedfromtheoriginalvalues,takingtheamountoflengthofthecapillary,whichisabout5cm.Theleft-Figure9.(a)ComparisonofthemeasuredTPpitch,thepitchdeterminedfromthefingerprintpattern,andthecholestericpitchofabulksample.Thecolorcodecorrespondstotheregimes(b)−(e).(b)HeterochiralandhomochiralTPstructureswherepTPismuchlargerthanthecapillarydiameterD.(c)TPstructurewherepTPismuchsmallerthanD.Thepitchlinesfromthecholestericpitchpmakeachevronatthecenterofthecell(seeexplanationinthetext).2753https://dx.doi.org/10.1021/acs.langmuir.0c03500Langmuir2021,37,2749−2758

5Langmuirpubs.acs.org/LangmuirArticlehandednessofthedoublehelixisgovernedbythesignofthetwistelasticityoftheformer.Thecylindricalconfinementhelicaltwistingpowerofthedopant.easilyenhancesanytwistpromotedbytheintrinsicchirality.InThesystemseemstobecomehomochiralwithanincreaseinthermotropicLCs,whereallthreeelasticconstantsareofthetheamountofthedopantatthesamepointaswhenpTPstartssameorderofmagnitude,possibly,thereisnosuch“twisttodecrease.Ataround0.060mol%,pTPisclearlyinfluencedenhancement”effectfromcylindricalconfinementandthebythedopant,andataboutthisconcentration,theperiodicityTER(ifpresent)isnotobservable.oftheTPdoublehelixshrinksabruptly.Furthermore,theDiscussion:TPconfiguration.IncontrasttotheER20disclinationlinesarepushedtowardthecapillarysurface.scenarioobservedbyKitzerowetal.,describedabove,thereAtevenhigherdopantconcentrations(≥0.9mol%),aisnopriorsimilarstudyreportedconcerningtheinfluenceofcholestericfingerprinttexturesuperimposesitselfontheTPintrinsicchiralityandcholestericpitchontheTPconfig-configurationandanevenmorecomplexstructureisobtained,uration.WethereforediscusstheTPcaseinmuchmoredetail.whereboththeTPdouble-helixdisclinationlinesandTPwithNoChiralDopant.ThepureTPstructureischolestericpitchlines(fingerprinttexture)arepresentatthestabilizedbytheformationoftwistdisclinationsinsteadofsametime.Thestripesofthefingerprintstructure,theperiodplanarwedgedisclinationsasaresultoftheverylowtwistaofwhichrepresentsthedistanceof180°rotationofthemodulusoftheLC.Theoverallstructure(Figure10)exhibitsspiralingdirector,formachevronatthecenterofthecapillary(seeFigure9e).Discussion:TwistedEscapedRadialConfiguration.Complexchiralnematicliquidcrystalstructureshavebeen22−2420,25investigatedtheoreticallyandexperimentally.Kitzer-owetal.studiedathermotropicchiralnematicLCconfinedin20cylindricalcapillarieswithhomeotropicboundaryconditions.Theirsystemexhibitedatemperature-dependentpitchwithsigninversionatacertaintemperature.Bychangingthetemperatureofthesample,theycouldthereforeelegantlystudytheevolutionofthetextureasafunctionofthemagnitudeandhandednessofthecholestericpitchp.Attheinversiontemperature,i.e.,whenpbecameinfinite,thesampleadoptedthe(nontwisted)ERconfiguration.Awayfromthistemper-ature,thesamplefirstadoptedtheundulatingstructurebeforeapproachingtheexpectedfingerprinttexturewhenthepitchbecamesmallcomparedtothecapillarydiameterD.TheobservationsbyKitzerowetal.seemanalogoustowhatweobserveinourlyotropicsystem,exceptforourobservationofthetwistedescapedradial(TER)configurationatsmalldopantconcentrations.