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Concepts, Phenomena, and Applications

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Names:vanSaarloos,Wim,author.|Vitelli,Vincenzo,author.|Zeravcic,Zorana,author.

Title:Softmatter:concepts,phenomena,andapplications/WimvanSaarloos,VincenzoVitelli, ZoranaZeravcic.

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1.1Therelevanceandattractivenessofacontinuumdescriptionofﬂuids..............

1.2Hydrodynamicsasabalanceequationofﬂuidelements.....................

1.3.1Thematerialorconvectivederivative............................

1.3.2Separatingoutthevariouscomponentsofﬂow......................

1.4Oncemore:Reﬂectionsontheunderlyingpicture.........................

1.5Thedissipativeterms:Onsagerreciprocityrelations........................

1.6ThestresstensorandheatcurrentforaNewtonianﬂuid.....................

1.6.1Stresstensorandheatcurrent................................

1.6.2Theresultinghydrodynamicequations...........................

1.7.1Theequationforsoundpropagation............................

1.7.2Analysisoftheequationwithdamping...........................

1.8Whencanwetreataﬂowasincompressible?............................

1.9TheNavier-Stokesequations.....................................

1.10Thedimensionsofphysicalquantities,dimensionlessnumbers,andsimilarity.........

1.11FromsmalltolargeReynoldsnumbers...............................

1.11.1LowReynoldsnumberhydrodynamics...........................

1.11.2IntermediateReynoldsnumbers...............................

1.11.3VerylargeReynoldsnumbers................................

2.8.3Thegeneralforceandtorquebalanceequationsforstaticrods..............

2.8.4Equationsinthesmalldeﬂectionapproximation......................

2.10.5Thecrossoverlengthscale..................................

2.10.6Jammedpackingsversusdisorderedcrystals........................

2.10.7Towarddesignergranularmatter..............................

3.2LangevinequationforBrownianmotion..............................

3.2.1BasisoftheLangevinequation................................

3.2.2TheLangevinequation....................................

3.2.3Meansquarevariationsofvelocityandposition:Diﬀusion................

3.2.4TheStokes-Einsteinequationforthediﬀusioncoeﬃcient.................

3.2.5Cuttingcornersandwhatwelearnfromit.........................

3.3TheFokker-Planckequationfortheprobabilitydistribution...................

3.3.1TheFokker-Planckequation:EquivalencetoaLangevinequation............

3.3.2TheFokker-PlanckequationforthevelocityoftheBrownianparticle..........

3.3.3TheFokker-PlanckequationforthepositionofaBrownianparticlein anexternalpotential.....................................

3.3.4ThediﬀusionequationanditsGaussiansolution.....................

3.3.5Self-similarityandself-similarsolutions..........................

3.3.6TheKramersproblem:Fluctuation-drivenescapeoverabarrier.............

3.4Themasterequation..........................................

3.5SizemattersfordiﬀusionanddispersionofBrownianparticles.................

3.5.1Diﬀusion............................................

3.5.2Dispersionsversusgranularmedia.............................

3.6Probingﬂuctuationsandtakingadvantageofthemasaprobe..................

3.6.1Measuringforceconstantsofbiomatterexperimentally..................

3.6.2DirectedBrownianmotionofmolecularmotors......................

3.6.3Bendingmodulusorsurfacetensionfromshapeﬂuctuationmeasurements......

3.6.4Thermalﬂuctuationsinabucklingcolloidalchain.....................

3.7Probingsoftmatterwithscatteringtechniques...........................

3.7.1Essentialsofscatteringexperiments.............................

3.7.2Probingsmallﬂuctuationsincontinuumsystemswithlaserlightscattering......

3.8Whathavewelearned.........................................

3.9Box3:Calculatingthermalaverages

4.1.1Colloids:Fundamentalstudies................................

4.3.1TheVanderWaalsattraction.................................

4.3.2Depletioninteraction.....................................

4.3.3Inducedattractiveinteractionduetoperturbationsofthesurroundingmedium....

4.4.2Stericstabilizationbygraftingpolymersonthesurface..................

4.5Playingwithcolloidsasmodelsystems...............................

4.5.1Colloidalaggregates.....................................

4.5.2Fromspheres,rods,andplatestocubesandbeyond...................

4.5.3Theuseofcolloidalcrystalstomakeopticalbandgapmaterials.............

4.5.4Colloidalglasses........................................

4.5.5Colloidalmotifsasthebuildingblocksofdesignermatter................

4.5.6Colloidsasactivematter...................................

4.6Non-Newtonianrheologyofcolloidaldispersions.........................

4.6.1Shearthinningandshearthickening............................

4.6.2Atemporaltransitionduetocompetitionbetweenagingandrejuvenation.......

4.7Whathavewelearned.........................................

4.8Problems ................................................

5Polymers

5.1Theever-broadeningﬁeldofpolymerscience............................

5.2Polymers:Longchainmoleculeswithmanyaccessibleconformations..............

5.3Idealchains,excludedvolumeeﬀects,andtheFloryargument..................

5.3.2Excludedvolumeinteractionandself-avoidingwalks...................

5.3.3TheFloryargumentfortheexcludedvolumeinteraction.................

5.4.1Thewormlikechainmodelanditspersistencelength...................

5.4.2Chargeeﬀectsonthepersistencelength...........................

5.4.3Whyexcludedvolumeeﬀectsaresmall...........................

5.4.4Theforce-extensioncurveoftheWLC............................

5.5.1Thediluteregime.......................................

5.5.2Fromsemi-dilutetoconcentratedsolutions.........................

5.5.3Concentratedsolutions....................................

5.7Flory-Hugginsmean-ﬁeldtheory..................................

5.7.1Flory-Hugginsapproach...................................

5.7.2Flory-Hugginsasamean-ﬁeldtheory............................

5.8.1Biopolymernetworks.....................................

5.8.2Theslackorthermal-ﬂuctuation-inducedcontraction...................

5.8.3Thestress-strainresponseofanetwork...........................

5.8.4Beyondthesimpleapproximation..............................

5.9Reptationandtheviscosityofpolymermelts............................

5.9.1Thepolymerviscosityplaysonlyalimitedroleinseveralrelevantﬂoweﬀects.....

5.9.2Reptation............................................

5.10Non-Newtonianrheologyofpolymersolutionsandmelts....................

5.10.1Importanceofpolymerstretchingeﬀects..........................

