Self-Assembly, Pattern Formation and GrowthPhenomena in Nano-Systems

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Series II: Mathematics, Physics and Chemistry – Vol. 216

Self-Assembly, Pattern Formationand Growth Phenomena in Nano-Systems

edited by

Alexander A. GolovinNorthwestern University,

Evanston, IL, U.S.A.

and

Alexander A. NepomnyashchyIsrael Institute of Technology, Haifa, Israel

Published in cooperation with NATO Public Diplomacy Division

A C.I.P. Catalogue record for this book is available from the Library of Congress.

ISBN-10 1-4020-4353-8 (PB)ISBN-13 978-1-4020-4353-6 (PB)ISBN-10 1-4020-4354-6 (HB)ISBN-13 978-1-4020-4354-3 (HB)ISBN-10 1-4020-4355-4 (e-book)ISBN-13 978-1-4020-4355-0 (e-book)

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Printed in the Netherlands.

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Proceedings of the NATO Advanced Study Institute on

August 28 September 11, 2004– St. Etienne de Tinee, France Phenomena in Nano System s Self Assembly, Pattern Formation and Growth-

-

This book is dedicated to thememory of Lorenz Kramer

v

Contents

Dedication v

Contributing Authors xi

Foreword xiii

Preface xv

Acknowledgments xvii

General Aspects of Pattern Formation 1

Alexander A. Nepomnyashchya and Alexander A. Golovinb

1 Introduction 12 Basic models for domain coarsening and pattern formation 33 Pattern selection 114 Modulated patterns 225 Beyond the Swift-Hohenberg model 416 Wavy patterns 437 Conclusions 508 Acknowledgement 52

References 52

Convective patterns in liquid crystals driven by electric field 55

Agnes Buka, Nándor Éber, Werner Pesch, Lorenz Kramer

Physical properties of nematics 57Electroconvection 61

References 80

Dynamical phenomena in nematic liquid crystals induced by light 83

Dmitry O. Krimer, Gabor Demeter, and Lorenz Kramer

Simple setups - complicated phenomena 84Theoretical description 85Obliquely incident, linearly polarized light 91Perpendicularly incident, circularly polarized light 98Perpendicularly incident, elliptically polarized light 107

115

120

Introduction 561

Finite beam-size effects and transversal pattern formation

2

79

Introduction 83

Acknowledgments

21

3456

vii

Acknowledgements

viii PATTERN FORMATION IN NANO-SYSTEMS

References 120

Self-Assembly of Quantum Dots from Thin Solid Films 123Alexander A. Golovin, Peter W. Voorhees, and Stephen H. Davis

1 Introduction 1232 Mechanisms of morphological evolution of epitaxial films 1243 Elastic effects and wetting interactions 1274 Surface-energy anisotropy and wetting interactions 1395 Conclusions 156

References 156

Macroscopic and mesophysics together: the moving contact lineproblem revisited 159Yves Pomeau

References 166

Nanoscale Effects in Mesoscopic Films 167L. M. Pismen

Hydrodynamic Equations 1691Thermodynamic Equations 1732Fluid-Substrate Interactions 1783Dynamic Contact Line 184Mobility Relations 186

References 192

Dynamics of thermal polymerization waves 195V.A. Volpert

1 Introduction 1952 Mathematical model 1983 Gasless combustion 2024 Analysis of base FP model 2305 Other thermal FP studies 2386 Conclusion 239

References 239

Spatiotemporal Pattern Formation in Solid Fuel Combustion 247Alvin Bayliss Bernard J. Matkowsky Vladimir A. Volpert

1 Introduction. 2482 Mathematical Model 2543 Analytical Results 2574 Computational Results 267

References 280

157

Introduction 167

45

192

Acknowledgment

Acknowledgements

Contents ix

Maxwell Model and Orientational Instability 285Spatial Localization 288Aster and Vortex Solutions 291Conclusion 293