(Notethatthestatedenoting“twistedescapedradial”byKitzerowetal.correspondstoaspiralingoftheescapedirectionandhencetheDTERstate,Figure5,inourstudy.)Animportantdifferencebetweenthetwostudies,inadditiontothedifferenceintypesofLCsstudied(thermotropicand20lyotropic,respectively),isthatwhileKitzerowetal.couldFigure10.SchematicrepresentationoftheTPstructureinacontinuouslytunethecholestericpitchbychangingthecylindricalcapillarywithinnerdiameterD.Thedisclinationlinesaretemperatureinasinglecapillarysample,wehadtomakemarkedinredandthedirectorisrepresentedbybluecylinders.In(a),separatesamplesforeachpitchvalue,i.e.,onesampleforeachthetransverseandaxialtwistsareofthesameorderofmagnitude,anddopantconcentration.WhileitispossiblethatthetwopTP∼4D.In(b),pTP=∞andthedirectortwists180°betweenthedifferentsamplehistoriesmightproducedifferentresults,therenowparallellinedefects.In(c),pTP≪Dandthetransversetwistisnoreasontosuspectthattheoverallbehaviorrelativetotheapproacheszero.Thedirectorfieldaroundthetwistdisclinationlinescholestericpitchandthecylinderdiametershoulddifferisnotshown.significantlyinthetwoexperiments.Hence,inbothcases,asthepitchapproachesthediameter,theescapedirectionstartstwistofthedirectoralongthecapillaryaxis(axialtwist),aswelltospiralaboutthecylinderaxis,andasthepitchbecomesastwistnormaltotheaxis(transversetwist).Theaxialtwistismuchsmallerthanthediameter,thefingerprintstructureclearlydisplayedinthedoublehelixoflinedefects,whiletheappears.transversetwistisdisplayedinthelackofopticalextinctionTheextremelyslowrelaxationfromTERtoERisanotherbetweencrossedpolarizerswhenthetransversetwistaxisisstrongindicationthattwistdeformationscostverylittleenergy,alongtheviewingdirection(markedwith“O”inFigure10a)i.e.,thatthetwistmodulusissmallinthestudiedmicellarLC.andbytheasymmetriccolorshiftwhendecrossingthe11Importantly,thereareneithertopologicalconstraintsnoranpolarizers.TheaxialandtransversetwistdeformationshaveenergybarrierbetweenERandTERand,asaconsequence,athesamehandedness(inFigure10a,thetwotwistsareleft-finiteamountofchiraldopantimmediatelyturnsERtoTER.handed)andtheyaremutuallycoupled.IftheaxialtwistgoesFurthermore,thefactthattheTERstructureisobservedinthetozero(i.e.,theTPpitchpTPgoestoinfinity),thelinedefectslyotropicLCsbutisnotmentionedinthethermotropicLCbecomeparallelandthetotaltransversetwistbetweenthe20studiedbyKitzerowetal.isprobablyduetotheverysoftdefectsbecomes180°;cf.Figure10b.Ontheotherhand,ifthe2754https://dx.doi.org/10.1021/acs.langmuir.0c03500Langmuir2021,37,2749−2758

6Langmuirpubs.acs.org/LangmuirArticleaxialtwistgoestoinfinity(i.e.,pTPgoestozero),thetransverseextensivetheoreticalstudyofthebranchingfroma+1defecttotwistbecomeszero;cf.Figure10c.Inadditiontotheaxialandtwo1/2disclinationsasafunctionofthecylinderdiametertransversetwistdeformationsshowninFigure10,therearetheusingtheoneelasticconstantapproximation.However,thelocaltwistdeformationsclosetothedisclinationlines(seethecaseofsofttwistelasticityandthereforetheformationofchiralSupportingInformation,FigureS2).Forelasticreasons,twisttwistdisclinationshasnotbeenconsideredyet.disclinationsalwaysinvolvebothsensesofdirectortwist.Inthedouble-helixTPconfiguration,thetwistdeformationsHence,betweenthetwistdisclinationandtheinnercapillaryaroundthetwodisclinationlineshavethesamesenseofsurface,thereisasmallregionofweakminortwistwithchirality,i.e.,wecandescribeeachpairofdisclinationsasrightoppositesensecomparedtothemajortwistofthedisclinationhanded−righthanded(RR)orlefthanded−lefthanded(LL)andthedoublehelix(fordetailsseetheSupporting(seeFigure12).IntheachiralLLCsystemcase,RRandLLInformation,FigureS2).Whenaddingachiraldopantthatmustbeformedwiththesameprobability.But,ifthetwosupportsthemajorleft-handedtwist,theminorright-handeddisclinationsareformedwithoutmutualinfluence,wecouldtwistregion,disfavoredbythedopant,islikelypushedoutalsoimaginethatthecombinationsrighthanded−lefthandedfromthevolume,makingthedisclinationsapproachtheinner(RL)orlefthanded−righthanded(LR)mightoccur,i.e.,thatcapillarysurface,whichinfactisobservedinoursystem.Inthisthetwolinescanhavetheoppositechirality(seeFigure11,reasoning,wehaveassumedthattheconcentrationofthebottomandmiddle).Inthiscase,thetwolinestendtospiralinchiraldopantisthesameeverywhereinthesample.Onecouldoppositedirectionsand,hence,thereisnodoublehelixenvisagethatchiraldopantmoleculesareattractedtoregionsformed.Rather,thetwolinesintheRL(aswellasintheLR)withtwistmatchingthesignofthehelicaltwistingpowerofsituationazimuthallyheadtowardeachotherastheymovethedopant.Inprinciple,suchtwist-inducedlocalenrichmentalongthecapillary(seetheSupportingInformation,FigureS3,ordepletionofchiraldopantcouldhaveasecond-ordereffectforanillustration).But,whenthelinesapproacheachother,onthedetailedstructure.thetotalelasticenergyincreases.Toavoidthis,theyfliptheirImportantly,theTPstructureonlyappearswhenthesystemrespectivechiralities(fromRLtoLR),repeatingthisprocessisslowlycooledfromtheisotropicphaseunderanaxialmoreorlessregularlyalongthecapillary,andthereforemagneticfieldH.WeproposethattheH-fieldsqueezestheapproximatelykeepthelinesatamaximumdistance.directorintoaplanenormaltothecylinderaxisduetotheMacroscopically,itlooksliketwoparalleldisclinationlinesnegativemagneticsusceptibilityanisotropy.Incombinationrunningalongthecapillary,butaclose-uplook(Figure8)withthehomeotropicboundaryconditions,aplanarradialrevealsthedistinctkinkswheredisclinationchiralityflips.configurationwithas=+1centerdisclinationline(Figure1a)Importantly,ifonlyoneofthedisclinationlinesflipsitsisthenpromoted.Thisstructureis,however,notstablebutchirality,e.g.,LR→RRorLR→LL,thestructureischangedshouldbranchintoalessenergeticallycostlystructurewithtwointothepureTPstructurewithawell-defineddoublehelix1/2disclinations.TheactionofthemagneticfieldcanbewithapitchpTPovermacroscopicdistances.ThisscenarioillustratedasinFigure11.WhentheH-fieldisswitchedoff,thewouldexplainthe,oftenobserved,coexistenceofright-handedsystemcannotgobackfromthelocalminimumstate(TP)toandleft-handedTPdomains,separatedbyregionswithnotheglobalminimumERstatewithoutpassingtheenergeticallymacroscopicdoublehelixbutwithapproximatelyparallel,costlyPRstate.Asaresult,themagneticfield-inducedTPstaterapidlykinking,disclinationlines(schematicallyillustratedinpersistsforverylongtimes.Shamsetal.7−9havemadeanFigure12,middle).Fromthefactthatthedouble-helixTPstructureseemstobeprevalent,wemightdrawtheconclusionthattheRRandLLconfigurationsinfacthavelowertotalenergythanthemixedRLandLRconfigurations.TheremainingquestionnowiswhyLL,RR,RL,andLRstructurescoexist,i.e.,whyareonlytheLLorRRstructuresnotadopted?ThereasonfortheformationofeitherRR/LLorRL/LRregionsinanappliedH-fieldcouldberelatedtothedegreeofthemutualelasticinteractionbetweenthetwistdisclinationsduringtheirformation.WeknowthattheERgroundstateisachiral,i.e.,thesplay-benddeformationisnotenergeticallycostlyenoughtoberelievedbytwistdeformation(TER).However,undertheaxialH-field,thesplay-bendregionisconfinedtoanarrowregionclosetothecenterofthecapillary.Onemightenvisagethatinthishighlysqueezedstate,partsofthenowenergeticallycostlysplayandbenddeformationsarepartlyreplacedbytwistdeformationand,hence,reflectionsymmetrybreakingoccurswithacertainTERhandedness.Ifthefurtherbranchingintotwo1/2disclinationsoccursfromthisfield-inducedchiralTERstate,wecouldhypothesizethatthechiralityaroundbothdisclinationlineswouldhavetheFigure11.