5.10.2ThedimensionlessWeissenbergnumber..........................

5.10.3TheOldroyd-BandupperconvectedMaxwellmodelforpolymerrheology......

5.10.4Polymerﬂowinstabilitiesduetohoopstresses.......................

5.11Whathavewelearned.........................................

5.12Problems

6.1Liquidcrystalsasmesophases....................................

6.1.1Abewilderingvarietyofliquidcrystalphases.......................

6.1.2Molecularliquidcrystalsversuscolloidalliquidcrystalphases.............

6.1.3Thepowerofcoarse-graininginthespiritofLandau...................

6.1.4Thedirectorﬁeld ˆ n ......................................

6.2Landau–deGennesapproachtotheisotropic-nematictransition.................

6.3Frankenergyexpressionforthenematicdirectorﬁeld.......................

6.3.1TheFrankfreeenergy.....................................

6.3.2Splay,twist,andbenddistortions..............................

6.3.3Boundaryconditions.....................................

6.4Analysisofequilibriumsolutions..................................

6.5Switchingthedirectorwithaﬁeld:TheFréedericksztransitionandLCDs...........

6.5.1TheFréedericksztransition..................................

6.5.2Liquidcrystaldisplays....................................

6.6Topologicaldefectsinthedirectororientation...........................

6.6.1Defectsinthedirectorﬁeld..................................

6.6.2Visualizationofdefectsinthinsamplesbetweencrossedpolarizers...........

6.6.3Interactionofdefectsintwodimensions..........................

6.7Nematohydrodynamicsbasedonnon-equilibriumthermodynamics..............

6.8Playingwiththemolecularshape..................................

6.9Opportunitiesandchallengesatinterfaceswithotherﬁelds...................

6.9.1Biologicalliquidcrystals...................................

6.9.2Liquidcrystalsindropletsandotherconﬁnedgeometries................

6.9.3Colloidalliquidcrystalsandbeyond............................

6.9.4Mesophasesoflipidmoleculesrelevanttopharmaceutics,cosmetics, andfood............................................

6.9.5Epithelialcellsdieanddisappearnear +

6.10Renormalizationgroupanalysisofthedefectunbindingtransition...............

6.10.1StatisticalmechanicsofagasofCoulombcharges.....................

6.10.2TheideabehindtheRGcalculation:Screening.......................

6.10.3SettinguptheRGcalculation.................................

6.10.4Howtoderivetherenormalizationgroupﬂowrelations.................

6.10.5Criticalscaling.........................................

7.2Helfrichfreeenergyformembranes.................................

7.3Virusshapesandbucklingtransitionsinsphericalshells.....................

7.4Crumplingofmembranesandsheets................................

7.4.1Acrumplingtransitioninthermalsystems?........................

7.4.2Athermalcrumplingbycompression............................

7.5Asoftmatterrealizationoftheone-dimensionalKPZequation.................

7.6Whathavewelearned.........................................

8PatternFormationoutofEquilibrium

8.1Spontaneouspatternformationresultingfrominstabilities....................

8.2Gearingupforstudyingpatternsinspatiallyextendedsystems.................

8.2.1Thepitchforkbifurcationofdynamicalsystems......................

8.2.2TheSwift-Hohenbergmodelequation...........................

8.2.3Supercriticalversussubcriticaltransitions.........................

8.3Inspiration:Rayleigh-BénardconvectionandTuringpatterns...................

8.3.1TheRayleigh-Bénardinstability...............................

8.3.2Turinginstabilities.......................................

8.4Threetypesoflinearinstabilities...................................

8.5AmplitudeequationsforstationarytypeIinstabilities.......................

8.5.1Inspirationfromasimpleperturbativecalculationfor theSwift-Hohenbergequation................................

8.5.2Amplitudeequationinonedimensionfor

8.5.3Two-dimensionalpatterns..................................

8.6DynamicsjustaboveatypeIIinstability..............................

8.7AmplitudeequationsforoscillatorytypeIinstabilities......................

8.7.1Amplitudeequationsforone-dimensionaltravelingwaves................

8.7.2Dominantstructures:Sourcesandsinks..........................

8.8AmplitudeequationsfortypeIIIinstabilities............................

8.9.1Box4:Summaryofinsightsfromamplitudeequationapproach

9.3.1ActiveBrownianparticles..................................

9.6.1Movingandself-propelledsolids..............................

9.6.2Oddelasticity.........................................

9.6.3Oddelastodynamics.....................................

9.7.1Hydrodynamicsofself-spinningparticles.........................

9.7.2Oddviscosity.........................................

9.8Nonreciprocalphasetransitions...................................

9.8.1Chiralphasesinnonreciprocalactivematter........................

9.8.2Nonreciprocalpatternformation:Acasestudy......................

9.8.3Exceptionalpointsandparity-breakingbifurcations....................

9.9.2Activemattereﬀectsduringmorphogenesis........................

9.9.3Tissuemechanicsandvertexmodels............................

I.11991NobelPrizecitationforP.-G.deGennes.............................

I.2Arangeofsoftmatterbehaviorobtainedbymodifyingacolloidalparticle............

I.3TheoriginaldrawingofPerrinshowingBrownianmotion.....................

I.4IllustrationofanexperimentinwhichonepullsonDNAwithanopticaltrap..........

I.5Afractalaggregategrowninapetridish...............................

I.6Illustrationofshearthinningandshearthickeningbehaviorofcolloidaldispersions......

I.7Cornstarch:Itsmicrostructureandillustrationofthepossibilityofwalkingonit.........

I.8Illustrationofthemicrostructureofpaintandmayonnaise.....................

I.9Moderntechniquesallowonetoprobethestrainresponseofacolloidalpacking........

I.10Therelaxationtimeofpolydispersecolloidsdivergesonapproachingtheglasstransition...

I.11Hardcorepolyhedracanformallkindsofinterestingphases....................

I.12Playingwiththeinteractionsallowsonetomakeself-assemblystronglydirected........

I.14Microtubulesandmolecularmotorsareactivematterwithliquidcrystal–likeordering.....

1.1Liquidandgasphasesofatoms....................................

1.2Illustrationofcoarse-grainingandthescalesofhydrodynamicphenomena............

1.3Euler’sarticlefrom1757.........................................

1.4TheLagrangianandEuleriandescriptionsofaﬂuidelement....................

1.5Illustrationofvarioustypesofﬂow..................................

