Nanocomputing: Computational Physics for Nanoscience and Nanotechnology by James Hsu


935a5ab2135a8c8-261x361.jpg Author James Hsu
Isbn 9789814241267
File size 4MB
Year 2009
Pages 384
Language English
File format PDF
Category physics



 

Published by Pan Stanford Publishing Pte. Ltd. 5 Toh Tuck Link Singapore 596224 Distributed by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. NANOCOMPUTING Computational Physics for Nanoscience and Nanotechnology Copyright © 2009 by Pan Stanford Publishing Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN-13 978-981-4241-26-7 ISBN-10 981-4241-26-1 Typeset by Research Publishing Services E-mail: [email protected] Printed in Singapore. PREFACE The contents of this book are based on the material of Nano Computing course I taught at National Tsing Hua University since 2004. Nanotechnology is catching attention and gaining importance in both academia and industry alike, and students are very much interested in this emerging topic. There is the need to have a coherent presentation on the related disciplines, namely, theoretical physics, computer science, applied mathematics, and engineering study. In considering the importance of the four technologies for the future, Nano Technology (NT), Biomedical Technology (BT), Information Technology (IT), and Ecology Technology (ET), the course is designed to give breadth on related subjects, but keep depth on computation and physics. On the theoretical side, we cover the Mesoscopic Physics and Nonlinear Many Body Physics. On the computer science, Object Oriented Programming and Parallel Computing are incorporated. On the applied mathematics, Asymptology and Algorithm are reviewed. For the engineering training, some applications and MATLAB are presented. Students are introduced to the multiscales and multisciences from this book, and are requested to solve all the problems by either MATLAB or C++. The target audience for the book is students at the senior and graduate level. The emphasis of this book is to teach students to solve problems from the features and characteristics of the problem itself, and not from a presumed methodology or a predefined tool. It tries Preface to avoid the students from falling into the mind frame of what the old saying, “If you are a hammer, everything else is a nail.” The rightful problem solving mentality is let the problem reveal where the solution might be, and study the clues to find the answers. Therefore, start from the asymptotic analysis once the problem is translated into a mathematical equation, and get all the hints possible even if a numerical solution is inevitable. This book is organized as follows: It introduces the issues in nanoscience, reviews the mathematical tools both numerical and analytical, and then applies the tools to more advanced problems through a repetition of the ideas and an increase in the level of sophistication so as to allow a deeper understanding of the physics and the problem solving techniques. Finally, it applies the scientific knowledge for practical applications. The ultimate goal of this book is to prepare students with enough background to start working on a research dissertation in theoretical nanoscience. James J. Y. Hsu March 2008 viii James J Y Hsu ACKNOWLEDGEMENTS I would like to thank Professor T. L. Lin for suggesting the course title, and ESS faculty and students for giving me the opportunity to teach this course. The interaction with Professor C. H. Tsai’s Carbon Nanotube group was most beneficial. Many insightful help from colleagues, post-doctors and students at both NCKU and NTHU are gratefully acknowledged. Some derivations and programs were aided byYee Mou Kao,Young-Chung Hsue, Chun Hung Lin, Eugene Pogorelov, Chieh-Wen Lo, Ying-Chi Chung, Chi-Yeh Chen, Robert Weng, Wellin Yang, Lichung Ko, and Cheng Hao Wu. This book was proofread by Dr. Fay Sheu. I also thank my wife, Dr. Yen-Hwa Hsu, and my daughters, Ingrid and Jessica, for their support to let me concentrate on research in Taiwan for the past few years. CONTENTS Preface v Acknowledgement Chapter One vii Little Big Science 1 1.1 Tools for Measurement — To See is to Believe . . . 4 1.2 Carbon Tells Us First . . . . . . . . . . . . . . . . . 7 1.3 Mother Nature Knows Best . . . . . . . . . . . . . . 10 1.4 Challenges in the New Millennium . . . . . . . . . . 12 Chapter Two Tools for Analysis 19 2.1 MATLAB . . . . . . . . . . . . . . . . . . . . . . . 20 2.2 Program Control . . . . . . . . . . . . . . . . . . . 29 2.3 Asymptology . . . . . . . . . . . . . . . . . . . . . 33 Chapter Three Mesoscopic Systems 59 3.1 Review on Quantum Physics . . . . . . . . . . . . . 59 3.2 Quantum Chemistry . . . . . . . . . . . . . . . . . . 78 3.3 Molecular Biology . . . . . . . . . . . . . . . . . . 88 3.4 Condensed Matter Physics . . . . . . . . . . . . . . 