Table Of ContentSpringer Series in Materials Science 260
Tian-You Fan
Wenge Yang
Hui Cheng
Xiao-Hong Sun
Generalized
Dynamics
of Soft-Matter
Quasicrystals
Mathematical Models, Solutions and
Applications
Second Edition
Springer Series in Materials Science
Volume 260
SeriesEditors
RobertHull,CenterforMaterials,Devices,andIntegratedSystems,Rensselaer
PolytechnicInstitute,Troy,NY,USA
ChennupatiJagadish,ResearchSchoolofPhysicsandEngineering,Australian
NationalUniversity,Canberra,ACT,Australia
YoshiyukiKawazoe,CenterforComputationalMaterials,TohokuUniversity,
Sendai,Japan
JamieKruzic,SchoolofMechanical&ManufacturingEngineering,
UNSWSydney,Sydney,NSW,Australia
RichardM.Osgood,DepartmentofElectricalEngineering,ColumbiaUniversity,
NewYork,USA
JürgenParisi,UniversitätOldenburg,Oldenburg,Germany
UdoW.Pohl,InstituteofSolidStatePhysics,TechnicalUniversityofBerlin,
Berlin,Germany
Tae-YeonSeong,DepartmentofMaterialsScience&Engineering,
KoreaUniversity,Seoul,Korea(Republicof)
Shin-ichiUchida,ElectronicsandManufacturing,NationalInstituteofAdvanced
IndustrialScienceandTechnology,Tsukuba,Ibaraki,Japan
ZhimingM.Wang,InstituteofFundamentalandFrontierSciences-Electronic,
UniversityofElectronicScienceandTechnologyofChina,Chengdu,China
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· · ·
Tian-You Fan Wenge Yang Hui Cheng
Xiao-Hong Sun
Generalized Dynamics
of Soft-Matter Quasicrystals
Mathematical Models, Solutions
and Applications
Second Edition
Tian-YouFan WengeYang
SchoolofPhysics CenterforHighPressureScience
BeijingInstituteofTechnology andTechnologyAdvancedResearch
Beijing,China Shanghai,China
HuiCheng Xiao-HongSun
HebeiUniversityofEngineering ZhengzhouUniversity
Handan,China Zhengzhou,China
ISSN0933-033X ISSN2196-2812 (electronic)
SpringerSeriesinMaterialsScience
ISBN978-981-16-6627-8 ISBN978-981-16-6628-5 (eBook)
https://doi.org/10.1007/978-981-16-6628-5
1stedition:©SpringerNatureSingaporePteLtd.andBeijingInstitutionofTechnologyPress2017
2ndedition:©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringer
NatureSingaporePteLtd.2022
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Preface to the Second Edition
Duetolimitedexperimentaldatareportedsincethepublicationofthefirstedition,
thestudyongeneralizeddynamicsofsoft-matterquasicrystalshasnotachievedgreat
progress. In this second edition, we still mainly focus on the mathematical model
butprovidesomeapplicationsadditionaltothefirstedition.
Nevertheless, there are still some steady progress in the experimental study in
the field. The observation of the 10-fold symmetry soft-matter quasicrystal is an
example,1theimportanceofwhichwillbebeyondthatofthefirstdiscovered12-fold
one,althoughthedetailshavenotbeenopenlydiscussedyet.Thisfindingextended
thepresenceofsoft-matterquasicrystalsinabroaderrangeandwouldbringfruitful
expectationsinbothexperimentalandtheoreticalstudies.
Another progress is the experimental and theoretical study on the correlations
between the Frank-Kasper phase and soft-matter quasicrystals in giant molecules.
ThiscontributionwasmadebythegroupofProf.StephenZ.D.Chengandwillbe
introducedinChap.2inthesecondedition.
Intheoreticalaspects,wewillalsointroducetherecentprogress.
In this circumstance, we strengthen the discussions on possible applications of
thetheoryandthemethodinnewareas,forexample,thermodynamicstability,three-
dimensionalproblems,devicephysics,liquidcrystals,generalsoftmatter,etc.,which
willbeintroducedinChaps.13–16.Ofcourse,theapplicationsareinthepreliminary
phase.
