Soft matter physics: an introduction

664 Pages·2003·11.209 MB·English

by  Maurice Kleman, Oleg D. Lavrentovich

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.
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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
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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