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Springer 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 TheSpringerSeriesinMaterialsSciencecoversthecompletespectrumofmaterials research and technology, including fundamental principles, physical properties, materials theory and design. Recognizing the increasing importance of materials science in future device technologies, the book titles in this series reflect the state-of-the-art in understanding and controlling the structure and properties of allimportantclassesofmaterials. Moreinformationaboutthisseriesathttps://link.springer.com/bookseries/856 · · · 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 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSingaporePteLtd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore 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

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