Soft matter physics: an introduction PDF
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Soft Matter Physics: An Introduction Maurice Kleman Oleg D. Lavrentovich Springer Partially Ordered Systems EditorinChief: L.Lam SanJoseStateUniversity SanJose,California,USA EditorialBoard: E.Guyon D.Langevin E`coleNormaleSupe´rieure LaboratoiredePhysiquedesSolides Paris,France Baˆtiment510 Universite´ParisdeSud H.E.Stanley F-91405Orsay,France BostonUniversity Boston,Massachusetts,USA AdvisoryBoard: G.Ahlers J.Charvolin UniversityofCalifornia InstitutLaue-Langevin SantaBarbara,California,USA Grenoble,France W.Helfrich P.A.Lee FreieUniversita¨t MassachusettsInstituteofTechnology Berlin,Germany Cambridge,Massachusetts,USA J.D.Litster D.R.Nelson MassachusettsInstituteof HarvardUniversity Technology Cambridge,Massachusetts,USA Cambridge,Massachusetts,USA M.Schadt Hoffman–LaRoche Basel,Switzerland Springer NewYork Berlin Heidelberg HongKong London Milan Paris Tokyo Partially Ordered Systems Editorial Board: L. Lam•E.Guyon •D. Langevin•H.E.Stanley SolitonsinLiquidCrystals LuiLamandJacquesProst,Editors Bond-OrientationalOrderinCondensedMatterSystems KatherineJ.Strandburg,Editor DiffractionOpticsofComplex-StructuredPeriodicMedia V.A.Belyakov FluctuationalEffectsintheDynamicsofLiquidCrystals E.I.KatsandV.V.Lebedev NuclearMagneticResonanceofLiquidCrystals,SecondEdition RonaldY.Dong ElectroopticEffectsinLiquidCrystalMaterials L.M.BlinovandV.G.Chigrinov LiquidCrystallineandMesomorphicPolymers ValeryP.ShibaevandLuiLam,Editors Micelles,Membranes,Microemulsions,andMonolayers WilliamM.Gelbart,AvinoamBen-Shaul,andDidierRoux PatternFormationinLiquidCrystals A.BukaandL.Kramer,Editors Spatio-TemporalPatternFormation D.Walgraef Sands,Powders,andGrains:AnIntroductiontothePhysics ofGranularMaterials J.Duran ChiralityinLiquidCrystals Heinz-SiegfriedKitzerowandChristianBahr,Editors SoftMatterPhysics:AnIntroduction MauriceKlemanandOlegD.Lavrentovich Maurice Kleman Oleg D. Lavrentovich Soft Matter Physics An Introduction Foreword by J. Friedel With256Illustrations,4inFullColor 1 Springer MauriceKleman OlegD.Lavrentovich LaboratoiredeMine´ralogie-Cristallographie ChemicalPhysicsInterdisciplinary deParis Program Universite´PierreetMarieCurie LiquidCrystalInstitute 4PlaceJussieu,Case115 KentStateUniversity F-75005Paris Kent,OH44242 France USA [email protected] [email protected] EditorialBoard: LuiLam DominiqueLangevin DepartmentofPhysics LaboratoiredePhysiquedesSolides SanJoseStateUniversity Baˆtiment510 OneWashingtonSquare Universite´ParisdeSud SanJose,CA95192 F-91405Orsay USA France EtienneM.Guyon H.EugeneStanley E´coleNormaleSupe´rieure CenterforPolymerStudies 45RueD’Ulm PhysicsDepartment F-75005Paris BostonUniversity France Boston,MA02215 USA Coverillustration:PaintingbyJacksonPollock:ShimmeringSubstancefromtheSoundsintheGrassSeries. (1946)Oiloncanvas,301/8x241/4”(76.3x61.6cm).TheMuseumofModernArt,NewYork.Mr.andMrs. AlbertLewinandMrs.SamA.LewisohnFunds.Photograph(cid:1)c 2001TheMuseumofModernArt,NewYork. LibraryofCongressCataloging-in-PublicationData Kleman,Maurice. Softmatterphysics:anintroduction/MauriceKleman,OlegD.Lavrentovich. p. cm.—(Partiallyorderedsystems) Includesbibliographicalreferencesandindex. ISBN0-387-95267-5(alk.paper) 1. Softcondensedmatter. 2. Order-disordermodels. I.Lavrentovich,OlegD. II.Title III. Series. QC173.458.S62K552001 (cid:2) 530.413—dc21 2001020449 ISBN0-387-95267-5 Printedonacid-freepaper. (cid:1)c 2003Springer-VerlagNewYork,Inc. Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermission ofthepublisher(Springer-VerlagNewYork,Inc.,175FifthAvenue,NewYork,NY10010,USA),exceptforbrief excerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorage andretrieval,electronicadaptation,computersoftware,orbysimilarofdissimilarmethodologynowknownor hereafterdevelopedisforbidden. Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenot identifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietary rights. PrintedintheUnitedStatesofAmerica. 