K10520 Cover 11/10/10 1:38 PM Page 1 Composite C M Y CM MY CY CMY K While the relevant features and properties of nanosystems necessarily depend on nanoscopic details, their performance resides in the macroscopic world. To rationally develop and accurately predict performance of these systems we must tackle problems where multiple length and time scales are coupled. Rather than forcing a single modeling approach to predict an event it was not designed for, a new paradigm must be employed: multiscale modeling. A brilliant solution to a pervasive problem, Multiscale Modeling: From Atoms to Devices offers a number of approaches for which more than one scale is explicitly considered. It provides several alternatives, from coarse-graining sampling of the atomic and mesoscale to Monte Carlo- and thermodynamic-based models that allow sampling of increasingly large scales up to multiscale models able to describe entire devices. Beginning with common techniques for coarse-graining, the book discusses their theoretical background, advantages, and limitations. It examines the application-dependent parameterization characteristics of coarse-graining along with the “finer-trains-coarser” multiscale approach and describes three carefully selected examples in which the parameterization, although based on the same principles, depends on the actual application. The book considers the use of ab initio and density functional theory to obtain parameters needed for larger scale models, the alternative use of density functional theory parameters in a Monte Carlo method, and the use of ab initio and density functional theory as the atomistic technique underlying the calculation of thermodynamics properties of alloy phase stability. Highlighting one of the most challenging tasks for multiscale modelers, Multiscale Modeling: From Atoms to Devices also presents modeling for nanocomposite materials using the embedded fiber finite element method (EFFEM). It emphasizes an ensemble Monte Carlo method to high field-charge transport problems and demonstrates the practical application of modern many-body quantum theories. Materials Science/Nanoscience MULTISCALE MODELING FROM ATOMS TO DEVICES EDITED BY PEDRO DEROSA TAHIR CAGIN DEROSA CAGIN MULTISCALE MODELING MULTISCALE MODELING EDITED BY PEDRO DEROSA & TAHIR CAGIN FROM ATOMS TO K10520 6000 Broken Sound Parkway, NW Suite 300, Boca Raton, FL 33487 270 Madison Avenue New York, NY 10016 2 Park Square, Milton Park Abingdon, Oxon OX14 4RN, UK an informa business MULTISCALE MODELING F R O M A T O M S TO D E V I C E S MULTISCALE MODELING F R O M A T O M S T O D E V I C E S E D I T E D B Y PEDRO DEROSA TAHIR CAGIN CRC Press is an imprint of the Taylor & Francis Group, an informa business Boca Raton London New York CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2011 by Taylor and Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-13: 978-1-4398-1040-8 (Ebook-PDF) This book contains information obtained from authentic and highly regarded sources. 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To my children, Kerem, Elif, and wife Gul, TC vii © 2011 by Taylor & Francis Group, LLC Contents Preface ix Contributors xiii Chapter 1 Overcoming Large Time- and Length-Scale Challenges in Molecular Modeling: A Review of Atomistic to Mesoscale Coarse-Graining Methods 1 Timothy Morrow Chapter 2 Coarse-Graining Parameterization and Multiscale Simulation ofHierarchical Systems. Part I: Theory and Model Formulation 13 Steve Cranford and Markus J. Buehler Chapter 3 Coarse-Graining Parameterization and Multiscale Simulation ofHierarchical Systems. Part II: Case Studies 35 Steve Cranford and Markus J. Buehler Chapter 4 Coarse Molecular-Dynamics Analysis of Structural Transitions in Solid Materials 69 Dimitrios Maroudas, Miguel A. Amat, and Ioannis G. Kevrekidis Chapter 5 Multiscale Modeling Approach for Studying MDH-Catalyzed Methanol Oxidation 91 Nirmal Kumar Reddy Dandala, A.P.J.Jansen, and DanielaSilvia Mainardi Chapter 6 First-Principles Alloy Thermodynamics 113 Axel van de Walle Chapter 7 Nonlinear Finite Element Model for the Determination of Elastic and Thermal Properties of Nanocomposites 135 Paul Elsbernd and Pol Spanos viii Contents © 2011 by Taylor & Francis Group, LLC Chapter 8 Ensemble Monte Carlo Device Modeling: High-Field Transport in Nitrides 165 Cem Sevik Chapter 9 Modeling Two-Dimensional Charge Devices 193 Af Siddiki ix © 2011 by Taylor & Francis Group, LLC Preface Nanoscience, or nanotechnology, has become an omnipresent keyword in most sci- entic and technological advances. It has been shown to hold the promise of a large impact on a number of applications, especially on novel devices. Computational methods such as ab initio, density functional theory (based on quantum theories of electronic structure), molecular mechanics, molecular dynamics, and Monte Carlo methods (based on classical mechanics and statistical mechanics of many-body sys- tems) are well-established and used extensively in studying the nanoscale phenomena. All of these methods are well-developed and have captivated the interest of research- ers, especially within the third quarter of the twentieth century. The increasingly widespread use of computational methods in the rational design of novel materials applications and devices has led to an increasing effort to employ these methods, based on fundamental theories of physics, in problems involving phenomena cou- pling different length and time scales within the same application. The simplest path to take has been to force the existing methods and models to make predictions on systems and phenomena for which they simply have not been designed. To tackle problems where multiple length and time scales are coupled, a new paradigm needs to be employed: multiscale modeling and simulation. Indeed, a common property of nanosystems is that they are multiscale systems. Nanosystems are systems in which the relevant features and properties depend on nanoscopic details, yet their performance resides in the macroscopic world and, thus, all scales are relevant. This requires the use of theories and methods that are accurate enough for the nanoscale but also able to be scaled up in