91 Chapter Four Analytical Chapter 115 4.1 Multiple Time Scales . . . . . . . . . . . . . . . . . 116 4.2 Multiple Space Scales . . . . . . . . . . . . . . . . . 124 Contents Chapter Five Numerical Chapter 5.1 Recursion and Divide-and-Conquer . . . . . . . . . 136 5.2 Probabilistic Algorithm . . . . . . . . . . . . . . . . 139 5.3 Evaluation and Search . . . . . . . . . . . . . . . . 150 5.4 Molecular Dynamics . . . . . . . . . . . . . . . . . 159 5.5 Finite Element Method . . . . . . . . . . . . . . . . 164 Chapter Six Nonlinear Many Body Physics and Transport 187 6.1 Density Functional Theory . . . . . . . . . . . . . . 189 6.2 Correlation and Coherence . . . . . . . . . . . . . . 199 6.3 Green’s Function Method . . . . . . . . . . . . . . . 204 6.4 Transport . . . . . . . . . . . . . . . . . . . . . . . 218 Chapter Seven OOP, MPI and Parallel Computing 227 7.1 C++ and Object Oriented Programming . . . . . . . 228 7.2 Message Passing Interface . . . . . . . . . . . . . . 233 7.3 OpenMP . . . . . . . . . . . . . . . . . . . . . . . . 242 Chapter Eight Low Dimensionality and Nanostructures 245 8.1 Quantum Dot and Quantum Wire . . . . . . . . . . . 245 8.2 Nanostructure Electronic Properties . . . . . . . . . 252 Chapter Nine x 135 Special Topics 261 9.1 Plasmon . . . . . . . . . . . . . . . . . . . . . . . . 261 9.2 Quantum Hall Effect . . . . . . . . . . . . . . . . . 277 9.3 Chaos and Stochasticity . . . . . . . . . . . . . . . . 284 James J Y Hsu Contents Chapter Ten Applications 303 10.1 Carbon Nanotube . . . . . . . . . . . . . . . . . . . 303 10.2 Water Dynamics . . . . . . . . . . . . . . . . . . . . 314 10.3 Molecular Computer . . . . . . . . . . . . . . . . . 324 References 333 Function Index 345 Author Index 349 Keyword Index 353 Nano Computing xi Chapter One LITTLE BIG SCIENCE “Look deep into nature, and then you will understand everything better.” Albert Einstein (1879–1955) I n a talk given in 1959, Richard Feynman asked, “Why cannot we write the entire 24 volumes of the Encyclopedia Brittanica on the head of a pin?” He went ahead to suggest that devices and materials could someday be manipulated to atomic specifications, and “The principles of physics, as far as I can see, do not speak against the possibility of maneuvering things atom by atom.” Nevertheless, there was not much progress in this direction after perhaps that owing to the lack of instruments needed to perform what was desired. More importantly, scientists could not really “see” what nature was doing. This, however, changed in the 1980s when progress was made on detection devices capable of looking deep into nature. The electron optics and the scanning tunneling microscope (STM) won Ernst Ruska, Gerd Binnig and Heinrich Rohrer the Nobel Prize in 1986. The other developments such as the atomic force microscopy (AFM) helped open up the nano domain. Nanoscience provides new approaches to material science and material engineering, and offers a great opportunity to upgrade existing industries from bottom up. When manipulated from the atomic Little Big Science level, ample examples of products can be magically improved. Of the four major leading industries in this century — electronics and IT (Information Technology), biomedical, energy, and transportation — nano science will impact greatly on them. In particular, there will be optimized materials, biomaterials, and smart materials. Not only will it be a new technology, but also a new man-nature relationship. Scientists and engineers have to rethink the environmental, health, and ethical issues. The ever-improved man-made materials will optimize to meet the conflicting demands and to provide solutions for the resource-hungry human society to reduce, reuse and recycle. A matured product is, as a rule, optimized and versatile. A case in point is the cellular phone. It is made with ever-greater functionalities such as digital video camera and Internet connectivity, not to mention the clock, the alarm, and the address book. This in fact makes the traditional wrist watch obsolete, and also opens up many Internet services and applications. Nature has no shortage of biological examples of optimized and versatile construct, perfected through tens of thousands of years of evolution. Some species of squid is capable of rocketing at 20 miles per hour by ejecting a jet of water. Such force is derived through its muscular contraction coupled with a smooth outer lining of least hydro-resistance. Its muscles maximize the elasticity and minimize the viscosity. Another example is the spider’s web which provides a net that resists the wear and tear under the sun, the rain and the wind. It is not perfect but economically optimized. Biomaterials in the greater sense include medicine. The ultimate success in the stem cell technologies will create biomaterials with a patient’s signature to allow for cell therapy or organ transplant. Another exciting breakthrough in 2007 is the discovery that human skin cells can be re-programmed to become “induced pluripotent stem cells”. After the human genome project was completed in 2002, the book of life was opened for further reading as a recipe to prolong life. The race for genomic medicine has just 2 James J Y Hsu Little Big Science begun. Drug discovery will benefit tremendously from nano computing. For example, once the 3D structure of a protein is known, potential inhibitors capable of blocking specific active sites can be screened through computer simulation. This will greatly shorten the time to market, and reduce the cost of animal tests and clinical trials. And the dream is to have personalized medicine, prescribed according to an individual’s genetic makeup, perhaps even accommodating in human genomes the 0.1% differences due to single nucleotide polymorphism (SNP). A purpose of nanobio studies is to be able to confirm many findings inferred from the inductive biological methods, with results developed from reductive physics methods from the first principles. On the other hand, the Princeton group at the Biologically Inspired Materials Institute proclaims the possibility of creating the selfhealing skin to alleviate the problems such as the failed protective tiles on the space shuttle Columbia in 2003. This is a biomaterial similar to living beings like blood clotting to protect a cut in the skin. In the ultimate sense, it will be able to program the material to confer with the intelligence of an agent, a robot or a catalyst to make things happen as needed. Biodegradable plastics could be the least of these examples. There is no shortage of examples of intelligence in living organisms, just think of how a fertilized egg is programmed to hatch into a chick, or a dandelion flower spreads its seeds. Will humans be one day smart enough to design drugs that defeat drug resistance by microorganisms and viruses? So far the strategy of drug design is to find a way of inhibiting or killing the virus. Unfortunately the survived virus such as HIV may find proper mechanisms to defeat the purpose. If the drug takes advantage of similar mechanisms from the virus, viz., mutating according to what the enemy is doing and developing a new medicine strategy accordingly, we would have a smart medicine. This could be the ultimate smart material man could make. Nano Computing 3 Little Big Science 1.1 Tools for Measurement — to See is to Believe Observations enabled the ancient Chinese to record events of comets, solar eclipses, and supernovae, and to practice acupuncture and herbal medicine. Scientists, from the onset of modern scientific thought in Greece, struggled for centuries to learn about the sizes of atoms and molecules. Recent developments in microscopy allow scientists to see and manipulate particles of nanometer dimensions, thus signifies the beginning of nanotechnology. Microscopy, in its many forms, is one of the most important techniques used to study the size, shape and characteristics of small objects. These include Scanning Tunneling Microscopy, Electron Microscopy, Atomic Force Microscopy, Soft X-Ray Microscopy and Optical Microscopy. The scanning tunneling microscope (STM) provides a threedimensional profile of a surface at the atomic scale. It is one of the most powerful and widely employed tools for surface analysis, very useful in characterizing roughness and defects and determining the size and conformation of molecules and aggregates on the surface. The STM utilizes quantum tunneling to draw up an electron current.A stylus, or atomically sharp tip, scans the surface of a sample at certain distance. The study of surfaces has important physical, chemical and biological implications, ranging from the studies of semiconductors, microelectronics, high precision optical components, metals, surface chemistry, to those of enzymatic effect and viral infection. The STM works best with conducting materials, but it is also possible to affix organic molecules on a surface and study the deposited structures. The atomic force microscope (AFM) measures topography with a force probe. Invented by Binnig, Quate and Gerber in 1986, AFM can be used for surveying the material surface or measuring electric, magnetic, and other physical or chemical properties in the nanometerscale. The AFM operates by measuring attractive or repulsive forces between a tip and the sample to achieve atomic-scale resolution. It is equipped with sensitive and sharp tips, flexible cantilevers, optical 4 James J Y Hsu Tools for Measurement — to See is to Believe lever, and force feedback circuit. The optical lever operates by reflecting a laser beam off the cantilever, thus greatly magnifies motions of the tip since the cantilever-to-detector distance generally measures thousands of times the length of