Nano Mechanics and MaterialsTheory, Multiscale Methods and Applications

Wing Kam LiuNorthwestern University, Illinois, USA

Eduard G. KarpovNorthwestern University, Illinois, USA

Harold S. ParkVanderbilt University, Tennessee, USA

Innodata0470035218.jpg

Nano Mechanics and Materials

Nano Mechanics and MaterialsTheory, Multiscale Methods and Applications

Wing Kam LiuNorthwestern University, Illinois, USA

Eduard G. KarpovNorthwestern University, Illinois, USA

Harold S. ParkVanderbilt University, Tennessee, USA

Copyright 2006 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester,West Sussex PO19 8SQ, England

Telephone (+44) 1243 779777

Email (for orders and customer service enquiries): cs-books@wiley.co.ukVisit our Home Page on www.wiley.com

All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmittedin any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, exceptunder the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by theCopyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission inwriting of the Publisher. Requests to the Publisher should be addressed to the Permissions Department, JohnWiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or emailed topermreq@wiley.co.uk, or faxed to (+44) 1243 770620.This publication is designed to provide accurate and authoritative information in regard to the subject mattercovered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. Ifprofessional advice or other expert assistance is required, the services of a competent professional should besought.

Other Wiley Editorial Offices

John Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USA

Jossey-Bass, 989 Market Street, San Francisco, CA 94103-1741, USA

Wiley-VCH Verlag GmbH, Boschstr. 12, D-69469 Weinheim, Germany

John Wiley & Sons Australia Ltd, 42 McDougall Street, Milton, Queensland 4064, Australia

John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01, Jin Xing Distripark, Singapore 129809

John Wiley & Sons Canada Ltd, 22 Worcester Road, Etobicoke, Ontario, Canada M9W 1L1

Wiley also publishes its books in a variety of electronic formats. Some content that appearsin print may not be available in electronic books.

British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library

ISBN-13: 978-0-470-01851-4ISBN-10: 0-470-01851-8

Typeset in 10/12pt Times by Laserwords Private Limited, Chennai, IndiaPrinted and bound in Great Britain by Antony Rowe Ltd, Chippenham, WiltshireThis book is printed on acid-free paper responsibly manufactured from sustainable forestryin which at least two trees are planted for each one used for paper production.

http://www.wiley.com

To Our Families

Contents

Preface xi

1 Introduction 11.1 Potential of Nanoscale Engineering . . . . . . . . . . . . . . . . . . . . . . 11.2 Motivation for Multiple Scale Modeling . . . . . . . . . . . . . . . . . . . . 21.3 Educational Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Classical Molecular Dynamics 72.1 Mechanics of a System of Particles . . . . . . . . . . . . . . . . . . . . . . 7

2.1.1 Generalized Coordinates . . . . . . . . . . . . . . . . . . . . . . . . 82.1.2 Mechanical Forces and Potential Energy . . . . . . . . . . . . . . . 82.1.3 Lagrange Equations of Motion . . . . . . . . . . . . . . . . . . . . 102.1.4 Integrals of Motion and Symmetric Fields . . . . . . . . . . . . . . 122.1.5 Newtonian Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 132.1.6 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2 Molecular Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2.1 External Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.2.2 Pair-Wise Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2.3 Multibody Interaction . . . . . . . . . . . . . . . . . . . . . . . . . 242.2.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.3 Molecular Dynamics Applications . . . . . . . . . . . . . . . . . . . . . . . 28

3 Lattice Mechanics 373.1 Elements of Lattice Symmetries . . . . . . . . . . . . . . . . . . . . . . . . 37

3.1.1 Bravais Lattices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.1.2 Basic Symmetry Principles . . . . . . . . . . . . . . . . . . . . . . 403.1.3 Crystallographic Directions and Planes . . . . . . . . . . . . . . . . 42

3.2 Equation of Motion of a Regular Lattice . . . . . . . . . . . . . . . . . . . 423.2.1 Unit Cell and the Associate Substructure . . . . . . . . . . . . . . . 433.2.2 Lattice Lagrangian and Equations of Motion . . . . . . . . . . . . . 453.2.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.3 Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.3.1 Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.3.2 Laplace Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.3.3 Discrete Fourier Transform . . . . . . . . . . . . . . . . . . . . . . 53

