Modeling of Soft Matter (eBook)

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2008 | 2005
X, 250 Seiten
Springer New York (Verlag)
978-0-387-32153-0 (ISBN)

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This IMA Volume in Mathematics and its Applications MODELING OF SOFT MATTER contains papers presented at a very successful workshop with the same ti­ tle. The event, which was held on September 27-October 1, 2004, was an integral part of the 2004-2005 IMA Thematic Year on 'Mathematics of Ma­ terials and Macromolecules: Multiple Scales, Disorder, and Singularities. ' We would like to thank Maria-Carme T. Calderer (School of Mathematics, University of Minnesota) and Eugene M. Terentjev (Cavendish Laboratory, University of Cambridge) for their superb role as workshop organizers and editors of the proceedings. We take this opportunity to thank the National Science Foundation for its support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Arnd Scheel, Deputy Director of the IMA PREFACE The physics of soft matter in particular, focusing on such materials as complex fluids, liquid crystals, elastomers, soft ferroelectrics, foams, gels and particulate systems is an area of intense interest and contemporary study. Soft matter plays a role in a wide variety of important processes and application, as well as in living systems. For example, gel swelling is an essential part of many biological processes such as motility mecha­ nisms in bacteria and the transport and absorption of drugs. Ferroelectrics, liquid crystals, and elastomers are being used to design ever faster switch­ ing devices. Experiments of the last decade have provided a great deal of detailed information on structures and properties of soft matter.
This IMA Volume in Mathematics and its Applications MODELING OF SOFT MATTER contains papers presented at a very successful workshop with the same ti- tle. The event, which was held on September 27-October 1, 2004, was an integral part of the 2004-2005 IMA Thematic Year on "e;Mathematics of Ma- terials and Macromolecules: Multiple Scales, Disorder, and Singularities. "e; We would like to thank Maria-Carme T. Calderer (School of Mathematics, University of Minnesota) and Eugene M. Terentjev (Cavendish Laboratory, University of Cambridge) for their superb role as workshop organizers and editors of the proceedings. We take this opportunity to thank the National Science Foundation for its support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Arnd Scheel, Deputy Director of the IMA PREFACE The physics of soft matter in particular, focusing on such materials as complex fluids, liquid crystals, elastomers, soft ferroelectrics, foams, gels and particulate systems is an area of intense interest and contemporary study. Soft matter plays a role in a wide variety of important processes and application, as well as in living systems. For example, gel swelling is an essential part of many biological processes such as motility mecha- nisms in bacteria and the transport and absorption of drugs. Ferroelectrics, liquid crystals, and elastomers are being used to design ever faster switch- ing devices. Experiments of the last decade have provided a great deal of detailed information on structures and properties of soft matter.

FOREWORD 6
PREFACE 7
CONTENTS 9
AN ENERGETIC VARIATIONAL FORMULATION WITH PHASE FIELD METHODS FOR INTERFACIAL DYNAMICS OF COMPLEX FLUIDS: ADVANTAGES AND CHALLENGES 11
1. Introduction 11
2. An energy-based phsuse-field theory. 13
3. Numerical scheme. 16
4. Advantages of the diffuse-interface model. 18
5. Physical and numerical subtleties. 22
6. Concluding remarks. 31
7. Acknowledgments. 32
REFERENCES 32
NON-EQUILIBRIUM STATISTICAL MECHANICS OF NEMATIC LIQUIDS 37
1. Introduction. 37
2. Kinetic equation. 40
3. Viscous stress tensor. 51
4. Microscopic viscosity coefficients. 58
5. Rotational friction constant. 72
6. Spatial inhomogeneities and domain structure. 85
REFERENCES 92
ANISOTROPY AND HETEROGENEITY OF NEMATIC POLYMER NANO-COMPOSITE FILM PROPERTIES 95
1. Introduction. 95
2. Plane Couette film flow of nematic polymers. 96
3. Conductivity properties across the phase diagram of flowinduced film structures. 99
REFERENCES 107
NON-NEWTONIAN CONSTITUTIVE EQUATIONS USING THE ORIENTATIONAL ORDER PARAMETER 108
1. Introduction. 108
2. Dynamics of the orientational order parameter tensor. 109
3. Stress tensor. 111
4. Dynamic stress tensor equation. 112
6. Summary. 116
REFERENCES 116
SURFACE ORDER FORCES IN NEMATIC LIQUID CRYSTALS 119
1. Introduction. 119
2. Energy and stresses. 122
3. Twist cell 125
4. Torque and force. 129
5. Surface biaxial force. 135
6. Conclusion. 137
REFERENCES 139
MODELLING LINE TENSION IN WETTING 141
1. Introduction. 141
2. Line tension effects on equilibria. 144
3. Modelling surface tension. 147
4. Modelling line tension. 153
5. Line tension elSects on stability. 157
6. Wetting transition. 166
7. Dewetting Transition. 170
8. Conclusions. 172
REFERENCES 173
VARIATIONAL PROBLEMS AND MODELING OF FERROELECTRICITY IN CHIRAL SMECTIC C LIQUID CRYSTALS 177
1. Introduction. 177
2. Free energy functions of smectic materials. 179
4. Asymptotic form of the energy minimizers. 186
5. Applied constant electric fields and boundary conditions. 190
6. Variable electric fields. 193
7. Conclusions. 194
REFERENCES 195
STRIPE-DOMAINS IN NEMATIC ELASTOMERS: OLD AND NEW 197
1. Introduction. 197
2. A minimalist model. 198
3. Stripe - domain patterns: the classics. 203
4. Stripe-domain patterns: recent observations. 205
5. Conclusions and Outlook. 209
REFERENCES 210
NUMERICAL SIMULATION FOR THE MESOSCALE DEFORMATION OF DISORDERED REINFORCED ELASTOMERS 212
1. Introduction. 212
2. Description of the model. 214
4. Results. 222
5. Conclusion. 232
6. Acknowledgments. 235
APPENDIX 235
REFERENCES 238
STRESS TRANSMISSION AND ISOSTATIC STATES OF NON-RIGID PARTICULATE SYSTEMS 241
1. Introduction. 241
LIST OF WORKSHOP PARTICIPANTS 253
IMA SUMMER PROGRAMS 257
IMA "HOT TOPICS" WORKSHOPS 258

Erscheint lt. Verlag 26.8.2008
Reihe/Serie The IMA Volumes in Mathematics and its Applications
Zusatzinfo X, 250 p.
Verlagsort New York
Sprache englisch
Themenwelt Mathematik / Informatik Mathematik Angewandte Mathematik
Naturwissenschaften Physik / Astronomie Festkörperphysik
Technik
Schlagworte complex fluid • Helium-Atom-Streuung • Mathematical Modeling • soft matter • Statistica
ISBN-10 0-387-32153-5 / 0387321535
ISBN-13 978-0-387-32153-0 / 9780387321530
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