Helical Wormlike Chains in Polymer Solutions

517 Pages·2016·11.655 MB·English

by  Hiromi Yamakawa, Takenao Yoshizaki (auth.)

Hiromi Yamakawa
Takenao Yoshizaki
Helical Wormlike
Chains in
Polymer
Solutions
Second Edition
Helical Wormlike Chains in Polymer Solutions

Hiromi Yamakawa • Takenao Yoshizaki
Helical Wormlike Chains
in Polymer Solutions
Second Edition
123
HiromiYamakawa TakenaoYoshizaki
DepartmentofPolymerChemistry DepartmentofPolymerChemistry
KyotoUniversity,Katsura KyotoUniversity,Katsura
Kyoto,Japan Kyoto,Japan
ISBN978-3-662-48714-3 ISBN978-3-662-48716-7 (eBook)
DOI10.1007/978-3-662-48716-7
LibraryofCongressControlNumber:2016931908
SpringerHeidelbergNewYorkDordrechtLondon
©Springer-VerlagBerlinHeidelberg1997,2016
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Preface
A rather large amount of material has been accumulated in the field during the
past nearly two decades since the publication of the first edition by the present
senior author in 1997. The new material may be divided into three groups. The
firstcontainsmainlyexperimentalresultssuccessivelyobtainedforstatic,transport,
anddynamicalproperties,the seconddealswith ringpolymers(includingcircular
DNA) studied both experimentally and theoretically with the use of Monte Carlo
simulation, and the third concerns such simulations on excluded-volume effects,
includingthoseinpolyelectrolytes.Theseresultsandsomeadditionaldescriptions
wereincludedinthechapters(exceptChaps.4and10)ofthepresentedition,whose
Chap.9wasnewlyadded.ThisworkwasdoneunderjointauthorshipwithProfessor
T. Yoshizaki. On that occasion, the authors also attempted their efforts to correct
errorsinthefirsteditionasmuchaspossible.
Finally,itisapleasuretoacknowledgetheassistanceofDr.D.Idawhoprepared
newly some of the tables and figures and of the author and subject indexes and
correctedsomeoftheerrors.
Kyoto,Japan HiromiYamakawa
September2015
v

Preface to the First Edition
This book is intended to give a comprehensive and systematic description of the
statistical-mechanical,transport,anddynamictheoriesofdilute-solutionproperties
of both flexible and semiflexible polymers, including oligomers. This description
was developed on the basis of the “helical wormlike chain” model along with an
analysis of extensive experimental data. Chapter 2 and the fundamental parts of
Chaps.3,4,6,and9arebasedontheauthor’slecturenotesforcoursesinpolymer
statistical mechanics given at the Graduate School of Kyoto University in 1978
through1994. Much of the material in the bookarises from his research reported
sincethetimeofpublication(1971)ofhisearlierbook,ModernTheoryofPolymer
Solutions.
The accomplishment of this research was made possible by the collaboration
of his students, postdoctoral students, and other collaborators, especially F. Abe,
Y. Einaga, M. Fujii, W. Gobush, T. Konishi, K. Nagasaka, M. Osa, N. Sawatari,
J.Shimada,W.H.Stockmayer,Y.Takaeda,andT.Yoshizaki.ProfessorW.H.Stock-
mayergavetheauthoranopportunitytostayinHanoverin1971/1972,andindeed
the research in this book was started at that time. Professor T. Norisuye, who is
not a collaborator of the author but his colleague, kindly provided him with the
unpublishedmaterialonthethirdvirialcoefficientdealtwithinChap.8.
The author is indebted to Dr. J. Shimada for his careful checking of the
mathematicalequationsinthe manuscript.Finally,it isa pleasureto acknowledge
the assistance of Prof. T. Yoshizaki and Mr. M. Osa who prepared some of the
tablesandfiguresandalsotranslatedthemanuscriptintothecompuscriptwithMiss
M.Fukui.
Kyoto,Japan HiromiYamakawa
January1997
vii

Contents
1 Introduction................................................................. 1
1.1 HistoricalSurvey..................................................... 1
1.2 Scope.................................................................. 5
References.................................................................... 7
2 ModelsforPolymerChains................................................ 9
2.1 DiscreteModels...................................................... 9
2.1.1 AverageChainDimensions ................................ 9
2.1.2 Random-FlightChains:TheGaussianChain ............. 11
2.1.3 FreelyRotatingChains..................................... 11
2.1.4 Chains with Coupled Rotations:
TheRotationalIsomericStateModel...................... 13
2.2 ContinuousModels................................................... 15
References.................................................................... 18
3 ChainStatistics:WormlikeChains....................................... 21
3.1 DefinitionoftheModel.............................................. 21
3.2 DiffusionEquations.................................................. 23
3.2.1 GreenFunctions ............................................ 23
3.2.2 Fokker–PlanckEquations .................................. 24
3.2.3 PathIntegralsandFormalSolutions....................... 27
3.3 Moments.............................................................. 31
3.3.1 h.R(cid:2)u0/ni................................................... 31
3.3.2 hR2mi ........................................................ 33
3.4 DistributionFunctions ............................................... 34
3.4.1 AsymptoticBehavior:Daniels-TypeDistributions........ 34
3.4.2 NeartheRodLimit......................................... 39
3.5 DiscreteVersionoftheWormlikeChain............................ 43
References.................................................................... 57
ix