1.6Illustrationofthevariouscomponentsofthestresstensor.....................

1.7Swimmingbacteriaasanexampleofanactiveﬂuid.........................

1.8Behavioroflongpolymersinsimpleshearﬂow...........................

1.9OnsagerrelationsillustratedwiththePeltierandSeebeckeﬀects..................

1.10Illustrationofvariouswaystoanalyzealinearmodewithdampinginspaceortime......

1.11Taylor-Couetteﬂowanditsrichphasediagram...........................

1.12OsborneReynoldsinthelabprobingthetransitiontoturbulenceinpipeﬂow..........

1.13FlowpastacylinderatdiﬀerentReynoldsnumbers.........................

1.14IllustrationofﬂowreversalatsmallReynoldsnumbers.......................

1.15IllustrationofthevariousﬂowregimesforincreasingReynoldsnumbers.............

1.16CloudformationpatternresultingfromtheKelvin-Helmholtzinstability.............

1.17Simulationsofthevorticitygeneratedbyadragonﬂywing.....................

1.18Sketchofathinlayerinthediscussionofthelubricationapproximation.............

1.19Entrainmentofairunderaliquiddroplet...............................

1.20Contactangle,wetting,andMarangoniﬂow.............................

1.21Waterdropletsonaplant’sleaf.....................................

1.22Coﬀeestainsduetoenhancedevaporationofthedropletattherim................

1.23Bubbleoscillationsinsoftmatter....................................

1.24AbouncingdropletduetoMarangoniﬂow..............................

1.27BasicsetupfortheRayleigh-TaylorandKelvin-Helmholtzstabilitycalculations.........

1.28SimulationsofaﬂuidinterfaceexhibitingtheRayleigh-Taylorinstability.............

1.29Lubricationapproximationforﬂowbetweentwospheresapproachingeachother........

Chapter2

2.1Illustrationofthenaturaltendencyofanauxetictobend......................

2.2Bucklingpatternsinabilayersysteminwhichthesubstratelayerisinitiallyprestressed....

2.3Illustrationofthespontaneouscurvatureofabilayer........................

2.4Adriedapplegetswrinkled......................................

2.5Illustrationofthechangeofpositionofmaterialelementsofasolidunderstress.........

2.6Fluctuationsofagraphenesheetcausequiteabitofenergy....................

2.7StretchingofabarintheanalysisofthePoissonratio........................

2.8Cork,amaterialwithaPoissonratioofaboutzero..........................

2.9EvolutionofthePoissonratioofvariousrubberypolymerswithtime...............

2.10Dynamicmodulusofanultrasoftelastopolymergel.........................

2.11TheMaxwellmodelandtheKelvin-Voigtmodelfortime-dependentresponse..........

2.15Examplesofwrinklingsheetsduetocouplingofstretchingandbending.............

2.19ThesimilarityofthebucklingtransitionwiththeLandautheoryofphasetransitions......

2.22Theelastictorqueassociatedwithabentsheetorrod........................

2.23Illustrationofmicrotubules,thecellular’rails’ofmicromotors...................

2.25Auxeticandprogrammablesoftmatterstructures..........................

2.26Responseofametamaterialwithtwotypesofholesfordiﬀerentprestrains............

2.27Diﬀerencesinforcesbetweenmoleculesandsmallparticles....................

2.28Manysoftmattersystemsconsistofparticleswithstrongrepulsiveforces............

2.30Illustrationofjammingbyincreasingthedensityofpolydispersedisks..............

2.31Variationoftheratioofelasticconstantsuponapproachingtheisostaticpointatjamming...

2.32Theevolutionofthedensityofstatesuponapproachingthejammingpoint...........

2.33Lowest-frequencyeigenmodesatandfarabovethejammingpoint................

2.34Evolutionoftheratio µ/K ofelasticnetworksuponpruningvarioustypesofbonds......

2.35Optimizationoftheshapeofmotifsinagranularpacking.....................

2.36TheBurgersvectorandtwobounddefectsonatriangularlattice..................

2.37Colloidalexperimentshowingthetransitionfromsolidtohexaticandliquidphasein2D...

2.38Agyroscopelatticewithavibrationaledgemode..........................

2.39Topologicalzero-energyedgemodesinamechanicalstructure...................

2.40Triangularandhoneycomblattices...................................

2.41Dislocationsanddisclinations.....................................

Chapter3

3.1IllustrationofaBrownianparticle...................................

3.2Sketchofwhitenoise..........................................

3.3Meansquaredisplacement (∆X (t)2) ofcolloidalparticlesofvarioussize...........

3.4Evolutionoftheprobabilitydistributioninphasespace.......................

3.5TitleandabstractoftheoriginalpaperofKramers..........................

3.6Thepotential U (X ) inthecaseoftheKramersproblemofescapeoverabarrier.........

3.7Illustrationofthetransitionprobabilitiesinthemasterequation..................

3.8Densitymatchinginacolloidalsystem................................

3.9ExtractionoftheforceonDNAfromtheﬂuctuationsofthebeadattachedtoit..........

3.10ExperimentallowingustopullandtwistaDNAstrandwithamagneticparticle........

3.11Illustrationofthehand-over-handandinchwormmotionofBrownianmotors..........

3.12Stepsandﬂuctuationsofmolecularmotors..............................

3.13Variousmembraneshapeﬂuctuations.................................

3.14Bucklingofacolloidalchainundercompression...........................

3.15Illustrationofthesetupofascatteringexperiment..........................

3.16Light-scatteringspectrumofwater...................................

3.17Interchangingtheorderoftheintegrals................................

3.18Fermiacceleration............................................

Chapter4

4.1Thetobaccomosaicvirus........................................

4.2Collageofcolloidalparticlesofvariousshapesandsizes......................

4.3DipoleﬂuctuationsleadingtotheVanderWaalsinteraction....................

4.4Thedepletioninteractionillustrated..................................

4.5Attractionbetweentwocolloidsataﬂuidinterface.........................

4.6Chargescreeningofcolloids......................................

4.7TheDLVOinteractionbetweencolloids................................

4.8Stericrepulsionresultingfromgraftingcolloidswithpolymers..................

4.9Diﬀusion-limitedaggregationclusters.................................

4.10Schematicbehaviorofthescatteringintensity S(q) ofDLAclusters................

4.11Measuredscatteringintensity S(q) fromfractalaggregates.....................

4.12Colloidalparticleswiththeshapeofaroundedcube........................