(a)WhenastrongaxialmagneticfieldHisapplied,thesamesign,i.e.,RRorLL.Ontheotherhand,ifthebranchingenergybalanceamongtheER,PR,andPP/TPstatesisshiftedandainsteadoccursfromaperfect,field-inducedplanarradialstatetransition,likelyviatheintermediatePRconfiguration,tothenewlowest-energystatePP/TPoccurs.(b)WhentheH-fieldisswitched(whichinfactisachiral),ordirectlyattheisotropic-to-nematicoff,therelaxationbacktotheERconfigurationishinderedasthetransitiononslowcooling,the(chiral)interactionbetweentheintermediatePRstate,withans=+1disclination,providesanenergytwolinesformingshouldbesmallerthaninthe“squeezed”barrier.state.Therefore,thechiralityadoptedbyeachofthetwo2755https://dx.doi.org/10.1021/acs.langmuir.0c03500Langmuir2021,37,2749−2758

7Langmuirpubs.acs.org/LangmuirArticleFigure12.SchematicillustrationsofproposedstructuresinaTPcapillary.Top:cylindricalcapillarywherethedisclinationlinesareindicated.TwooppositelytwistedTPdouble-helixdomainswithdisclinationchiralitiesRRandLLareseparatedbyamixedregionwithRLchiralities.RRgivesaright-handedwhileLLgivesaleft-handedTPhelix(seetheSupportingInformation,FigureS2).Bottom:illustrationofthecorrespondingdirectorconfigurationsintheRR,RL,andLLcases.Bluecylindersrepresentthelocaldirectorplacedonstringsinacircularframe,representingthecylinder26walls.Thiswayofillustrating3DdirectorstructuresisinspiredbytheworkofBouligand.singularitiesismoremutuallyindependent;therefore,LRanddependentonthehistoryofthesample,i.e.,magneticfieldRLconfigurationsmightbeallowed.Aperfectfield-inducedtreatment,coolingspeed,etc.,aswellasthecapillaryplanarpolarstateshouldinfacthave(achiral)wedgedimensions.Therefore,wecannotdefinesuchathresholdfordisclinations,which,onremovaloftheH-field,shouldbechiralinduction,atwhichtheTPbecomeshomochiral.Ontransformedinto(chiral)twistdisclinations.Tofinallyresolveaddingmorechiraldopant,pfurtherdecreasesandthetheseissues,however,itwouldbenecessarytoobservetheunwindingeffectfromthecapillaryconfinementfadesaway.IncapillariesusingthemicroscopewhiletheH-fieldisapplied.Inthisregime,pTPisstronglyinfluencedbythedopantandfact,suchinvestigationsmightalsoprovidenewinformationapproachesthecholestericpitchpfromabovewhilepaboutthefundamentalquestionofthenatureofthes=+1continuestoslowlydecreasewithincreasingdopantconcen-defectcore,i.e.,whetherthecoreofthedefectinducedbythetration.Atthesametime,thetransversetwist(seeFigure10)magneticfieldisachiralorchiral(becauseifanisotropicanddecreases.WenowgetintoaregimeinwhichpTPisclosetopescaped,itislikelytobechiralwhenthetwistelasticconstantandmuchsmallerthanthediameterofthecapillary.Hence,isverysmall).theelasticpenaltyrelatedtothedecreasingdistancebetweenTPwithChiralDopant.InFigure9a,thecholestericpitchpthedisclinationlinesinconsecutiveturnsoftheTPdoubleandtheinversepitch1/pasfunctionsofchiraldopantarehelixstronglyincreases.Asaresult,pTPself-limitsandbecomesshown(pinkcurves).Obviously,inthelimitofzerochiralessentiallyfixedwhilepcontinuestodecrease.Thisleadstoandopant,pgoestoinfinityandpTPissolelydeterminedbytheinstabilityanda“chevronstructure”isformed,withthecapillarydimensionsandtheelasticconstantsoftheLC.Inthischolesterichelixsymmetricallytiltedawayfromthecapillaryregime,thechiralityoftheLChaslittleornoinfluenceontheaxis;Figure9,bottom.TPstructure.Hence,thecapillaryconfinementwindstheLCWecanqualitativelyunderstandtheinstabilityanddirectorstructureintoaTPhelixwithpTP≪p.ThisisfurtherformationofthischevronfingerprintconfigurationfromtheverticalchevronformationinsmecticC*electroopticdevicereflectedinthefactthatbothright-andleft-handedTPhelices27−34cells.Intheso-calledbookshelfgeometry,thesmecticAareobserved;thecapillariesareheterochiral.Butatadopantlayersareverticallyarrangedbetweenthetwoglassplateslikeconcentrationof∼0.010mol%,p≈5mmissmallerthanour27−34booksinabookshelf.WhenthesmecticA-to-smecticCmeasuredpTP,i.e.,pp”.Furthermore,abovethisconcentration,weonlywhilethepinnedsmecticAperiodicityatthesurfaceobserveonehandednessoftheTPstructure,i.e.,thecapillarycorrespondstothetopologically,andelastically,locked-inpTP.hasbecomehomochiral.Asimilarchangefromheterochiraltohomochiralreflectionbrokensymmetryconfigurationswhenaddingachiraldopantintoacylindricallyconfinedchromonic■CONCLUSIONS25LCwasdescribedbyEunetal.forachromonicLCinTheinterplaybetweenconfinement-inducedchiralityandcapillarieswithplanaranchoring.Theydiscussedtheirinherentchiralityoftheliquidcrystalproducesarichvarietyobservationsintermsofadopantconcentrationthresholdoftexturesandphenomena.Themainfeaturesaregovernedbyforchiralinduction.IntheTPcase,theadoptedstructureistherelativeinfluencesofconfinementandintrinsicchirality,for2756https://dx.doi.org/10.1021/acs.langmuir.0c03500Langmuir2021,37,2749−2758

8Langmuirpubs.acs.org/LangmuirArticlewhichthelatterincreaseswithchiraldopantconcentration.InCompletecontactinformationisavailableat:ourcylindricallyconfinedmicellarlyotropicsystem,thehttps://pubs.acs.org/10.1021/acs.langmuir.0c03500remarkablesoftnesstotwistdeformationsincombinationwithanaxialmagneticfieldleadstothetopologicallystabilizedAuthorContributionstwistedpolardirectorconfiguration.IntheachiralLCcase,Themanuscriptwaswrittenthroughthecontributionsofallbothleft-andright-handedTPdoublehelicesarefoundwithauthors.Allauthorshavegivenapprovaltothefinalversionofthesameprobability.Whenaddingachiraldopant,onethemanuscript.handednessoftheTPstructureispromoted.ThisistrueforNotesthehandednessofthetwistaroundthedisclinations,theTheauthorsdeclarenocompetingfinancialinterest.transversetwist,andtheaxialtwist,allofwhichadoptthesamesenseoftwistsetbythehelicaltwistingpowerofthedopant.■ACKNOWLEDGMENTSAtverysmalldopantconcentrations,thedopanthasverylittleTheauthorsgratefullyacknowledgefinancialsupportfromtheeffectontheTPstructureandthesampleisstillheterochiral.AlexandervonHumboldtFoundation.TheyalsothankZoeyS.Whenincreasingthedopantconcentration,theTPstructureDavidsonforthehelpfuldiscussions.becomeshomochiralbuttheTPpitchismuchlargerthantheintrinsiccholestericpitch.Atevenhigherdopantconcen-■trations,pTPapproachesthecholestericpitch,butelasticABBREVIATIONSrepulsionbetweenthedoublytwisteddisclinationlinesLC,liquidcrystal;LLC,lyotropicliquidcrystal;TER,twistedpreventspTPfromfollowingpwhenp≪D.Theresultingescapedradialdirectorconfiguration;TP,twistedpolarinstabilityinducesachevroninthecholestericfingerprintdirectorconfiguration;n̂,director;K11,splayelasticconstantstructure.Finally