Calderer / Terentjev / Scheel Modeling of Soft Matter

1. Auflage 2008
ISBN: 978-0-387-32153-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 141, 250 Seiten

Reihe: The IMA Volumes in Mathematics and its Applications

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.

Autoren/Hrsg.

Scheel, Arnd

Calderer, Maria-Carme T.

Terentjev, Eugene M.

Inhaltsverzeichnis

1;FOREWORD;6
2;PREFACE;7
3;CONTENTS;9
4;AN ENERGETIC VARIATIONAL FORMULATION WITH PHASE FIELD METHODS FOR INTERFACIAL DYNAMICS OF COMPLEX FLUIDS: ADVANTAGES AND CHALLENGES;11
4.1;1. Introduction;11
4.2;2. An energy-based phsuse-field theory.;13
4.3;3. Numerical scheme.;16
4.4;4. Advantages of the diffuse-interface model.;18
4.5;5. Physical and numerical subtleties.;22
4.6;6. Concluding remarks.;31
4.7;7. Acknowledgments.;32
4.8;REFERENCES;32
5;NON-EQUILIBRIUM STATISTICAL MECHANICS OF NEMATIC LIQUIDS;37
5.1;1. Introduction.;37
5.2;2. Kinetic equation.;40
5.3;3. Viscous stress tensor.;51
5.4;4. Microscopic viscosity coefficients.;58
5.5;5. Rotational friction constant.;72
5.6;6. Spatial inhomogeneities and domain structure.;85
5.7;REFERENCES;92
6;ANISOTROPY AND HETEROGENEITY OF NEMATIC POLYMER NANO-COMPOSITE FILM PROPERTIES;95
6.1;1. Introduction.;95
6.2;2. Plane Couette film flow of nematic polymers.;96
6.3;3. Conductivity properties across the phase diagram of flowinduced film structures.;99
6.4;REFERENCES;107
7;NON-NEWTONIAN CONSTITUTIVE EQUATIONS USING THE ORIENTATIONAL ORDER PARAMETER;108
7.1;1. Introduction.;108
7.2;2. Dynamics of the orientational order parameter tensor.;109
7.3;3. Stress tensor.;111
7.4;4. Dynamic stress tensor equation.;112
7.5;6. Summary.;116
7.6;REFERENCES;116
8;SURFACE ORDER FORCES IN NEMATIC LIQUID CRYSTALS;119
8.1;1. Introduction.;119
8.2;2. Energy and stresses.;122
8.3;3. Twist cell;125
8.4;4. Torque and force.;129
8.5;5. Surface biaxial force.;135
8.6;6. Conclusion.;137
8.7;REFERENCES;139
9;MODELLING LINE TENSION IN WETTING;141
9.1;1. Introduction.;141
9.2;2. Line tension effects on equilibria.;144
9.3;3. Modelling surface tension.;147
9.4;4. Modelling line tension.;153
9.5;5. Line tension elSects on stability.;157
9.6;6. Wetting transition.;166
9.7;7. Dewetting Transition.;170
9.8;8. Conclusions.;172
9.9;REFERENCES;173
10;VARIATIONAL PROBLEMS AND MODELING OF FERROELECTRICITY IN CHIRAL SMECTIC C LIQUID CRYSTALS;177
10.1;1. Introduction.;177
10.2;2. Free energy functions of smectic materials.;179
10.3;4. Asymptotic form of the energy minimizers.;186
10.4;5. Applied constant electric fields and boundary conditions.;190
10.5;6. Variable electric fields.;193
10.6;7. Conclusions.;194
10.7;REFERENCES;195
11;STRIPE-DOMAINS IN NEMATIC ELASTOMERS: OLD AND NEW;197
11.1;1. Introduction.;197
11.2;2. A minimalist model.;198
11.3;3. Stripe - domain patterns: the classics.;203
11.4;4. Stripe-domain patterns: recent observations.;205
11.5;5. Conclusions and Outlook.;209
11.6;REFERENCES;210
12;NUMERICAL SIMULATION FOR THE MESOSCALE DEFORMATION OF DISORDERED REINFORCED ELASTOMERS;212
12.1;1. Introduction.;212
12.2;2. Description of the model.;214
12.3;4. Results.;222
12.4;5. Conclusion.;232
12.5;6. Acknowledgments.;235
12.6;APPENDIX;235
12.7;REFERENCES;238
13;STRESS TRANSMISSION AND ISOSTATIC STATES OF NON-RIGID PARTICULATE SYSTEMS;241
13.1;1. Introduction.;241
14;LIST OF WORKSHOP PARTICIPANTS;253
15;IMA SUMMER PROGRAMS;257
16;IMA "HOT TOPICS" WORKSHOPS;258