9 8 7 6 5 4 3 2 1 SPIN10556875 www.springer-ny.com Springer-Verlag NewYork Berlin Heidelberg AmemberofBertelsmannSpringerScience+BusinessMediaGmbH Foreword Introductions to solid state physics have, ever since the initial book by F. Seitz in 1940, concentratedonsimplecrystals,withfewatomspercell,bondedtogetherbystrongionic, covalent,ormetallicbonds.Referencestoweakerbonds,suchasvanderWaalsforcesin raregases,ortogeometricorchemicaldisorder(e.g.,alloysorglasses)havebeenlimited. The physicalunderstandingof thisfieldstartedwellbeforeSeitz’sbookandledtoa number of Nobel prizes after the last war. Applications cover classical metallurgy, elec- tronics,geologyandbuildingmaterials,aswellaselectricalandionictransport,chemical reactivity,ferroelectricityandmagnetism. But in parallel with this general and well publicized trend, and sometimes earlier as farasphysicalconceptswereconcerned,anexplorationandincreasinglysystematicstudy of softer matter has developed throughthe twentiethcentury. More oftenin thehands of physical chemists and crystallographers than those of pure physicists, the field had for a longtimeareputationofcomplexity.Ifprogressinpolymerswassteadybutslow,interest inliquidcrystalshadlaindormantforfortyyears,afterabrightstartlastingthrough1925, to be revived in the late 1960s based on their possible use in imaging techniques. The optoelectronicpropertiesofthefieldingeneralareevenmorerecent. Maurice Kleman’s initial research interests have been in the study of magnetoelastic effects in ferromagnetic crystals and films, a field where he was able to apply Kro¨ner’s techniquesofinfinitesimaldislocationstothestudyofinhomogeneousmagnetisminwalls, lines,andpoints,asinitiatedbyP.WeissanddevelopednotablybyL.Ne´el.WhenP.G.de GennesstarteddevelopinganinterestinliquidcrystalsinOrsay,itwasnaturalforKleman to turn his own attention to this field, where many mesoscopic phenomena have to be attacked fromsomewhatsimilar pointsof view.Truetohis initialinterests,Klemankept asamainobjectivetheunderstandingofthepossibledefectsofsuchstructures,alineof attack firstexploredby mygrandfatherG. Friedelandrevivedinthe 1950s byKleman’s friendC.F.Frank.Klemanisnowwellknownforhisworkinthegeneralfieldofdefectsin softmatter,summarizedinpartinalittlebookonpoints,lines,andwalls.Theotherauthor, Oleg D. Lavrentovich, studied in Kiev the structures of liquid crystal droplets, which he producedbyanewmethod,withcontrolledsurfaceanchoringconditions,whichallowed him to recognize rather early the presence of a TGB phase as foreseen by analogy with superconductorsofthesecondkind.AfteralongstayasavisitingscientistinOrsaywith v vi Foreword Kleman,wherehestudied,withP.Boltenhagen,thesplittingofoilystreaksintofocalconic domains, he has taken a position at Kent State University. Maurice Kleman and Oleg D. Lavrentovich nowpresent ustheresults of theirresearches andteachingsatthe graduate and postgraduate levels in soft matter physics. Structure properties only are considered here. AsmadeclearinChapters1to4,softmatterisheremostlymadeofmoleculesweakly boundbyintermolecularforcesofvariousorigins,excludingmetallic,covalent,andionic bonds. Thus soft matter can encompass biological matter, although not much of this is treatedinthisbook,exceptforsomepropertiesofassembledDNAmolecules.Becauseof the often complex and flexible forms of the molecules involved, entropy plays a leading roleattheoriginofvariouspossibleformsof“mesomorphic”phasesoftheliquidcrystals, aswellasofmanyeasilyproduceddistortionsordefects.Extensionsofsimilarconcepts to liquid, amorphous, or quasicrystalline phases met in “strong” solids are stressed. To study simplythe phase changes involved, one has first to define an order parameter with itscharacteristicphaseandamplitude,smoothlyvaryinginspaceandtime.Thisapproach, popularized by Landau, effectivelyneglects local atomic or thermal inhomogeneities but providesageneralframeworkapplicabletosimilarmesoscopicproblemsinsuperfluidity, magnetism, or phase changes in strong solids. The general concepts derived for analyz- ing phase changes in the main types of liquid crystals are thus compared with similar approachesforstrongsuperconductivityorveryanisotropicmagnetism. The two following chapters relate to possible static or dynamic distortions in liquid crystals: Chapter 5, on elasticity, gives a particularly clear presentation of a field