Acknowledgments 294

References 294

295Maxim D. Frank-Kamenetskii

1 Introduction 2952 Major structures of DNA 2963 DNA functioning 3004 Global DNA conformation56 Conclusion

References

Topic Index

Self-organization of microtubules and motors 283Igor S. Aranson, Lev S. Tsimring

Introduction 28312

The DNA stability

3

Physics of DNA

4

303317322

322

327

Contributing Authors

xi

Dr. Igor S. Aranson, Argonne National Laboratory, 9700 South Cass Avenue,Argonne, Illinois 60439, USA

Prof. Alvin Bayliss, Department of Engineering Sciences and Applied Mathe-matics, Northwestern University, 2145 Sheridan Rd, Evanston, IL 60208, USA

Prof. Agnes Buka, Research Institute for Solid State Physics and Optics of theHungarian Academy of Sciences, Konkoly-Thege Miklos u. 29-33, H-1121Budapest, Hungary

Prof. Stephen H. Davis, Department of Engineering Sciences and AppliedMathematics, Northwestern University, 2145 Sheridan Rd, Evanston, IL 60208,USA

Dr. Gabor Demeter, Research Institute for Particle and Nuclear Physics ofthe Hungarian Academy of Sciences, Konkoly-Thege Miklos ut 29-33, H-1121Budapest, Hungary

Prof. Nandor Eber, Research Institute for Solid State Physics and Optics ofthe Hungarian Academy of Sciences, Konkoly-Thege Miklos u. 29-33, H-1121Budapest, Hungary

Prof. Maxim D. Frank-Kamenetskii, Department of Biomedical Engineer-ing, Boston University, 36 Cummington St., Boston, MA 02215, USA

Prof. Alexander A. Golovin, Department of Engineering Sciences and Ap-plied Mathematics, Northwestern University, 2145 Sheridan Rd, Evanston, IL60208, USA

xii PATTERN FORMATION IN NANO-SYSTEMS

Prof. Lorenz Kramer (deceased).

Dr. Dmitry Krimer, Physikalisches Institut der Universitaet Bayreuth, D-95440 Bayreuth, Germany

Prof. Bernard J. Matkowsky, Department of Engineering Sciences and Ap-plied Mathematics, Northwestern University, 2145 Sheridan Rd, Evanston, IL60208, USA

Prof. Alexander A. Nepomnyashchy, Department of Mathematics, Technion– Israel Institute of Technology, Haifa 32000, Israel

Prof. Werner Pesch, Institute of Physics, University of Bayreuth, D-95440Bayreuth, Germany

Prof. Leonid M. Pismen, Department of Chemical Engineering, Technion –Israel Institute of Technology, Haifa 32000, Israel

Prof. Yves Pomeau, Laboratoire de Physique Statistique de l’Ecole normalesup«erieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France

Dr. Lev S. Tsimring, Institute for Nonlinear Science, University of California,San Diego, La Jolla, CA 92093-0402, USA

Prof. Vladimir A. Volpert, Department of Engineering Sciences and Ap-plied Mathematics, Northwestern University, 2145 Sheridan Rd, Evanston, IL60208, USA

Prof. Peter W. Voorhees, Department of Materials Science and Engineering,Northwestern University, 2145 Sheridan Rd, Evanston, IL 60208, USA

Foreword

Lorenz Kramer, who was the main driving force behind the PHYSBIO pro-gram, died suddenly on 5 April 2005. This was a shock to his numerous friendswho were not aware that this strong, vigorous and buoyant man struggled formany years with a deeply rooted decease which all of a sudden went out ofcontrol.

Lorenz has always been an innovator working with enthusiasm and persua-sion on the leading edge of scientific exploration. The three main subjects ofhis work: superconductivity from 1968 to 1981; pattern formation out of equi-librium starting from 1982 ; biophysics from 1975 to 1980 and again from thestart of this century – were intertwined and supplied each other with ideas andtechniques. One example will suffice here: a direct interpretation of superflowsolutions as saddle points in transitions between different patterns – therebyconnecting two opposites: conservative and gradient systems. He was one ofthe principal players in the field of nonlinear science during its acme in 1990s,and one who directed this field, when it came of age, to new applications,in particular, in physics of liquid crystals and biophysics. Some of the mostbrilliant nonlinear scientists, both theorists and experimentalists, now in theirforties, are his former students and junior colleagues.