4.13Acolloidalcrystalandaphotonicbandgapmaterialmadefromacolloidalcrystal.......

4.14Colloidalglassesasamodelsystem..................................

4.15Viscosityofapolydispersecolloidaldispersionasafunctionofvolumefraction.........

4.16Functionalcolloidalmotifs.......................................

4.17ColloidalparticlescoatedwithDNApatchestogivedirectionalbonding.............

4.18Theworkhorseofactivecolloids:TheJanusparticle.........................

4.19Akaleidoscopeofwaysofmakingandmanipulatingactivecolloids................

4.20Colloidaldispersionsascomplexﬂuids:Non-Newtonianrheologicalbehavior..........

4.21Snapshotofclusterformationincolloidrheology..........................

4.22Bifurcationbehavioroftheviscosityofabentonitesolution....................

4.23Scalingplotofthestressversusshearratenearthejammingpoint.................

4.24Anexampleofthefrictioncoeﬃcientofgranularmediaasafunctionoftheshearrate.....

4.25Typicalinteractionpotentialbetweencolloids............................

4.26Twosemi-inﬁniteslabsattractingviatheVanderWaalsinteraction................

4.27TwospheresandthecalculationoftheDerjaguinapproximation.................

4.28Interactionbetweenlockandkeycolloids...............................

4.29Regularfractals:TheKochcurveandSierpinkigasket........................

4.30Thepercolationtransition........................................

4.31Coarse-grainingaone-dimensionalmodel..............................

4.32Self-similarityinthepercolationtransition..............................

4.33Renormalizationgroupfor2Dpercolation..............................

Chapter5

5.1Polyethyleneandpolystyrene......................................

5.2Illustrationofvitrimers,andself-healingofarubberysupramolecularpolymer.........

5.3Transandgaucheconformationsofpolyethylene..........................

5.4Illustrationofdiﬀerentconformationsofashortpieceofapolymer................

5.5AFMpictureofDNAonasurfacewithapersistencelengthofabout50nm...........

5.6Theidealchainmodel..........................................

5.7Illustrationofrandomwalksandself-avoidingwalks........................

5.8Interactionofamonomerwiththeaveragenumberofmonomersinaballaroundit......

5.9TheFloryfreeenergyasafunctionofthepolymerradius

5.11TheorganizationoftheDNAmoleculeonvariouslengthscales..................

5.14SketchofDNAatlargepullingforce..................................

5.15Force-extensioncurveofDNAﬁttedwiththewormlikechainexpression.............

5.16Measuringtheforce-extensioncurveofoverstretchedDNA.....................

5.17Neutron-scatteringintensity S(q) fordeuteratedpolystyrene....................

5.18Illustrationofthediluteregimeandthecrossovertothesemi-diluteregime...........

5.19Thecrossoverlength ξφ andtheblobpictureinthesemi-diluteregime..............

5.20Neutron-scatteringdatafrompolystyreneatvariousconcentrationsabove

5.21Scalingplotoftheosmoticpressureofpolymersolutions......................

5.22Sketchofapolymerbrush.......................................

5.23SketchoftheFlory-Hugginsfreeenergy................................

5.24PhasediagramofdiblockcopolymersasobtainedfromFlory-Hugginsmean-ﬁeldtheory...

5.25Phasediagramofdiblockcopolymerswithﬂuctuationeﬀectsincluded..............

5.26Biopolymernetworksandtheirresponse...............................

5.27Theforce-extensioncurveofabiopolymerinanetwork.......................

5.28Illustrationofpolymerstretchinginanetworkunderaﬃnestrain.................

5.29Diﬀerentialelasticmodulusofactinﬁlamentnetworks........................

5.30Illustrationofanathermalnetworkundershear...........................

5.31Illustrationofthereptationprocessofpolymerrelaxation.....................

5.32Illustrationofreptation.........................................

5.33Theviscosityasafunctionofdegreeofpolymerizationforseveralpolymermelts........

5.34Surprisingdemonstrationsofthenon-Newtonianrheologyofpolymers.............

5.35Illustrationofhoopstressesduetocurvedstreamlines.......................

5.36TheOldroyd-BandupperconvectedMaxwellmodelrepresentdumbbells............

5.37Examplesofviscoelasticﬂowinstabilities..............................

5.38Stressasafunctionofshearrateinviscoelasticﬂowdrivenbyarotatingdisk..........

5.39IllustrationofthecoordinatesanddistancesintheOdĳklengthcalculation............

5.40Schematicillustrationofaserpentilechannelusedtostudyviscoelasticﬂowinstabilities....

5.41CriticalWeissenbergnumberforviscoelasticﬂowinserpentinechannels.............

5.42Polymermelttransformingintoacrosslinkedmelt..........................

Chapter6

6.1Thenematic,smectic,andcholestericliquidcrystalphases.....................

6.2Phasediagramofhardcorespherocylinders.............................

6.3Discoticmoleculesandliquidcrystalphases.............................

6.4IllustrationoftheliquidcrystalbluephaseII.............................

6.5Illustrationofthedirectorasacoarse-grainedorientationﬁeld..................

6.6Illustrationofthemicroscopicoriginofthe

symmetryofthenematicphase......

6.7FormoftheLandau–deGennesfreeenergyneartheisotropic-nematictransition........

6.8Inverseofthelight-scatteringintensityof8CBandMBBAasafunctionoftemperature.....

6.9Splay,twist,andbenddistortionsofanematicliquidcrystal....................

6.10Thehomeotropicandhomogeneousboundaryconditionsofaliquidcrystal...........

6.11ThemagneticﬁeldFréedericksztransition..............................

6.12IllustrationofapixelofanLCD....................................

6.13Twonematicdisclinationswith s = 1

6.14Thetwohalf-integerdisclinationsand s

6.15Topologicalpointdefectsinnematics:Hedgehogsandboojums..................

6.16Howliquidcrystaldefectsshowupbetweencrossedpolarizers..................

6.17IllustrationoftherotationdirectionoftheSchlierenimageofdefects...............

6.18Schlierenimageofapairofsurfaceboojums.............................

6.19Polarwedge-shapedliquidcrystalmoleculesformingsplayedstripeddomains.........

6.20Illustrationoftheﬂexoelectriceﬀect..................................

6.21Elecronmicrographofthefdvirus...................................

6.22Liquidcrystaldropletswithboojumsorahedgehog.........................