where boundaryconditionsplayaleadingrole;Chapter6presentsmanyaspectsofdynamicsand viscosity. Chapter 7, on fractals and growth phenomena, introduces the subject of surface ef- fects, which is pursued further in Chapter 13. Here again, the two aspects of static and dynamicalpropertiesareclearlydistinguished,evenifthefieldtreatedcouldjustifylonger developments. Finally, a large part of the book covers the problems of line and point defects in the various liquid crystal phases, as compared with classical strong crystals. This rich field, which covers much original work by the authors, is presented in a rather complete and originalway.Thetwolastchapterscovercolloidsandpolymersinaclear,albeitsummary, way. Taken as a whole, this book provides a good introductionto the general background inthestudyofsoftmatter.Themainconceptsinvolvedarepresentedinaclearandsimple way.Shortexercisesattheendofeachchaptertogetherwithashortbibliographyhelpread- erstobroadentheirknowledge.Thecoreofthebookconcentratesonliquidcrystals,their numerousphases and their possible staticand dynamicconformations,withan emphasis ontheroleplayedbyboundaryconditionsandespeciallyfreesurfaces.Butsoftmatteris notrestrictedtoliquidcrystals:Polymersandcolloidsarealsoconsidered,ifmorebriefly. Andthevariousconceptsdevelopedforthestudyofliquidcrystalsfindtheirequivalentsin someproblemsof“strong”matter:theroleoflinesandpointsdefectsinmagnetism,var- Foreword vii ious types of dislocations in liquids,amorphousor quasicrystallinephases; these various aspectsareproperlymentioned,thoughnottreatedtothesamedepth. As rightlyemphasized by the authors, a strikingfeatureof soft matter is the specific roleplayedbythemesoscopicrange.Inmostcases,thedirectmolecularinteractionsareof shortrange.Butthewaytopavespacewithsuchmolecules,ofvariousforms,flexibilities, andviscosities,keepingareasonablycompactandstablearrangement,canleadtoavariety ofdifferentsolutionsthatmightdifferatlongrangeonly.Inthesearchforsuchsolutions, theconceptofcoherencelengthwasfirstdevelopedinsimilarproblemsofmagnetismand superfluidity: This is a measure of the size of the mesoscopic range where a type of ar- rangementimposedontheborderofarangeistransmitted,withdecreasingstrength,tothe otherborder.Butfromthestudyofsoftmatter,anewconcepthasemerged,thatofrangeof frustration;inmanycases,alocalorespeciallystablearrangementofatomsormolecules cannotbeextendedfar,becauseitcreatestoolargeintermoleculartensions.Examplesre- ferred to in this book are the double twist in cholesterics and the icosahedral packing of atomsinliquid,amorphous,orquasicrystallinephases.Insuchcases,thefrustrationrange islimitedbythedevelopmentandsuitablefoldingofdisclinationlines,asforinstancein bluephases.Thusthenatureandsymmetryofshort-rangeintermolecularforcescandom- inate not only the size of the network of dislocations but the long-range structure of the network.Theauthorshavecontributedgreatlytotheemergenceofsuchaconcept,andif anything,itcouldhavebeendevelopedevenfurtherinthisbook. Like most of their predecessors, the authorsintroducethe line singularities (disloca- tions, disclinations) by the Volterra process, then classify possible singularities (points, lines,walls)bythetopologicalapproachintroducedbyG.ToulouseandM.Kleman.The subjectistreatedinaprogressiveway,firstinsolids,theninsmecticsA,withtheirdislo- cations,disclinations,andspecificfocalconics,wheretheauthorshaverecentlyaddedto our knowledge.Cholestericsand nematicsare thentreatedindepth,with adiscussion of liquidrelaxationandthegeneralimportanceoftopologicalclassification. ItisindeedrightlystressedthattheVolterraprocessstartswithasolidmedium,while the topological approach assumes complete viscous relaxation of stresses on an at least partly liquid medium. As this relaxation increases from smectics to cholesterics and ne- matics, the passage through a Volterra process might look more and more artificial, and indeed it is a pity that no more has been done on the physical propertiesof disclinations innematics,relatedtothenoncommutativityoftheirtopology:Whatistheequivalentof F.C.Frank’s“kinks,”producedbythecrossingoftwodislocationsinacrystal,whentwo disclinationscrossinanematic? However, liquid