Thankstothesuggestionsfromthereaders,wepaidmoreattentiontosupplement
recentcomputationalmodelsandsimulationresultsinthesecondeditiontovisualize
thetheoreticalformulas.Inaddition,althougherrorsandmistakesinthefirstedition
havebeencorrected,theremightstillbeerrorsandmistakes.Theauthorsaregrateful
toanycriticismfromthereaderssothatwecancontinuouslyimprovethebook.
1The10-foldsymmetryquasicrystalsinsoftmatterwillbereportedbyExpandingQuasiperiodicity
inSoftMatter:DecagonalQuasicrystalsbyHierarchicalPackingFrustrations.Authors:YuchuLiu,
TongLiu,XiaoyunYan,Qing-YunGuo,HuanyuLei,ZongwuHuang,RuiZhang,YuWang,Jing
Wang, Feng Liu, Feng-Gang Bian,E.W. Meijer,Takuzo Aida, Mingjun Huang, Stephen Z. D.
Cheng,Proc.Natl.Acad.Sci.,inpress,2021.
v
vi PrefacetotheSecondEdition
The first author thanks the National Natural Science Foundation of China and
theAlexandervonHumboldtFoundationofGermanyfortheirsupportoverthelast
decades. The work is also partially supported by the School of Physics, Beijing
InstituteofTechnology.
We thank Professors T. C. Lubensky from the University of Pennsylvania, the
USA,StephenZ.D.ChengfromtheUniversityofAkron,theUSAandSouthChina
UniversityofTechnology,Yu-GuiYaofromBeijingInstituteofTechnology,Wei-Qiu
ChenfromZhejiangUniversity,Xian-FangLifromCentralSouthUniversity,Ming-
JunHuangfromSouthChinaUniversityofTechnology,ChinaandC.Pengfromthe
UniversityofMemphis,theUSAfortheirkindadviceandhelpfuldiscussions.
The authors are grateful to researcher in metallic materials Prof. Zi-Tong Li,
formerstudentFangWangfromBeijingInstituteofTechnologyfortheirhardwork
duringthepreparationofthissecondedition.
Due to their important contributions to the second edition, Wenge Yang, Hui
Cheng,andXiao-HongSunareinvitedasco-authorstotakechargeofthebookwith
me.
Beijing,China Tian-YouFan
December2021
Preface to the First Edition
Since 2004, quasicrystals have been discovered in various kinds of soft matters,
including liquid crystals, colloids, polymers, and nanoparticles. In particular, 18-
fold symmetry quasicrystals in colloids were observed in 2011. More recently the
quasicrystals with 12-fold symmetry were also found in surfactants. The forma-
tion mechanisms of these kinds of quasicrystals are associated closely with the
self-assembly of spherical building blocks by supramolecules, compounds, and
block copolymers, and so on, which is quite different from that of the metallic
alloy quasicrystals. They can be identified as soft-matter quasicrystals, exhibiting
naturesofquasicrystalswithsoft-mattercharacters.Soft-matterbehaviorisbetween
solid and simple fluid, while the quasicrystals form in highly ordered structures
withcrystalline-forbiddensymmetry.Thesefeaturesareverycomplexyetextremely
interestingandattractive.Since2004,soft-matterquasicrystalstudieshaveattracted
attentioninmathematics,physics,chemistry,andmaterialsscience.
Sofarallobservedsoft-matterquasicrystalsaretwo-dimensionalquasicrystals.It
iswellknownthattwo-dimensionalquasicrystalsconsistofonlytwodistincttypes,
onepresents5-,8-,10-,and12-foldsymmetries,theother7-,9-,14-,and18-fold
onesaccordingtothegroupsymmetrytheory.Therefore,twoterminologicalphrases
canbedefinedsuchasthefirstandsecondkindsoftwo-dimensionalquasicrystals
respectively. The two-dimensional solid quasicrystals observed so far only belong
tothefirstkind,whilesoft-matterquasicrystalsdiscovereduptonowbelongtoboth
kinds.Itislikelyothersoft-matterquasicrystalsbeyond12-and18-foldsymmetries
couldbefound.Therefore,itisquiteimportanttodevelopasuiteofgeneralprinciples
todescribeelasticityandfluiddynamics.