viii CONTENTS

3.4 Standing Waves in Lattices . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.4.1 Normal Modes and Dispersion Branches . . . . . . . . . . . . . . . 553.4.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.5 Greens Function Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.5.1 Solution for a Unit Pulse . . . . . . . . . . . . . . . . . . . . . . . 593.5.2 Free Lattice with Initial Perturbations . . . . . . . . . . . . . . . . . 613.5.3 Solution for Arbitrary Dynamic Loads . . . . . . . . . . . . . . . . 613.5.4 General Inhomogeneous Solution . . . . . . . . . . . . . . . . . . . 623.5.5 Boundary Value Problems and the Time History Kernel . . . . . . . 623.5.6 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.6 Quasi-Static Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . 663.6.1 Equilibrium State Equation . . . . . . . . . . . . . . . . . . . . . . 663.6.2 Quasi-Static Greens Function . . . . . . . . . . . . . . . . . . . . . 673.6.3 Multiscale Boundary Conditions . . . . . . . . . . . . . . . . . . . . 67

4 Methods of Thermodynamics and Statistical Mechanics 794.1 Basic Results of the Thermodynamic Method . . . . . . . . . . . . . . . . . 80

4.1.1 State Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.1.2 Energy Conservation Principle . . . . . . . . . . . . . . . . . . . . . 844.1.3 Entropy and the Second Law of Thermodynamics . . . . . . . . . . 864.1.4 Nernsts Postulate . . . . . . . . . . . . . . . . . . . . . . . . . . . 884.1.5 Thermodynamic Potentials . . . . . . . . . . . . . . . . . . . . . . . 89

4.2 Statistics of Multiparticle Systems in Thermodynamic Equilibrium . . . . . 914.2.1 Hamiltonian Formulation . . . . . . . . . . . . . . . . . . . . . . . 924.2.2 Statistical Description of Multiparticle Systems . . . . . . . . . . . 934.2.3 Microcanonical Ensemble . . . . . . . . . . . . . . . . . . . . . . . 974.2.4 Canonical Ensemble . . . . . . . . . . . . . . . . . . . . . . . . . . 1014.2.5 MaxwellBoltzmann Distribution . . . . . . . . . . . . . . . . . . . 1044.2.6 Thermal Properties of Periodic Lattices . . . . . . . . . . . . . . . . 107

4.3 Numerical Heat Bath Techniques . . . . . . . . . . . . . . . . . . . . . . . 1114.3.1 Berendsen Thermostat . . . . . . . . . . . . . . . . . . . . . . . . . 1124.3.2 NoseHoover Heat Bath . . . . . . . . . . . . . . . . . . . . . . . . 1184.3.3 Phonon Method for SolidSolid Interfaces . . . . . . . . . . . . . . 119

5 Introduction to Multiple Scale Modeling 1235.1 MAAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1245.2 Coarse-Grained Molecular Dynamics . . . . . . . . . . . . . . . . . . . . . 1265.3 Quasi-Continuum Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 1265.4 CADD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1285.5 Bridging Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

6 Introduction to Bridging Scale 1316.1 Bridging Scale Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . 131

6.1.1 Multiscale Equations of Motion . . . . . . . . . . . . . . . . . . . . 1336.2 Removing Fine Scale Degrees of Freedom in Coarse Scale Region . . . . . 136

6.2.1 Relationship of Lattice Mechanics to Finite Elements . . . . . . . . 1376.2.2 Linearized MD Equation of Motion . . . . . . . . . . . . . . . . . . 139

CONTENTS ix

6.2.3 Elimination of Fine Scale Degrees of Freedom . . . . . . . . . . . . 1416.2.4 Commentary on Reduced Multiscale Formulation . . . . . . . . . . 1436.2.5 Elimination of Fine Scale Degrees of Freedom:

3D Generalization . . . . . . . . . . . . . . . . . . . . . . . . . . . 1436.2.6 Numerical Implementation of Impedance Force . . . . . . . . . . . 1506.2.7 Numerical Implementation of Coupling Force . . . . . . . . . . . . 151

6.3 Discussion on the Damping Kernel Technique . . . . . . . . . . . . . . . . 1526.3.1 Programming Algorithm for Time History Kernel . . . . . . . . . . 157

6.4 CauchyBorn Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1586.5 Virtual Atom Cluster Method . . . . . . . . . . . . . . . . . . . . . . . . . 159

6.5.1 Motivations and General Formulation . . . . . . . . . . . . . . . . . 1596.5.2 General Idea of the VAC Model . . . . . . . . . . . . . . . . . . . . 1636.5.3 Three-Way Concurrent Coupling with QM Method . . . . . . . . . 1646.5.4 Tight-Binding Method for Carbon Systems . . . . . . . . . . . . . . 1676.5.5 Coupling with the VAC Model . . . . . . . . . . . . . . . . . . . . 169

