Reinforcement of Polymer Nano-Composites

223 Pages·2009·2.586 MB·English

by  Vilgis T.A., Heinrich G., Klueppel M.

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REINFORCEMENT OF POLYMER NANO-COMPOSITES
Reinforced rubber allows the production of passenger car tires with improved
rollingresistanceandwetgrip.Thisbookprovidesin-depthcoverageofthephysics
behindelastomerreinforcement,withaparticularfocusonthemodificationofpoly-
merpropertiesusingactivefillerssuchascarbonblackandsilica.Theauthorsbuild
afirmtheoreticalbasethroughadetaileddiscussionofthephysicsofpolymerchains
andmatricesbeforemovingontodescribereinforcingfillersandtheirapplications
intheimprovementofthemechanicalpropertiesofhigh-performancerubbermate-
rials. Reinforcement is explored on all relevant length scales, from molecular to
macroscopic,usingavarietyofmethodsrangingfromstatisticalphysicsandcom-
puter simulations to experimental techniques. Presenting numerous technological
applicationsofreinforcementinrubbersuchastiretreadcompounds,thisbookis
idealforacademicresearchersandprofessionalsworkinginpolymerscience.
T.A.Vilgis is Professor of Theoretical Physics at the University of Mainz and a
researcher at the Max Planck Institute for Polymer Research. He is a member of
severalscientificsocietiesincludingtheGermanPhysicalSociety,EPS,andAPS.
He has written more than 250 scientific papers, three popular science books and
twoscientificcookbooks.
G.HeinrichisProfessorofPolymerMaterialsatTechnischeUniversitätDresden
andisalsoDirectoroftheInstituteofPolymerMaterialswithintheLeibnizInstitute
of Polymer Research. He has written or contributed to over 250 scientific papers
andbookchaptersonpolymerscience.
M. Klüppel is a Lecturer in Polymer Materials at Leibniz University, Hannover
and Head of the Department of Material Concepts and Modelling at the German
Institute of RubberTechnology (DIK). He has published more than 150 scientific
papersandisamemberoftheGermanPhysicalSociety,theGermanRubberSociety,
andtheRubberDivisionofACS.