Itisquitedifficulttostudythesenewphasesduetothecomplexityoftheirstruc-
turesandlimitedexperimentaldataincludingthebasicphysicalconstants.Itistrue
for theoretical studies as well. For example, the symmetry groups of soft-matter
quasicrystalshaveyetbeenthoroughlyinvestigated,andonlysomepreliminarywork
hasbeenreportedsofar(thedetailsarenotincludedinthebook).Inconjunctionwith
thisissue,thestudyonconstitutivelawsforphasonandphonon-phasoncouplingis
stilldifficult.
vii
viii PrefacetotheFirstEdition
Despite only very limited experimental and theoretical studies reported so far,
there is great potential to push these directions forward. For example, the soft-
matterquasicrystalsasaneworderedphaseareconnectedwithsymmetrybreaking,
like those discussed in solid quasicrystals. Thus, elementary excitations such as
phonon and phason are important issues in the study of quasicrystals based on
the Landau phenomenological theory. For soft-matter quasicrystals, furthermore,
anotherelementaryexcitation—fluidphononwillbeconsideredbesidesphononand
phason.AccordingtotheLandauschool,theliquidacousticwaveisafluidphonon
(refertoLifshitzEMandPitaevskiiLP,StatisticalPhysics,Part2,Pergamon,Oxford,
1980).Thisissuitablefordescribingtheliquideffectofsoftmatter,whichcanbe
seenascomplexliquidsorstructuredliquids.Theelementaryexcitations—phonon,
phason,andfluidphononandtheircouplingtermsconstitutethemainfeatureofthese
new phases. They will be discussed as a major issue through this book. The fluid
phononwasfirstintroducedinthequasicrystalsstudy.Correspondingly,theequation
ofstateshouldalsobeintroducedinsoft-matterquasicrystalstudy.Combiningthese
twokeyconceptswiththehydrodynamicsprincipleestablishedinsolidquasicrystals,
thedynamicsofsoft-matterquasicrystalscanbeconstructed.Forsolidquasicrystals,
therehasbeentremendousprogressoverlastdecades,forexample,LubenskyTC,
Symmetry, elasticity, and hydrodynamics in quasiperiodic structures, in Introduc-
tiontoQuasicrystals,edbyJaricMV,Boston:AcademicPress,190-289,1988;Hu
ZCetal,Symmetrygroups,physicalpropertytensors,elasticityanddislocationsin
quasicrystals,Rep.Prog.Phys.,63(1),1-39,2000;FanTY,MathematicalTheoryof
ElasticityofQuasicrystalsandItsApplications,Beijing:SciencePress/Heidelberg,
Springer-Verlag,1stedition,2010,2ndedition2016.Basedonthedevelopmentof
thetheoryofsolidquasicrystals,wewillextendthequantitativeanalysisintotherich
phenomenaofsoft-matterquasicrystals.
Someapplicationswillbediscussedonthedistribution,deformation,andmotion
ofsoft-matterquasicrystals.Themathematicalprinciplesandapplicationsrequired
arebrieflyreviewedinthefirstsixchaptersofthisbook(formoredetails,referto
Chaikin J and Lubensky TC, Principles of Condensed Matter Physics, New York:
CambridgeUniversityPress,1995).Thecomputationalapplicationsonsoft-matter
quasicrystalsarequitepreliminary,buttheyverifiedpartiallythemathematicalmodel
andexploredthedistinguisheddynamicbehaviorfromsolidquasicrystals.Inaddi-
tion, specimens and flow modes adopted in the computation modeling might be
intuitive,observable,andcanbeverifiedeasily.
The author thanks the National Natural Science Foundation of China and
AlexandervonHumboldtFoundationofGermanyfortheirfinancialsupportoverthe
yearsandProfessorsU.MesserschmidtfromMax-PlanckInstitutfurMikrostruktur-
physikinHalle,H.-R.TrebinfromStuttgardUniversitaetinGermany,T.C.Lubensky
from the University of Pennsylvania, Stephen Z. D. Cheng from the University of
PrefacetotheFirstEdition ix
Akron in the USA, H. H. Wensink from Utrecht University in Netherland, Xian-
FangLifromCentralSouthUniversityinChina,andWei-QiuChenfromZhejiang
UniversityinChinafortheircordialencouragementandhelpfuldiscussions.
Beijing,China Tian-YouFan
December2016