6.23AJanusparticlecoupledtoanematicﬁeld..............................

6.24Micellesandinversemicellesformedbylipidmolecules......................

6.25Themagiclipidmonoolein.......................................

6.26Lipidicmesophasesofvariousdimensionality............................

6.27Nematicorderanddefectsinepithelialcells.............................

6.28Illustrationofthescreeningofelasticconstantsbydefectpairs...................

6.29Renormalizationgroupﬂowsofthe2DCoulombgassystem....................

6.30Escapeofthedirectorinthethirddimension.............................

6.31Illustrationofacrystalline,acolumnar,andasmecticphase....................

Chapter7

7.1Sketchofaredbloodcell........................................

7.2Sketchofabilayermembrane......................................

7.3Thetworadiiofcurvatureofasurface.................................

7.4Illustrationofthegenusofaclosedsurface..............................

7.5BifurcationsandevolutionofmembraneshapesaccordingtotheHelfrichmodel........

7.6Theadenovirusandsalmonellaphagevirus.............................

7.7Alargeﬂattriangularnetwithadisclinationcanreleaseitsstrainbybuckling..........

7.8Theenergyofaﬂatelasticshellwithadisclinationandthatofacone...............

7.9Asphericityofvirusesasafunctionoftheirradius..........................

7.10Apieceofcrumpledpaper.......................................

7.11Crumplingtransitionofatetheredsurface..............................

7.12Compressionexperimentoncrumplingofpaper...........................

7.13Resultsofanumericalstudyofcrumpling..............................

7.14CurvatureandfacetsofweaklyandstronglycompactedMylarsheets...............

7.15KPZscalingofgrowinginterfacesinnematicelectroconvection..................

7.16ExperimentsandsimulationsofthepropagatingRayeighinstability................

7.17Sketchofawettingfront........................................

7.18ThederivationoftheEulerformula..................................

7.19Curvedspacecrystals..........................................

7.20Aphaseseparatedsystem........................................

Chapter8

8.1TopviewofBénard-Marangonicellsatthesurfaceofaﬂuidheatedfrombelow.........

8.2Sketchoftheamplitudeconcept....................................

8.3Theﬂowdynamicsofavariable

8.5ThedispersionrelationoflinearmodesintheSwift-Hohenbergequation.............

8.6EvolutionoftheenergyinasimulationoftheSwift-Hohenbergequation.............

8.7Supercriticalandsubcriticalbifurcations...............................

8.8SketchofaRayleigh-Bénardcell....................................

8.9ThedispersionrelationoftheRayleigh-Bénardproblemwithslipboundaryconditions.....

8.10Rayleigh-Bénardpatternsevolvewithdistancefromthreshold...................

8.11RangeofexistenceofstablestaticconvectionpatternsinRayleigh-Bénardconvection......

8.12SummaryoftheTuringstabilitydiagramoftwocoupledreactiondiﬀusionequations......

8.13TuringpatternsobservedinchemicalreactorsandintheMinproteinsystem...........

8.14Thethreepossibleinstabilityscenariosofspatiallyextendedsystems...............

8.15Scalingofgrowthrateandinstabilitybandofﬁnitewavelengthinstabilities...........

8.16Sketchofthebandofperiodicsolutionsasafunctionof

8.17Sketchofthestabilityofphasewindingsolutionsabovethresholdinonedimension......

8.18Sketchof σ(q) forarotationallysymmetrictwo-dimensionalsystem...............

8.19Thestabilityballoonforstripepatternsaccordingtothelowestorderamplitudeequation...

8.20Illustrationoftheoriginofthephaseinstabilitiesofstripepatternsintwodimensions.....

8.21Variousregularpatternsandtheirdominantmodesnearthreshold................

8.22Thethreeunitvectorsusedtodescribehexagonalpatterns.....................

8.23HexagonalpatternobservedjustbelowthresholdinaRayleigh-Bénardexperiment.......

8.24Autocorrelationpatternsintheneuralresponse...........................

8.25Simulationoftheone-dimensionalKuramoto-Sivashinskyequation...............

8.26Chaoticdynamicsinone-dimensionalhydrothermalwaves....................

8.27Sourcesandsinksinaheatedwireexperiment...........................

8.28Illustrationofsourcesandsinksintravelingwavesystems.....................

8.29Illustrationofadomainwallsolution.................................

8.30AsimulationofthecomplexGinzburg-Landauequationintwodimensions...........

8.31ThestabilityballoonofvegetationpatternsinAfrica.........................

8.32ThenullclinesoftheTuringmodelwhichgiverisetoexcitablemediumbehavior........

8.33Timedependenceoftheﬁeldsofanexcitabledynamicalsystem..................

8.34Apropagatingpulseinanexcitablemedium.............................

8.35ExampleofexcitablewavesintheBelousov-Zhabotinskyreaction.................

8.36Thesignalofthepropagationofanervepulse............................

8.37SymmetryofﬂowpatternsintheBoussinesqapproximation....................

Chapter9

9.1Agalleryofactivematter........................................

9.2Aﬂockofbirds..............................................

9.3Vicsekmodelsimulationsforvariousdensitiesandnoisestrengths................

9.4FlockingbehaviorobservedforQuinckerotationofcolloidalparticles...............

9.5TheeﬀectivepotentialintheToner-Tutheory.............................

9.6Numericalsimulationsofmotility-inducedphaseseparation....................

9.7Experimentalveriﬁcationofmotility-inducedphaseseparation..................

9.8Bacterialsuspensionsexhibitswarming,turbulence,andavanishingviscosity..........

9.9Runandtumblebehaviorofbacteria.................................

9.10Illustrationoftheroleofdefectsinproducingactiveturbulence..................

9.11Inducedﬂowﬁeldaround ± 1 2 defectsinanactivenematic.....................

9.12Threeexamplesofactivesolids.....................................

9.13Observationofstarﬁshembryoswhichself-organizeintolivingchiralcrystals..........

9.14Examplesofmetamaterialsinwhichoddelasticityplaysarole...................

9.15Aspringwithodd-elasticresponse..................................

9.16Layersofacolloidalchiralﬂuidexhibitinstabilities.........................

9.17Eﬀectofnonreciprocalinteractionsonﬂockingmodelsandpatternformation..........

9.18Space-timeplotsofnonreciprocallycoupledSwift-Hohenbergmodels..............

9.19Perturbativephasediagramoftheexceptionaltransition......................