,whenpbecomesmuchsmallerthantheofthenematicphase;K22,twistelasticconstantofthenematiccharacteristicdimensions(thediameterofthecapillary),thephase;K33,bendelasticconstantofthenematicphase;s,capillaryconfinementhasnoeffectonthecholestericstructurestrengthofadefect/disclination;ER,escapedradialdirectorandarandom,bulkcholestericfingerprinttextureisobserved.configuration;CDEAB,N,N-ethylhexadecylammoniumbro-Importantly,althoughweseeanevolutionfromheterochiralmide;DOH,decan-1-ol;D,diameterofthecapillary;p,tohomochiralTPstructureswithincreasingdopantconcen-cholestericpitch;ND,nematicphaseofdisk-shapedbuildingtration,thereisnosharpthresholdforchiralinductioninthisblocks;(R)-MA,(R)-mandelicacid;IMF,indexmatchingconfiguration.Inthissense,theescapedradialstructureisfluid;DTER,doublytwistedescapedradialdirectorconfig-muchmoresensitivethanthetwistedpolarconfigurationtouration;pTP,pitchofthetwistedpolarstructure;H-field,chiraldoping.Thereasonforthisisthatthereisneitheramagneticfield;PR,planarradialdirectorconfiguration;PP,topologicalconstraintnoranenergybarrieringoingfromtheplanarpolardirectorconfiguration;RR,righthanded−rightachiralERstructuretothechiralTERstructure.handed;LL,lefthanded−lefthanded;RL,righthanded−left■handed;LR,lefthanded−righthandedASSOCIATEDCONTENT■*sıSupportingInformationADDITIONALNOTEaTheSupportingInformationisavailablefreeofchargeatThetermtwistdisclinationisusednottorefertoapuretwisthttps://pubs.acs.org/doi/10.1021/acs.langmuir.0c03500.disclinationbuttodenoteadisclinationthatisnolongerapurewedgedisclinationduetotheintroductionoftwist.Experimentaldetails,e.g.,thesampleholderusedandtheeffectofusingwaterastheindexmatchingfluid(Figure■S1)anddetailedschematicsofthetwistdisclinationsREFERENCESandhowthetwistsensearoundthetwistdisclinations(1)Kralj,S.;Žumer,S.Saddle-splayelasticityofnematicstructuresconfinedtoacylindricalcapillary.Phys.Rev.E1995,51,366−379.affectsthetransverseandtheaxialtwistsofthetwisted(2)Schopohl,N.;Sluckin,T.J.Defectcorestructureinnematicpolardirectorconfiguration(FiguresS2andS3)(PDF)liquidcrystals.Phys.Rev.Lett1987,59,2582−2584.(3)Susser,A.L.;Harkai,S.;Kralj,S.;Rosenblatt,C.Transitionfrom■escapedtodecomposednematicdefects,andviceversa.SoftMatterAUTHORINFORMATION2020,16,4814−4822.CorrespondingAuthor(4)Ericksen,J.L.InLiquidCrystalsandOrderedFluids:ProceedingsFrankGiesselmann−InstituteofPhysicalChemistry,ofanAmericanChemicalSocietySymposiumonOrderedFluidsandUniversityofStuttgart,70569Stuttgart,Germany;LiquidCrystals,HeldinNewYorkCity,September10−12,1969;orcid.org/0000-0002-9974-9470;Johnson,J.F.;Porter,R.S.,Eds.;SpringerUS:Boston,MA,1970;ppEmail:f.giesselmann@ipc.uni-stuttgart.de181−193.(5)Meyer,R.B.OntheexistenceofevenindexeddisclinationsinAuthorsnematicliquidcrystals.Philos.Mag.1973,27,405−424.ClarissaF.Dietrich−InstituteofPhysicalChemistry,(6)Cladis,P.E.;Kléman,M.Non-singulardisclinationsofstrengthUniversityofStuttgart,70569Stuttgart,GermanyS=+1innematics.J.Phys.France1972,33,591−598.PerRudquist−MicrotechnologyandNanoscience,Chalmers(7)Shams,A.;Yao,X.;Park,J.O.;Srinivasarao,M.;Rey,A.D.UniversityofTechnology,41296Göteborg,Sweden;Theoryandmodelingofnematicdisclinationbranchingundercapillaryconfinement.SoftMatter2012,8,11135.orcid.org/0000-0002-7421-9617(8)Shams,A.;Yao,X.;Park,J.O.;Srinivasarao,M.;Rey,A.D.PeterJ.Collings−Departmentof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