the cantilever. The force is not measured directly, but calculated by measuring the deflection of the lever with the knowledge of the stiffness of the cantilever. The AFM combines the optical probe with the atomic interactions to achieve greater resolution than the traditional optical microscopy. Both AFM and optical microscopy are powerful tools for gaining information about structure and function of biomolecules and living cells. Owing to the fact that light cannot pass through an aperture smaller than its wavelength, the so-called diffraction limit, optical microscopy has its limitations. Optical microscopy however attracted great attention in the nano regime in 1998 when Ebbesen et al. demonstrated that a nano layer of silver aggregates enhances the nearfield strength and consequently its resolution. Optical microscopy, in general, is relatively inexpensive and reliable. It requires little sample preparation and works at room temperature and atmospheric pressure. These factors make near-field optics a favored tool as a biosensor in studying DNA, RNA, or protein. Light scattering over molecules has been well understood to result from the elastic scattering of Rayleigh and the inelastic scattering of Raman. The incident photon energy can excite vibrational modes of the molecules. A spectral analysis of the scattered light could reveal molecular structure. Raman scattering has applications in remote monitoring for pollutants, and widely used to examine for example, the diameter of carbon nano tube, single or multi-walled. The neutron’s magnetic moment is an ideal probe to study magnetic structures in condensed matter physics. It can be used to investigate solid state magnetism, magnetic nanostructures, structural and magnetic disorder, spin fluctuations and excitations in complex or nano-structured magnetic systems and highly correlated electron Nano Computing 5 Little Big Science systems. Small angle x-ray scattering (SAXS) can be an analytical tool to examine the structural characterization of solid and fluid materials in the nanometer range. SAXS is applied to investigate structural details in the 0.5 to 50 nm size range in materials such as: nanopowders, proteins, viruses, DNA complexes, polymer films and fibers, catalyst surface, and liquid crystals. The microarray is one promising device that will help unravel the secret of life. By far, it is one of the better tools to observe how a biological system is doing. Presently, extracting microarray data to get meaningful information, however, remains inadequate or even elusive. This may change as the methods of its analysis continue to improve. The impact will be strongly felt once this research tool becomes practical and effective for clinical applications. It has promising applications in determining a patient’s gene profile as well as in monitoring the progress during drug treatment. The era of personalized medical care will finally arrive when a patient’s genome can be deciphered within reasonable time duration. A few other tools such as mass spectrometer, AFM, and Near-Field Optics may be good candidates to help accomplish that. It is widely believed that thousands of genes and their products (i.e., RNA and proteins) in a given living organism function in a complicated and orchestrated way. However, traditional methods in molecular biology generally work on a “one gene, one experiment” basis, which means that the throughput is very limited and the “whole picture” of gene function is hard to obtain. The DNA microarray that is attracting tremendous interests has the promising capability of monitoring the entire genome on a single chip. Researchers can have a better picture of the interactions among thousands of genes from the microarray experiment. Base-pairing (i.e., A-T and G-C for DNA; A-U and G-C for RNA) or hybridization is the underlining principle of DNA microarray. Microarray is a powerful research tool and would be a very important clinical diagnostics method. Microarray designs might be categorized into genotype arrays, expression arrays, and protein arrays. 6 James J Y Hsu Carbon Tells Us First In each category, many more varieties are readily available. Protein microarrays have for example, antibody array, antigen array, lysate array, surface antigen array, human cytosine detection array, allergy antigen array, protein domain array, small molecular array, enzymeprotein array, etc. The sensitivity, specificity (correlation with the observable), and reliability define the quality of an array design. It has been used to do early detection of molecular signatures of cancer disease, to understand the metabolism and protein regulatory functions, to study drug resistant mechanisms during cancer treatment, and to profile patient prognosis signatures. The multi-gene based approach found the prognosis signature, which consists of