9.20Schematicbifurcationdiagramoftheexceptionaltransition....................

9.21Exceptionalpoints-inducedinstabilities................................

9.22Sketchofanactivegelcomposedofactinﬁlamentsandmyosinmotors..............

9.23Shapeofadividingcellcomparedtoanactivegelmodel......................

9.24Topologicaldefectsinaregenerated Hydra

9.25Myosinﬂowonthesurfaceofa

9.26Amachinelearningmodelanalysisoftissueﬂowin

9.27Sketchofavertexmodelforcelldynamics..............................

9.28TheVicsekmodelfornonmovingbirdsasanoisyspinmodel...................

9.29Exampleofanactiveﬂowdrivenbythedirectorﬁeldinanactivenematic............

9.30Simpliﬁedcelldivision.........................................

Chapter10

10.1Buildingblocksofdesignermatterfromthenanoscaletothemacroscale............

10.23Dprintingonthemacroscale.....................................

10.3Illustrationofathermalcloak.....................................

10.4Agranulararchitecture,anultra-lightweightmaterial,andanallostericnetwork.........

10.5Illustrationoftwodiﬀerentlatticestructuresrelatedbyduality...................

10.6Anextremelystretchablehydrogel..................................

10.7Aself-foldingorigamimadewiththeaidofahydrogel.......................

10.8Digitalalchemy:Designofnovelcrystalstructure..........................

10.9ColloidalcrystalsmadefromDNA-coatedcolloids.........................

10.10Designprinciplesforself-assemblyofrigidstructuresmadeofeightparticles..........

10.14Illustrationoftheconceptofreturn-pointmemory..........................

10.15Memorybehaviorresultingfromcyclicdrivingofashearedparticlesystem...........

10.19IllustrationofpathreversalinviscousliquidforsmallReynoldsnumber.............

Preface

Thisbookgrewoutofourexperienceteachingintroductorycoursesonsoftmatterin LeidenandChicago.ThechallengeinLeidenwastodevelopacourseaimedatﬁrstyearmaster’sstudents,studentswhojusthavecompletedathree-yearbachelordegree inphysicsorarelatedﬁeld.Theyhaveadiversebackgroundandwillchoosetheir specializationanddecidewhethertogointotheoreticalorexperimentalphysicsonly sometimeaftertakingthecourse.TheChicagocoursetargetsbeginninggraduate students,butwithsimilarlydiversebackgroundsandinterests.

Manycolleaguesweconsultedaboutteachingsoftmatterfromaphysicsperspective struggledwiththesamedilemmawefaced:howtodevelopacoursewhichintroduces someofthebasicconceptsdevelopedinthepreviouscentury,butwhichatthesame timegivesafeelforsomeoftheexcitingresearchquestionsthesedays,aswellasfor therevolutionizingnewopportunitiesofferedbymodernvisualizationtechniques anddigitalanalysis.Moreover,formanyofusthecharmofsoftmatterisitsdiversity, thefactthatitcannotsimplybetreatedonthebasisofasingleoverarchingtheoretical framework,andthatitpaystohaveanintuitiveunderstandingofmanydifferent approachesandmaterials.Howcanwebringacrossthenecessity,power,andfun ofbeingabletoshiftperspectivesandtobringknowledgefromvariousdisciplines tobearonaproblem?Wefoundourselvescombiningbitsandpiecesfromseveral classicalintroductionstothefieldandfrombooksfocusedonaparticularphaseof softmatter,excerptsfromliteratureonapplicationsandpresent-dayresearchtopics, andourownlecturenotes.

Thisbookreflectsourteachingapproachandphilosophy:itisintendedtobeessentiallythetypeofbookwewouldhavelikedtohaveavailableasabasisforthecourses wedeveloped.Inshort,wehavetriedtowriteasomewhatdifferentintroductory textbookonthebasicconceptsofsoftmatter.Itsaimistogiveadvancedundergraduateandbeginninggraduatestudentsanintroductoryoverviewofthevarioussoft matterphasesandtheirrheology,andtheconceptualframeworktoanalyzethem.We haveattemptedtochooseourapproachandtopicsinsuchawaythatstudentswho specializeinothersub-disciplineswillacquireagoodoverviewofthefield,andget familiarwithconceptsandtreatmentsthathavebroaderapplication.Moreover,as studentsandresearchersnowadaysaremotivatedmorethanevertopayattentionto possibleapplicationsoftheirinsightsandmethods,inbothscienceandtechnology, wepayattentiontothelargerangeofapplications.Forstudentswhocontinueinsoft matterresearch,thebookshouldbeasteppingstoneforfurtherspecialization,while forstudentswhosemainresearchfocusisinbiomatterorattheinterfaceofphysics withbiology,thisbookshouldgivethemthenecessarybackgroundtounderstand theapplicationofsoftmatterphysicsconceptsinbiology.Wehavemadeaneffortto includelinksbetweensoftmatterandbiomatterthroughoutthebook.

Adistinctivefeatureofourtreatment,especiallywhencomparedtomostotherintroductorysoftmatterphysicsbooks,isitsfocusonthepowerofphenomenology andthehydrodynamicapproach.Thebookreviewsthemainsoftmatterclassesand theirrheologywithembeddedexplanationsofkeyconceptsandmethods(scaling,

Landauapproach,bifurcations,correlationfunctions,renormalizationgroup,scatteringapproach,etc.)withoutassumingdetailedpreviousknowledgeofcontinuum mechanics.Wedoassumesomebackgroundinstatisticalphysicsandsomeelementaryknowledgeofphasetransitions,though.Quiteafewconceptsappearseveral timesindiﬀerentchaptersandexamples,asthisdeepensthestudents’understandingandstimulatesthemtoexplorehowthevarioustopicsareinterrelated.Through this,wehopetodevelopstudents’intuitionandgivethemakindofintellectual ’agility’inreasoningtheirwaythroughcomplexsoftmatterphenomena.