Lorenz’s e-mail signature once read: "Basic schedule: 0-24 - but variety isthe spice of life". And he didn’t lack variety: running alone to the highest peakin the Pyrenees after a busy week of lectures, testing the sturdy design of hisMac laptop in a backpack while biking to his office. It is thanks to him that thePHYSBIO workshops were invariably carried out at high altitude as well ason the highest scientific level. Variety was his birthmark: his father German,mother Italian, both biologists; his children branched off to industry, musicand architecture; and physics, music, poetry and mountaineering merged in hispersonality. There will be no one like him.

Leonid M. PismenTechnion, Israel

Igor S. AransonArgonne National Laboratory, USA

xiii

Preface

Non-linear dynamics and pattern formation in non-equilibrium system havebeen attracting a great deal of attention for several decades due to their tremen-dous importance in many physical, chemical and biological processes. How-ever, only recently was it realized that similar phenomena play a crucial role inthe vast majority of processes that occur on nanoscales. While on the macro-and micro-scales one has the advantage of controlling the processes by specialinstruments and devices, on nanoscales, such instruments are absent, or theiruse is prohibitively expensive. Therefore, spontaneous pattern formation, self-organization and self-assembly promise a unique route to the control of theseprocesses. The investigation of self-organization on nanoscales requires sub-stantial revision of the available scientific knowledge in pattern formation andnonlinear dynamics due to essentially new mechanisms and phenomena, thatcan be ignored in macro- and microworld, but play a decisive role in the worldwhere typical distances are measured in nanometers. The understanding of thebasic physical principles and mechanisms of self-assembly and pattern forma-tion on nanoscales can lead to a real breakthrough in nanotechnology and tothe creation of a new generation of electronic devices, sensors, detectors, aswell as “labs-on-a-chip".

The need for intensive investigation of basic mechanisms of self-assemblyand self-organization on nanoscales, as well as the need to draw the attentionof the broad scientific research community specializing in nonlinear dynam-ics and pattern formation in nonequilibrium systems to the fascinating area ofself-assembly and self-organization on nanoscales inspired the organization ofthe NATO Advanced Study Institute “Self-Assembly, Pattern Formation andGrowth Phenomena in Nano-Systems" that took place in St. Etienne de Ti-nee in France, August 28 - September 11, 2004. Fifteen lecturers from France,Germany, Hungary, Israel and the USA gave series of lectures to an audience ofgraduate students and postdocs from Belgium, France, Germany, Israel, Italy,Romania, Russia, Spain, the USA and Uzbekistan. The lectures were devotedto various aspects of self-assembly, pattern formation and nonlinear dynamicsin nano-scale physical, chemical and biological systems, or systems in whichnanoscale processes play a crucial role and determine the macroscopic behav-ior.

The present book consists of ten articles containing lecture notes written bythe lecturers of the NATO ASI. The first article discusses general aspects of pat-tern formation and universal features of self-organization in non-equilibriumsystems. The next two articles are devoted to pattern formation and nonlin-ear phenomena in liquid crystals – a most remarkable system in which nano-