length and time in a consistent manner, either through a hierarchical method of successive coarsening or by devising methods to handle the coupling of scales concurrently within a well-dened framework. There is a tendency to make a one-to-one association between coarse-graining and multiscale modeling. Clearly coarse-graining is a key multicale method, but multiscale is much more than just coarse-graining and that is what this book tries to highlight. The reader should keep in mind, however, that the key word here is “atomic.” The atomic scale is indeed where things actually happen and controlling this scale is key to successfully tailoring nanosystem properties at will. Thus, being able to model the connection between the large and the atomic scale is fundamental for predictive models to be able to assist in the design of novel nanomaterials and systems. With this in mind, in this book we put together a number of approaches—care- fully described by the contributors—for which more than one scale is explicitly con- sidered. Throughout the book, the reader will be guided to a number of alternatives, from coarse-graining sampling of the atomic and mesoscale to Monte Carlo– and thermodynamic-based models that allow sampling of increasingly large scales up to multiscale models able to describe entire devices. In Chapter 1, Morrow describes four of the most common techniques for coarse- graining, namely, rigorous matching correlation, force-matching, and empirical [...]... matrix properties due to effects occurring at the atomic level Complex physical systems like nanocomposites, fuel cell membranes, electrolyte systems, and polymer systems owe some of their properties to processes 15 16 Multiscale Modeling: From Atoms to Devices occurring at the atomic-length scale and femto-nanosecond timescale Controlling these small-scale properties can be the key to tuning the properties... approximation from geometrical arguments They were also able to use coarse-grained simulations to predict the phase diagram for mixtures with size 18 Multiscale Modeling: From Atoms to Devices ratios of 20:1 and 30:1, where ergodicity problems made simulations of the twocomponent system intractable Chennamsetty et al [4] have used Dijkstra’s method to coarse-grain a binary mixture of argon and krypton into an... g1(rij) 22 Multiscale Modeling: From Atoms to Devices are calculated, and Δg1(rij) is used in a linear equation to calculate a correction to the coarse-grained potential, Δu1(rij) The resulting coarse-grained potential is used in a simulation to calculate g2(rij), and the iteration procedure is repeated until gk(rij) = gref (rij) to within some acceptable tolerance The IMC procedure has been used to calculate... synergistic multiscale transitions from atomic to mesoscale to macroscale descriptions Hierarchical “handshaking” at each scale is crucial to predict structure–property relationships, to provide fundamental mechanistic understanding, and to enable predictive modeling and material optimization to guide synthetic design efforts Indeed, a finer-trains-coarser approach is not limited to bridge atomistic to mesoscopic... t CH2 CH2 t t t CH2 CH2 t t CH2 CH2 t t CH2 t CH2 t CH2 N+ CH3 CH3 h+ CH3 FIGURE 1.1  Coarse-graining of the atoms of the surfactant cation n-decyltrimethylammonium into nonpolar tail (t) groups and a positively charged, polar head group (h+) 20 Multiscale Modeling: From Atoms to Devices RDF to the direct correlation function c(r) An example is the Ornstein-Zernike [9] integral equation: ( ) ( ) ∫... full atomistic model of identical carbon nanotube using carbon–Â� carbon interactions (c) Top view of adhered bundle of coarse-grain carbon nanotubes using potentials developed from atomistic results Each transition involves an increase in accessible system size, length scale, and time scale, as well as a simplification of the governing theoretical models 16 Multiscale Modeling: From Atoms to Devices. .. which the intended structure–property relation is to be investigated 2.2  EXAMPLES OF COARSE-GRAINING METHODS In the past decade, various simple models have been used to describe the largescale motions of complex molecular structures where more detailed classical 20 Multiscale Modeling: From Atoms to Devices phenomenological potentials [6,7] involving all atoms cannot be used because of the restrictions... 111:11207 26 Multiscale Modeling: From Atoms to Devices 20 T Murtola, E Falck, M Patra, M Karttunen, and I Vattulainena 2004 Coarse-grained model for phospholipid/cholesterol bilayer Journal of Chemical Physics 121:9156 21 S Izvekov and G A Voth 2005 A multiscale coarse-graining method for biomolecular systems Journal of Physical Chemistry B 109:2469–2473 22 F Ercolessi and J B Adams 1994 Interatomic potentials... 18 Multiscale Modeling: From Atoms to Devices an accurate representation of the system-level behavior and response with confidence in the properties of the model components For example, a common application of system-level analysis is used in the study of structural frames Required loads and resistances are computed at the system-level, and the structural components are assumed to behave according to. .. of the underlying atomistic system This review discusses four popular methods for coarse-graining complex physical systems into models that can be simulated over large time and length scales: a rigorous coarse-graining technique; matching correlation function techniques; force-matching (FM) techniques; and empirical coarse-graining techniques 24 Multiscale Modeling: From Atoms to Devices In the rigorous . Science/Nanoscience MULTISCALE MODELING FROM ATOMS TO DEVICES EDITED BY PEDRO DEROSA TAHIR CAGIN DEROSA CAGIN MULTISCALE MODELING MULTISCALE MODELING EDITED BY PEDRO DEROSA & TAHIR CAGIN FROM ATOMS TO K10520 6000. approach to predict an event it was not designed for, a new paradigm must be employed: multiscale modeling. A brilliant solution to a pervasive problem, Multiscale Modeling: From Atoms to Devices. 9 References 11 16 Multiscale Modeling: From Atoms to Devices occurring at the atomic-length scale and femto-nanosecond timescale. Controlling these small-scale properties can be the key to tuning the