Ourapproachistodevelopmanysuchembeddedconcepts’onthefly,’ratherthanin separateappendicesorboxes,mirroringhowweourselvesoftenpickupnewconcepts whiledoingresearch,orfromtalks.Thesameholdsforsomeofthemoderntopics wetouchononlybrieflywithashortparagraph,afigure,oranoteinthemargin. Werealizethat,asaresult,suchtopicsaretypicallynotdevelopedinasmuchdepth orassystematicallyastheywouldbewereseparatesectionsorappendixesdevoted tothem.Butourownstudentsappreciatethismoreinformalstyle,whichiscloser tohowscienceisactuallyoftendoneinpractice.Moreover,theyfinditstimulates themtorealizeandexploreconnectionsbetweentopicsthatinthebeginningoftheir studiesweretreatedasseparatesubjects.Wehavealsoexperiencedthatithelps topromotetheiragilityandtoovercometheirhesitancetoworkwithaconcept theyhavenotmasteredcompletely.Weroutinelygivepointerstoliteraturewhere interestedstudentscanfindmoreinformation.

Wesupportthisstyleandapproachwithourlayoutanduseofreferences.Wedevelop themainstorylineinthetextasmuchaspossibleandwithoutinterruptions,andwe reservenotesinthemargintopointoutconnectionsortodrawthestudent’sattentiontoimportantsideissues.Weviewthesemarginnotes,whichoftenalsocontain referencestorelevantpapersortomoredetailedtreatmentsinothertextbooks,as anintegralpartofourapproach.Numberedendnotesareusedforbackingupsome oftheassertionsinthetext,orfordrawingattentiontosubtletiesorconnectionsto otherworks.Theseendnotesareintendedforstudentswhoareeagertolearneven more;sometimestheyprovideanswerstosubtlequestionswhichmightemergefrom studyingthemaintext.Weimagineareaderskippingtheseendnoteswhenstudying atopicfortheﬁrsttime.

Thephilosophysketchedaboveisalsoreflectedintheorganizationofthechapters. Theyalwaysstartwithafocusonintroducingandexplainingthebasicconcepts;we envisionalecturerwantingtotreatthesesectionsindetailifthebookisusedasthe basisforacourse.Towardtheend,mostchaptersshifttodescriptionsofinteresting examplesandapplications,whichstudentsshouldbeabletostudybythemselves. Thereare,ofcourse,ampleopportunitiesforlecturerstohighlightafewofthese topicsandexpandonthem,dependingonthefocusofthecourseandtheinterests ofthestudents.Butlecturersareadvisedtomakeaselectionhereandencouragethe studentstostudytheothermaterialbythemselvestoenhancetheirunderstanding ofthefieldanditsbreadth.Wehaveattemptedtoprovidesufficientreferencestothe literatureinalltheselatersections,whichcouldalsobeusedasabasisforstudent presentations.

Introducingwell-establishedconceptswhicharepartofatraditionalﬁeldorofthe softmattercanon,andconnectingthemwithpresent-daydevelopments,hasforcedus repeatedlytomaketoughchoicesaboutexamples.Wehavetriedtopickrepresentative

experimentsorresultsfromtopicswhicharelikelytocontinuetobeactivelyexplored inthecomingyears,andtoincludereferencestoreviewsthatwillgiveasuitableentry tothetopictostudentswhowouldliketoknowmore.Inevitably,theinterestsand knowledgeoftheauthorsintroduceanelementofbiasinthesechoices.

Wehavesplittheproblemswhichcomewitheverychapterasmuchaspossible intosmall,concretesteps.Here,too,wehavebeenledbyourexperiencewithundergraduatestudentsandthefeedbackwehavereceivedfromthem.Asmuchas possible,theproblemshavebeendesignedsothatifastudenthasdiﬃcultywithone particularstep,theyshouldbeabletomoveontothenext.Thestep-by-stepformat oftheproblemsshouldalsomakethemparticularlysuitableforactivelearningand reverseclassroomsettings.Similarly,instructorscaneasilytransformtheseproblems intoadvancedlecturesbyintegratingmathematicaldetailsintothemorequalitative introductionsweprovideinthemaintext.Wehavesuccessfullyadoptedthisapproachourselveswhenteachingthematerialingraduateclasses.Wehopethatthe step-by-stepsolutionsavailableintheinstructormanualwillhelpotherinstructors achievethisgoal.Themoreadvancedproblemsaremarkedwithanasterisk,themost challengingoneswithtwoasterisks.

Studentsarealsoencouragedtodeepentheirunderstandingofthevarioustopics bysimulatingsimpleprocessesonacomputer.Inordertofacilitateupdatingand downloadingofcode,andtoincludelinkstorelevantothermaterial,wehavemade suggestionsforcodingproblemsavailableonthewebsite www.softmatterbook.online complementingthisbook.

Thetopicstotreatifthisbookisusedforacoursewillnaturallydependonthe backgroundandlevelofthestudents.ThechaptersinpartIofthebookhavebeen includedforstudentslikemostofourown,whohavenotyethadanintroduction tofluiddynamicsandelasticitytheory,andwhowouldlikeashortrefresheron fluctuations.Eventhoughtheintroductorypartsofthesechapterscouldbeskipped bysomestudents,themoreadvancedpartsconnecttheclassicalfieldswithmore moderndevelopmentsthatmaybeneweventosomeprofessors.Sowerecommend payingattentiontotheseextensions.PartIIcontainsthecorematerialofthebook; ofthiswesuggeststudyingatleastchapters4–6,andtimepermittingalsochapter 7.WhetherornotanyoftheadvancedtopicsofpartIIIareincludedwilldepend verymuchonthebackgroundandinterestsofthestudentsandthenumberofhours available.Theycanbeleftoutofanintroductorycoursewithoutharm.Thematerial inthesechapters(possiblysupplementedbyselectedreadingsfromearlierchapters orfromintroductorytextbooksondynamicalsystems)couldformthebasisofanadvancedgraduatecourseemphasizingnon-equilibriumaspectsofsoftmatterphysics. Wehadpositiveexperiencesteachingpartsofthisadvancedmaterialinsummer schoolsalsoattendedbypostdocsandcolleagues.WeendthebookinpartIVwitha briefperspectiveonnewfrontiersinsoftmatterresearch.Unlikethepreviouschapters,theoneinthispartismuchlessinthestyleofatextbook—itprimarilygives aglimpseofemergingnewdirections,mostlybywayofexamples.Theseexamples andcorrespondingpointerstotheliteratureprovideplentyofinspirationforstudents topickend-of-courseprojectsaimedatindependentlystudyingpapersandpresentingtheminactivelearningsessions.Theprojectscancomplementourproblemsas amoredynamicwayofgettingstudentsengagedandfacilitatingtheirtransitionto research.