relaxation after a Volterra process in a frozen medium helps us to understandanumberofcharacteristicfeaturesofthesingularlinesinliquidcrystals:Itre- ducesthestoredenergyofdislocationsanddisclinationsandallowsallthesesingularlines tobeflexibleandmobile;fordisclinations,itfixestheorientationofthecutsurfaceofthe initialVolterraprocess,soastominimizetheenergy;itallowsthetopologicalelimination ofsomelinesbyanescapeintothethirddimension,thuscreatingpairsofsingularpoints; italsoallowsthecharacteristicrotationtobetangenttothedisclinationline,evenacurved viii Foreword one.TheVolterraprocesscanfinallyexplaininanaturalwaywhyanumberofdislocation configurationscanbe maintained,althoughnotpredictedby topologicalarguments:This canrefer,forinstance,toslipatlowtemperaturesinamorphoussolidsorinquasicrystals; itcanalsorefertoboundaryorinitialconditions,whichcanmaintainlineswitharelaxed andcontinuouscore,suchascracksinmotionanddisclinationsinatubeofnematicswith moleculesperpendiculartothesurfaceofthetube. These remarks justify, I think, the plan followed by the authors, although liquid re- laxation could have been introduced earlier in the book, for dislocations as well as for disclinationsorfocalconics.Thecontinuousdistributionofinfinitesimaldislocationspro- ducedbysuchrelaxationsispreciselythatfirstimaginedbyVolterraincontinuoussolids andwhichJ.F.Nye,B.A.Bilby,andE.Kro¨nerdevelopedlaterinthecontextofflexionand torsionofsolids,asrecalledearlierinthebook. Some other comments could be made in the presentation of the book, if not in its substance • Thelong-rangeLandauapproachtophasechangesneglectsshort-rangeordereffects, whichcanbesignificanteveninfirst-ordertransitions.Thus,asalreadypointedoutin 1930byG.Foe¨x,theshort-rangeeffectsobservedinthemagneticpropertiesonboth sides of anematicisotropictransitiondonotnecessarilyimplyasecond-orderphase transitionattheequivalentofaCuriepointinaferromagnet;buttheireffects,known in the nematic phase since before the First World War as “swarms” (responsible for turbidityandcorrectlyanalyzedinthelong-wavelimitbyP.G.deGennes),aswellas the equivalent effects observed by light scattering in G. Durand’s group in the early 1970sintheisotropicphase,stronglyreducethelatentheatandincreasethetemper- ature variations of the effective Landau parameters. Indeed, the large (optical) range ofthesefluctuationsposesthequestionoftheconvergenceofaLandaudevelopment, whichinfactlimitsitselftoverysmallgroupsofmolecules.Similarly,short-rangeori- entationalordercanexistinpolymerswithoutthemshowingatransitiontoanematic phase, as shown,forexample,byB. Delocheinmoltenpolymersas well as inpoly- mericmembranes,usingresonancetechniques.Byskippingratherquicklyover such effects,theauthorsmightgivetoorigidapictureofafieldwherefluctuationsareall important. • Some“historical”referencescouldhavebeenusefullymorefullydeveloped.Thusto say that dislocations in solids began to be studied just before the Second WorldWar probablyreferstothefundamentalworkproducedbyJ.W.BurgersandbyR.Peierls in1939;buttheconceptofdislocationanddisclinationlinesincontinuoussolidsdates from Volterra, before the First World War; and its transfer to crystals dates from the early1920s,togetherwithmanyapplicationstocrystalplasticity.Ontheotherhand, the“Cano”geometryofatiltboundaryofasmecticorcholestericinawedgeisdueto GrandjeanusingamicacrackandwasmostprobablyunderstoodaspresentedinFigure 8.22 by G. Friedel in the early 1930s. Cano only added a specific way of aligning moleculesinadefinitedirectionalongglassplates. Foreword ix • Finally,researchinsoftmatterhasbeenhelpedbyatransferofconceptsdevelopedin strongsolids,andthisismadeveryclearinthisbook.Conversely,conceptsdeveloped insoftmatterhavebeentransferredtothestudyofstrongsolidsorofbiologicalma- terials.This ismentionedhereinanumberof cases, butitis notthemainsubjectof thisbook.Itcanbehopedthatanotherpublicationwillcoverindepthrecentprogress inthesefields,wheretheauthorshavebeenactive. In conclusion, I am very happy to introduce a book that presents in a condensed but clearwaymanyfacetsofaveryrichandfascinatingfield. JacquesFriedel Paris,France January2001
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