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xvi PATTERN FORMATION IN NANO-SYSTEMS

scale anisotropic structure determines quite unusual and complex macroscopicbehavior. The fourth article describes the self-assembly of quantum dots –spatially-regular nano-scale structures – from thin semiconductor films. Thesestructures have been attracting a great deal of attention as a promising routeto creating a new generation of electronic devices. The fifth and sixth arti-cles discuss a remarkable example of the failure of a traditional approach to an“every day" macroscopic hydrodynamic phenomenon – a moving contact line.It is shown that it is only by introducing new, mesoscopic physics based on theliquid structure at nano-scales, that this phenomenon can be explained and un-derstood. The seventh and eighth articles are devoted to self-organization phe-nomena in systems where chemical processes that occur at nano-scales lead,due to nonlinear coupling with thermal and diffusion processes, to macroscopicnon-stationary structures which, in turn, as a result of instabilities, produce mi-croscopic texture in initially homogeneous media. Namely, these articles dis-cuss the propagation and instability of combustion fronts in self-propagatinghigh-temperature synthesis of solid materials, and the propagation and insta-bilities of polymerization fronts in frontal polymerization processes. The lasttwo articles deal with micro- and nano-scale self-organization phenomena inbiological systems. The ninth article considers the recently discovered, very in-teresting phenomenon of self-organization of biological micro-tubules and mo-tors. Finally, it would not be an exaggeration to say that the last, tenth article, isdevoted to the most remarkable and the most important example of nano-scaleself-assembly – the self-organization and behavior of DNA molecules. Thisarticle presents a comprehensive, contemporary review of the physics of DNA.

To summarize, this book attempts to give examples of self-organization phe-nomena on micro- and nano-scale as well as examples of the interplay betweenphenomena on nano- and macro-scales leading to complex behavior in vari-ous physical, chemical and biological systems. It is not accidental thereforethat this NATO ASI was organized in conjunction with the European SchoolPHYSBIO-04. Moreover, it was mainly due to the inspiration of the organiz-ers of PHYSBIO-04 – Prof. Agnes Buka, Prof. Pierre Coullet, Prof. LorenzKramer and Prof. Yves Pomeau – that the organization of the NATO ASI be-came possible. We are very grateful to them for their enthusiasm and support.Tragically, one of the organizers of PHYSBIO-04, Professor Lorenz Kramer,who was one of the world leading experts in pattern formation and nonlinearphenomena in non-equilibrium systems, suddenly passed away in April 2005,while this book was in preparation. This was a great loss to all of us as well asmany others. This book is dedicated to his memory.

ALEXANDER A. GOLOVIN

ALEXANDER A. NEPOMNYASHCHY

Acknowledgments

It took the efforts of many people to make the NATO ASI a very useful, suc-cessful, and pleasant event. It would have been impossible without the tremen-dous organizational work of Dr. Jean-Luc Beaumont of the Nonlinear Institutein Nice, France. It would also have been impossible without the encourage-ment and help of Dr. Igor Aronson of the Argonne National Laboratory in theUSA. We are very grateful to the lovely people of St Etienne de Tinee, a small,beautiful mountain village near Nice in France, and to the helpful efforts of St.Etienne’s major, Mr. Pierre Brun. Their hospitality created a warm atmospherethat made the stay of the NATO ASI participants in St Etienne de Tinee mostpleasant and made them want to return to this wonderful place again. Also,our special thanks go to Dr. Denis Melnikov and Ms Jessica Conway for theirinvaluable help in translation between French, English and Russian; this was abridge that helped connect together people from so many different countries.One of the editors and co-director of the NATO ASI (A.A.G.) is also very grate-ful to his son, Peter Golovin, for constant help in many organizational matters.Finally, we would like to thank Prof. Bernard Matkowsky and Prof. VladimirVolpert of Northwestern University as well as the graduate students: JessicaConway, Lael Fisher, Margo Levine, Christine Sample, Gogi Singh and LiamStanton, for enormous help with the preparation of this book. Without theirhelp this book would not have appeared.

This NATO Advanced Study Institute was financially supported by the NATOASI grant #980684. This support is gratefully acknowledged. Travel of someof the student participants from the US to the NATO ASI was partially sup-ported by the US National Science Foundation.

xvii

Lorenz Kramer lecturing at a conference “Pattern Formation at the Turn of the Millenium”,organized in La Foux d’Allos, France, in June 2002.

Lorenz Kramer at the summit of Mount Aneto (3400m) in the Pyrenees, Spain, during the European School PHYSBIO-2003.