Thisbookofcoursereflectsourownunderstandingofsoftmatter,aswellasour ownspecificinterestsandstyle.Bothhavebeenshapedbyourownteachersand byinteractionswithmanycolleaguesworldwidewhosharedtheirknowledgeand passionwithus.WvSwouldliketotakethisopportunitytoexpresshisindebtedness totwoformercolleaguesatBellLabs,JohnWeeksandthelatePierreHohenberg. VVwouldliketothankDavidNelsonforallowinghimtoseebeautyincondensed matterphysicsthroughhiseyes.ZZwouldliketothankSidNagel,MartinvanHecke, andMichaelBrennerfortheirlong-lastingmentorshipandcollaboration.Hopefully thisbookreflectshoweachofthem,inhisownway,setaninspiringexampleforour careers,forhowtoapproachphysics,andforwritingwithpassionandclarity.

Overtheyears,wehavehadtheprivilegeofinteractingandcollaboratingwithmany wonderfulcolleagueswhohavesharedtheirinsightswithus.Ourunderstanding ofthetopicstreatedinthisbookhasbenefitedinparticularfromdiscussionsand collaborationswithDanielAalberts,AlexanderAbanov,AndreaAlù,ArielAmir, DenisBartolo,KatiaBertoldi,JoséBico,DanielBonn,MarkBowick,ErezBraun, MichaelBrenner,CarolinaBrito,JasnaBrujic,ChristianeCaroli,MikeCates,Paul Chaikin,HuguesChaté,PatCladis,AdamCohen,ItaiCohen,CorentinCoulais, ChiaraDaraio,OlivierDauchot,BennyDavidovitch,JuanDePablo,MartinDepken, ZvonimirDogic,MarileenDogterom,UteEbert,WouterEllenbroek,NiktaFakhri, AlbertoFernandez-Nieves,DaanFrenkel,JoostFrenken,MichelFruchart,Margaret Gardel,LucaGiomi,PaulGoldbart,NigelGoldenfeld,RayGoldstein,RaminGolestanian,MingHan,SilkeHenkes,MartinHoward,DavidHuse,WilliamIrvine,HeinrichJaeger,RandyKamien,NathanKeim,KinneretKeren,DanielaKraft,Ludwik Leibler,StanLeibler,HenkLekkerkerker,DovLevine,PeterLittlewood,AndreaLiu, DetlefLohse,TeresaLopez-Leon,TomLubensky,AndyLucas,TonyMaggs,LakshminarayananMahadevan,VinnyManoharan,CristinaMarchetti,AlexanderMorozov, ArvindMurugan,SidNagel,DavidNelson,PeterPalffy-Muhoray,DebPanja,JiwoongPark,JaysonPaulose,JoeyPaulsen,DavidPine,WilsonPoon,PatrickOakes, SriramRamaswamy,PedroReis,OlivierRivoire,BenRogers,BenoitRomain,Chris Santangelo,SriSastri,MichaelSchindler,JimSethna,BorisShraiman,JaccoSnoeĳer, EllákSomfai,AntonSouslov,FrancescoStellacci,KeesStorm,SebastianStreichan, ShashiThutupalli,BrianTighe,JohnToner,FedericoToschi,AriTurner,SuriVaikuntanathan,Jan-WillemvandeMeent,WillemvandeWater,MartinvanHecke,Hans vanLeeuwen,BrianVansaders,DaveWeitz,MaxWelling,TomWitten,andMathieuWyart.Wesuspectvirtuallyallofthemwillbeabletoidentifyparticularchoices, viewpoints,orwordingswhichtheyrecognizeasreflectingourinteractions—weowe youabigthanks!

Inaddition,WvSwouldliketothankLucaGiomiforgraciouslysharinghisnotes fromanearliersoftmattercoursewhenWvSstartedteachingthecoursewhich eventuallystimulatedhiswritingthisbook,andZhihongYouandLudwigHoﬀmann whoasteachingassistantsdevelopedseveralproblemsforthecourse;someofthese foundtheirwaytothisbook.Similarly,VVwouldliketothankVinzenzKoning, RichardGreen,TaliKhain,NoahMitchell,Colin,Scheibner,JonathanColenandLuca ScharrerforservingasteachingassistantsinthecourseshetaughtatLeidenand Chicagoandhelpinginpreparingproblemsets,solutions,andlecturenotes.Wethank LucaScharrerandEgeErenforpreparingtypesetsolutionsoftheproblemsforthe instructormanual.Finally,wewouldliketothankYaelAvni,ChaseBroedersz,Sujit Datta,JohnDevany,MarjoleinDĳkstra,DaanFrenkel,MichelFruchart,TaliKhain,

DanielaKraft,HenkLekkerkerker,DetlefLohse,DavidMartin,AlexandreMorin, AlexanderMorozov,MichaelSchindler,DanielSeara,KeesStorm,SebastianStreichan,andMartinvanHecke,whoprovidedinputorfeedbackduringthewriting process,fortheirhelpandtheiradviceandAndrejMesarosforhisgeneroushelp, support,andadvicethroughoutthewholeprocess.

Wewouldalsoliketoexpressourgratitudetothegreatmanycolleagueswhowere kindenoughtoprovideuswithhigh-resolutionimagesorplotsfromtheirearlier work.Theirnamesaregiveninthecreditlistattheendofthebook.

Finally,wewouldliketothankseveralstaffmembersofPrincetonUniversityPress fortheirwarm,dedicated,andeminentsupport:IngridGnerlichforstimulatingus towritethisbook,andforadvisingandguidingusthroughtheapplication,writing, andreviewprocedure;WhitneyRauenhorstforherhelpandadviceonthefigures; NatalieBaanforoverseeingandcoordinatingtheproduction;DimitriKaretnikovfor invaluableadviceonfinalizingtheart;andcopyeditorsBhishamBherwaniandWill DeRooyformeticulouslygoingthroughthemanuscripttopreserveconsistencyof styleandpresentation,andensureuseofproperEnglish.

Youwillbeabletoﬁndsupplementarymaterialandcodingproblemsforeachchapter onourbook’swebsite www.softmatterbook.online.Wewillalsokeepalistoferrataon thiswebsiteandwillbegratefultoreaderswhosendusanycommentsonthematerial andthewaywepresentit,orsuggestionsforadditionalcomputersimulations.You cancontactusviathiswebsite.

Leiden,Chicago,andParis

WimvanSaarloos,VincenzoVitelli,ZoranaZeravcic

September2023