6.6 Staggered Time Integration Algorithm . . . . . . . . . . . . . . . . . . . . . 1706.6.1 MD Update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1706.6.2 FE Update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

6.7 Summary of Bridging Scale Equations . . . . . . . . . . . . . . . . . . . . 1726.8 Discussion on the Bridging Scale Method . . . . . . . . . . . . . . . . . . . 173

7 Bridging Scale Numerical Examples 1757.1 Comments on Time History Kernel . . . . . . . . . . . . . . . . . . . . . . 1757.2 1D Bridging Scale Numerical Examples . . . . . . . . . . . . . . . . . . . . 176

7.2.1 Lennard-Jones Numerical Examples . . . . . . . . . . . . . . . . . . 1767.2.2 Comparison of VAC Method and CauchyBorn Rule . . . . . . . . 1787.2.3 Truncation of Time History Kernel . . . . . . . . . . . . . . . . . . 179

7.3 2D/3D Bridging Scale Numerical Examples . . . . . . . . . . . . . . . . . . 1827.4 Two-Dimensional Wave Propagation . . . . . . . . . . . . . . . . . . . . . 1847.5 Dynamic Crack Propagation in Two Dimensions . . . . . . . . . . . . . . . 1877.6 Dynamic Crack Propagation in Three Dimensions . . . . . . . . . . . . . . 1957.7 Virtual Atom Cluster Numerical Examples . . . . . . . . . . . . . . . . . . 200

7.7.1 Bending of Carbon Nanotubes . . . . . . . . . . . . . . . . . . . . . 2007.7.2 VAC Coupling with Tight Binding . . . . . . . . . . . . . . . . . . 200

8 Non-Nearest Neighbor MD Boundary Condition 2038.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2038.2 Theoretical Formulation in 3D . . . . . . . . . . . . . . . . . . . . . . . . . 203

8.2.1 Force Boundary Condition: 1D Illustration . . . . . . . . . . . . . . 2078.2.2 Displacement Boundary Condition: 1D Illustration . . . . . . . . . . 2108.2.3 Comparison to Nearest Neighbors Formulation . . . . . . . . . . . . 2118.2.4 Advantages of Displacement Formulation . . . . . . . . . . . . . . . 212

8.3 Numerical Examples: 1D Wave Propagation . . . . . . . . . . . . . . . . . 2128.4 Time-History Kernels for FCC Gold . . . . . . . . . . . . . . . . . . . . . . 2138.5 Conclusion for the Bridging Scale Method . . . . . . . . . . . . . . . . . . 215

8.5.1 Bridging Scale Perspectives . . . . . . . . . . . . . . . . . . . . . . 220

x CONTENTS

9 Multiscale Methods for Material Design 2239.1 Multiresolution Continuum Analysis . . . . . . . . . . . . . . . . . . . . . . 225

9.1.1 Generalized Stress and Deformation Measures . . . . . . . . . . . . 2279.1.2 Interaction between Scales . . . . . . . . . . . . . . . . . . . . . . . 2319.1.3 Multiscale Materials Modeling . . . . . . . . . . . . . . . . . . . . 232

9.2 Multiscale Constitutive Modeling of Steels . . . . . . . . . . . . . . . . . . 2349.2.1 Methodology and Approach . . . . . . . . . . . . . . . . . . . . . . 2359.2.2 First-Principles Calculation . . . . . . . . . . . . . . . . . . . . . . 2359.2.3 Hierarchical Unit Cell and Constitutive Model . . . . . . . . . . . . 2379.2.4 Laboratory Specimen Scale: Simulation and Results . . . . . . . . . 239

9.3 Bio-Inspired Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2449.3.1 Mechanisms of Self-Healing in Materials . . . . . . . . . . . . . . . 2449.3.2 Shape-Memory Composites . . . . . . . . . . . . . . . . . . . . . . 2469.3.3 Multiscale Continuum Modeling of SMA Composites . . . . . . . . 2509.3.4 Issues of Modeling and Simulation . . . . . . . . . . . . . . . . . . 256

9.4 Summary and Future Research Directions . . . . . . . . . . . . . . . . . . . 260

10 BioNano Interface 26310.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26310.2 Immersed Finite Element Method . . . . . . . . . . . . . . . . . . . . . . . 265

10.2.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26510.2.2 Computational Algorithm of IFEM . . . . . . . . . . . . . . . . . . 268