genes that function in regulation of cell cycle, invasion, metastasis and angiogenesis. Patients having tumors with the poor prognosis signature tend to develop distant metastases shortly afterwards. From the profiling, proper course of treatment can be prescribed. Some patients may require surgery only; whereas patients with very poor prognosis signature may need radiation therapy and chemotherapy following surgery. The method defining the reporter genes that predict distant metastases appears to have wider validity to other cancer cases, and obviously is a research topic of great importance. Nanoscience and nanotechnology have evolved to encompass multi-disciplinary inputs from physics, biology, chemistry and engineering. The field is richly benefited from information technology, electronics and mechanics; they provide the ultimate tools for measurement. They also develop microsystems with multifunctionalities, optimized as examplied in microarrays. In fact, in microarray, what is achieved might be thought of as the first in its kind, a biochip that is equivalent to “the lab on a chip”. 1.2 Carbon Tells Us First Although water is the universal medium for life on Earth, most of the chemicals that make up living organisms are based on the element carbon. Of all chemical elements, carbon is unparallel in its ability to Nano Computing 7 Little Big Science form molecules that are large, complex, and diverse, and this molecular diversity has made possible the diversity of living beings that have evolved on Earth. Carbon atoms are the most versatile building blocks of molecules. The organic chemistry is the study of carbon compounds. The famous carbon family includes carbon nano tube (CNT), graphite, and diamond. In 1985 Robert F. Curl, Harold W. Kroto and Richard E. Smalley discovered the bucky ball, or fullerene, a striking compound of carbon atoms arranged in a closed shell or cage. It resembles the geodesic dome designed by the American architect R. Buckminster Fuller for the 1967 Montreal World Exhibition. The researchers named the newly-discovered structure buckminsterfullerene after Fuller. The carbon bucky ball C60 (see Function C60 in 2.1.4) serves as a good example of the greatness and beauty of nanostructures. The fullerene may be considered as a zero dimensional entity, the CNT a one dimensional entity, the graphite two dimensional, and diamond three dimensional. Fullerenes are formed when vaporized carbon atoms condense in the inert gas. A cluster of 60 carbon atoms (cf. P. 30), C60 , is the most abundant, and a molecular structure of great symmetry. Its cage structure may be ideal for drug delivery and its size may be just right as an inhibitor to attach to the active site of an enzyme. It may be made into perfect reproducible quantum dot for mass production. The discovery of fullerene and carbon nanotube (CNT) aroused renewed interest in nanotechnologies making Feynman’s prediction come closer to reality. After S. Iijima published his Nature paper on carbon nanotubes in 1991, researchers have been fascinated by these nanostructures and their extraordinary electrical and mechanical properties. The many potential usages of CNTs envisioned include: as field emitters for flat-panel display, as field effect transistor (FET), or as nano sensors affixed with reaction-specific molecules, and as tips for scanning probe microscopy. There are also potential applications in hydrogen 8 James J Y Hsu

Author James Hsu Isbn 9789814241267 File size 4MB Year 2009 Pages 384 Language English File format PDF Category Physics Book Description: FacebookTwitterGoogle+TumblrDiggMySpaceShare Based on MATLAB and the C++ distributed computing paradigm, this guide gives instructive explanations of the underlying physics for mesoscopic systems with many listed programs that readily compute physical properties into nano scales. Many generated graphical pictures demonstrate not only the principles of physics but also the methodology of computing. The volume starts with a review on quantum physics, quantum chemistry and condensed matter physics, followed by a discussion on the computational and analytical tools and the numerical algorithms used. With these tools in hand, the nonlinear many-body problem, the molecular dynamics, the low dimensionality and nanostructures are then explored. Special topics covered have include the plasmon, the quantum Hall effect, chaos and stochasticity. The applications explored here include graphene, carbon nanotube, water dynamics and the molecular computer.     Download (4MB) Handbook Of Carbon Nano Materials: World Scientific Series on Carbon Nanoscience Nano: The Essentials Quantum Tunneling And Field Electron Emission Theories Solid State Physics: An Introduction, 2nd Edition Handbook of Molecular Plasmonics Load more posts

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