REINFORCEMENT OF POLYMER
NANO-COMPOSITES
Theory, Experiments and Applications
T.A.VILGIS
Max-Planck-InstitutfürPolymerforschung,Mainz
G.HEINRICH
Leibniz-InstitutfürPolymerforschung,Dresden
M.KLÜPPEL
DeutschesInstitutfürKautschuktechnologie,Hannover
CAMBRIDGE UNIVERSITY PRESS
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São Paulo, Delhi, Dubai, Tokyo
Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521874809
© T.Vilgis, G.Heinrich and M.Klüppel 2009
This publication is in copyright. Subject to statutory exception and to the
provision of relevant collective licensing agreements, no reproduction of any part
may take place without the written permission of Cambridge University Press.
First published in print format 2009
ISBN-13 978-0-511-60501-7 eBook (NetLibrary)
ISBN-13 978-0-521-87480-9 Hardback
Cambridge University Press has no responsibility for the persistence or accuracy
of urls for external or third-party internet websites referred to in this publication,
and does not guarantee that any content on such websites is, or will remain,
accurate or appropriate.
Contents
Preface ix
Acknowledgement xii
1 Introduction 1
2 Basicsaboutpolymers 10
2.1 Gaussianchains–heuristicintroduction 10
2.2 Gaussianchains–pathintegrals 12
2.3 Self-interactingchains 15
3 Many-chainsystems:meltsandscreening 19
3.1 Somegeneralremarks 19
3.2 Collectivevariables 20
3.3 Thestatisticsoftaggedchains 26
4 Rubberformation 31
4.1 Classicaltheoryofgelation 31
4.2 Percolation 34
4.3 Vulcanization 37
5 Theelastomermatrix 40
5.1 Generalremarks 40
5.2 TheGaussiannetwork 42
5.3 Entanglementsandthetubemodel:amateriallaw 45
5.3.1 Entanglementsliding 47
5.3.2 Finiteextensibility 49
5.3.3 Tubeandsliplinks 52
v
vi Contents
5.4 Experiments 53
5.4.1 Thestress–strainrelationship 53
5.4.2 Theextendedtubemodelofrubberelasticity 55
5.4.3 Testingofthemodel 59
6 Polymersoflargerconnectivity:branchedpolymersand
polymericfractals 64
6.1 Preliminaryremarks 64
6.2 D-dimensionallyconnectedpolymersinagoodsolvent 64
6.3 D-dimensionallyconnectedpolymersbetweentwoparallel
platesinagoodsolvent 66
6.4 D-dimensionallyconnectedpolymersinacylindricalpore(good
solvent) 68
6.5 Meltsoffractalsinrestrictedgeometries 71
6.6 Oncemorethedifferences 74
7 Reinforcingfillers 75
7.1 Fillersfortherubberindustry 75
7.2 Carbonblack 77
7.2.1 Morphologyofcarbonblackaggregates 77
7.2.2 Surfaceroughnessofcarbonblacks 84
7.2.3 Energydistributionofcarbonblacksurfaces 92
7.3 Silica 96
8 Hydrodynamicreinforcementofelastomers 101
8.1 Reminder:Einstein–Smallwood 101
8.2 Rigidfilleraggregateswithfractalstructure 103
8.2.1 Effectivemediumtheoryandlinearelasticity 106
8.2.2 Screeninglengths 109
8.2.3 Reinforcementbyfractalaggregates 110
8.3 Core–shellsystems 111
8.3.1 Uniformsoftsphere 112
8.3.2 Softcore/hardshell 112
8.3.3 Hardcore/softshell 115
9 Polymer–fillerinteractions 118
9.1 Generalremarksandscaling 118
9.1.1 Flatsurface 119
9.1.2 Generalizationforfractalsurfaces 120
Contents vii
9.2 Variationalcalculationstatics 121
9.2.1 Variationalcalculation 121
9.3 TrialHamiltonian 122
9.3.1 Minimizationofthefreeenergy 123
9.3.2 Effectiveinteractionstrength 126
9.4 Somefurtherremarksontheinterpretation 130
9.4.1 Modelingbyrandompotentials 131
9.4.2 Annealedandquencheddisorder 134
9.4.3 Dynamicsoflocalizedchains–freezing,glasstransition
atfillersurfaces 135
9.5 Equationofmotionforthetimecorrelationfunction 137
9.5.1 Langevindynamics 137
9.5.2 Salf-consistentHartreeapproximation 139
9.5.3 Equationofmotion 142
9.6 Dynamicbehaviorofthechain 144
9.6.1 Anomalousdiffusion 144
9.6.2 Center-of-massfreezing 146
9.6.3 Rousemodesfreezingandatwomodetoymodel 147
9.7 Numericalanalysis 148
9.7.1 Bifurcationdiagram 149
9.8 Contributiontothemodulus 151
10 Filler–fillerinteraction 153
10.1 Fillernetworkinginelastomers 153
10.1.1 Flocculationoffillersduringheattreatment 153
10.1.2 Kineticsoffillerstructuresunderdynamicexcitation 156
10.2 Dynamicsmall-andmedium-strainmodeling–thePayneeffect 161
10.2.1 TheKrausmodel 161
10.2.2 Theviscoelasticmodel 164
10.2.3 ThevanderWalle–Tricot–Gerspacher(WTG)model 169
10.2.4 Thelinks–nodes–blobs(LNB)model 171
10.2.5 Themodelofthevariablenetworkdensity 172
10.2.6 Thecluster–clusteraggregation(CCA)model 174
10.3 Stress-softeningandquasistaticstress–strainmodeling–
theMullinseffect 182
10.3.1 Thedynamicflocculationmodel 182
10.3.2 TheKantor–Webmanmodelofflexiblechainaggregates 193
References 196
Index 204