10.3 Vascular Flow and Blood Rheology . . . . . . . . . . . . . . . . . . . . . . 26910.3.1 Heart Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26910.3.2 Flexible ValveViscous Fluid Interaction . . . . . . . . . . . . . . . 27010.3.3 Angioplasty Stent . . . . . . . . . . . . . . . . . . . . . . . . . . . 27010.3.4 Monocyte Deposition . . . . . . . . . . . . . . . . . . . . . . . . . 27210.3.5 Platelet Adhesion and Blood Clotting . . . . . . . . . . . . . . . . . 27210.3.6 RBC Aggregation and Interaction . . . . . . . . . . . . . . . . . . . 274

10.4 Electrohydrodynamic Coupling . . . . . . . . . . . . . . . . . . . . . . . . 28010.4.1 Maxwell Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 28110.4.2 Electro-manipulation . . . . . . . . . . . . . . . . . . . . . . . . . . 28310.4.3 Rotation of CNTs Induced by Electroosmotic Flow . . . . . . . . . 285

10.5 CNT/DNA Assembly Simulation . . . . . . . . . . . . . . . . . . . . . . . 28710.6 Cell Migration and CellSubstrate Adhesion . . . . . . . . . . . . . . . . . 29010.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295

Appendix A Kernel Matrices for EAM Potential 297

Bibliography 301

Index 315

Preface

Within the past decade, the emphasis of scientific research worldwide has shifted to thestudy of the behavior of materials at the atomic scale of matter. The proliferation of scien-tists and engineers studying matter at this length scale has led to the coining of the phrasenanotechnology. This term can generally be taken to imply the investigation and technolog-ical utilization of the properties of matter at length scales of one thousand nanometers orsmaller. Generally, a few thousand atoms will exist in the space of thousand nanometers.

As engineers typically study the mechanical properties of materials, the correspondingemphasis of research in the engineering community has been on nano mechanics . Theterm nano mechanics is typically associated with the study and characterization of themechanical behavior of individual atoms, atomic-scale systems and structures in responseto various types of forces and loading conditions. The specific nature of nano mechanicsresearch generally varies depending on the discipline of the engineer; the topic of interestcan involve the atomic-scale effect of fracture and wear on material performance, mechani-cal properties of nanocomposites, atomic-scale flow and locomotion of individual biologicalcells.

Regardless of the interest of the particular scientist or engineer, what is universallyagreed upon is the overall potential that nanotechnology, and particularly nano mechanics,has for the betterment of our society, including the sectors of private industry, nationaldefense and homeland security. An emphasis on nanoscale entities will make our manufac-turing technologies and infrastructure more sustainable in terms of reduced energy usageand environmental pollution. Recent advances made by the research community in thistopic have stimulated ever-broader research activities in science and engineering that aredevoted to their development and applications.

Many areas of research are rapidly advancing owing to the combined efforts of scienceand engineering. In mechanics and materials, we are particularly excited with the progressin research and education that can be achieved by combining engineering and basic sciencesthrough modeling and simulation together with experimentation. Owing to the combinationof constantly increasing computational power and the increased knowledge and understand-ing of material behavior, multiple scale modeling methods have recently emerged as thetool of choice to link the mechanical behavior of materials from the smallest scale of atomsto the largest scale of structures. Multiple scale methods offer the best hope for bridgingthe traditional gap that exists between experimental approach, the theoretical approach andcomputational modeling for studying and understanding the behavior of materials.

Owing to the central role that multiple scale methodology appears poised to play inthe computational mechanics and materials science in the foreseeable future, this bookaims to summarize the past and the current developments in multiple scale modeling to

xii PREFACE

provide a coherent starting point from which interested scientists and engineers can begintheir journey into this vast and rapidly expanding subject. We hope that this book is oneof the first systematic works aimed at providing knowledge about fundamental conceptsbehind nanoscale mechanics and materials and the relevant applications. The book containsboth published and previously unpublished material and is aimed at nanoscale engineers,designers, materials scientists and interested students and researchers.

A salient feature of this book is that it is also intended to be used as an educationaltool. The major reason is to synthesize the state of the art in multiple scale modelingtechniques into the classroom such that the crucial tools being made available today arepassed onto the next generation of scientists and engineers. Thus, the materials in this bookwhich were previously used for courses at Northwestern University and the National ScienceFoundation (NSF) Summer Institute on Nano Mechanics and Materials have been coherentlycombined with Powerpoint lecture notes and selected computer codes (available online atwww.wiley.com/go/nanomechanics) to make the material presented readily accessible forthose researchers who are interested in joining and contributing to the field of multiplescale modeling and analysis. Along with the review of basic theoretical concepts, theypresent the solutions and dynamic visualization of numerous practical problems, rangingfrom simple one-dimensional systems to state-of-the-art applications. The solutions of thesimple illustrative problems are augmented by Matlab and Mathematica codes which serveto highlight the numerical implementation of the theoretical approaches presented in thisbook.

There are many other novel and unique aspects to this book. As mentioned above,the integration of teaching and research is one of the key features. The material containsdetailed expositions on all the topics that are necessary to fully comprehend multiple scaleanalysis. As such, the book is logically divided into three parts. The first part consistsof Chapters 24, which cover the theoretical basis needed to understand the behavior ofmultiparticle atomistic systems. The second part consists of Chapters 58, and introducesmultiple scale methods. In particular, the bridging scale concurrent approach, which isbased on the theoretical considerations provided in the first part of the book, is givenspecial attention here. The third part comprising Chapters 910 is devoted to contemporaryapplications in the area of nanostructured and bioinspired materials, biofluidics and cellmechanics.

Chapter 1 contains an introduction, and emphasizes the need for multiple scale simu-lations by presenting case studies from different scientific disciplines, including materialsdesign and biofluidics. Chapter 2 introduces the notion of Lagrangian dynamics descriptionof systems of interacting particles, including nonconservative equations of motion, multi-body interatomic potentials and arbitrary molecular shapes. Chapter 3 details the extensionof the Lagrangian method to spatially periodic lattice structures; it reviews the relevant sym-metry concepts, and derives the basic response solutions for a general three-dimensionallattice in semianalytical forms that are important in nanoscale engineering applications.Chapter 4 gives a systematic, though condensed, exposition on contemporary approachesthat allow an averaged macroscopic characterization of multiparticle systems in thermo-dynamic equilibrium; these include the methods of thermodynamic potentials, statisticalaveraging, microcanonical and canonical ensemble theories.

Chapter 5 provides an overview of multiple scale modeling. As such, previously devel-oped multiple scale methods are reviewed and analyzed, and capabilities that are needed in

PREFACE xiii

multiple scale modeling are discussed and provided as a basis for the remaining chapters.Chapter 6 introduces the bridging scale concurrent method, which couples atomistic andcontinuum scale models; here, connections are made between the bridging scale, particledynamics and lattice mechanics concepts introduced in Chapters 23.

Numerical validation of the bridging scale approach is given in Chapter 7. The numericalexamples in one, two and three dimensions highlight the applicability of the bridging scaleto highly nonlinear physical phenomena, including the fracture and subsequent failure ofmaterials. The recent extension of the bridging scale to incorporate quantum mechanicalinformation into the coupling of length scales framework is also described in this chapter.Chapter 8 provides an extension of the MD impedance force such that it can be utilizedwith long-ranged interatomic potentials; this extension is crucial as most realistic interatomicpotentials incorporate non-nearest neighbor bonding. This chapter concludes the section onmultiple scale modeling with comments on future research directions.

Chapter 9 highlights applications of multiple scale methods in crucial areas of physi-cal interest. In the realm of solids, the topics covered are the hierarchical and concurrentdesign of realistic materials, including novel steel and metallic alloys, shape memory com-posites and self-healing materials. Lastly, Chapter 10 emphasizes new research in the areaof computational biofluidics, electrohydrodynamics, bioengineering and nano-bio interfa-cial problems. The topics include electrophoresis multiscale and multiphysics modeling ofred blood cell (RBC) aggregation and the effect on blood rheology, capillary flow, cellmigration, nanomanipulation and assembly of macromolecules.

We would like to thank our colleagues and graduate students for their contributionsto this book, in particular, Ted Belytschko, Antonio Bouze, Dmitry Dorofeev, David Far-rell, Mark Horstemeyer, Sukky Jun, Hiroshi Kadowaki, Adrian Kopacz, Yaling Liu, CahalMcVeigh, Sergey Medyanik, Dong Qian, Leonid Shilkrot, Shaoqiang Tang, Franck Vernereyand Sulin Zhang. Finally, we would like to thank and acknowledge the following spon-sors for their support: the National Science Foundation (NSF), the NSF Summer Instituteon Nano Mechanics and Materials, the NSF Integrative Graduate Education and ResearchTraineeship (IGERT) program, the Army Research Office (ARO), the Office of NavalResearch (ONR) CyberSteel 2020 project and the ONR Nanofilament-Based CombinedChemical/Biological Detectors Project.

Wing Kam LiuEvanston, Illinois Eduard G. KarpovNashville, Tennessee Harold S. Park